Is simultaneity necessary in economics?

I think it almost always is.

In a previous post I said that economics is a "non-linear" discipline, in the "Artsie" sense of that word. Most (all?) economic models involve simultaneous causation. They don't say that A causes B causes C causes D in a "linear" (Artsie sense) sequence like billiard balls. Instead they say that Price and Quantity are co-determined simultaneously by supply and demand. Or by Production Possibilities Frontier and Indifference curves. Or by IS and LM. Etc. There's always two (or more) curves crossing or kissing. Or always two (or more) equations being solved simultaneously for the solution.

Only in special cases, usually limiting cases or "degenerate" cases, can we sometimes avoid simultaneity. For example, if the supply curve is perfectly elastic, and the demand curve is perfectly inelastic, then everything is "linear": supply determines price, and demand determines quantity; price does not affect quantity, and quantity does not affect price. "Linear" causation is the exception. Simultaneous causation is the rule.

Economists never argue whether investment causes saving or saving causes investment. (OK, most economists don't). Most economists see this as a false dichotomy.

Economics, as we now know it, is that way. But does it have to be that way? I think it does. This post explains why I believe that.

Economics is about human interaction. Yes, it's about other things as well, but it is about human interaction. And yes, other social sciences are about human interaction too (and I would be interested to hear if sociologists and political scientists think the same way), but economics is too.

I am trying to think of the model of human interaction that is the simplest possible model, and the most fundamental possible model. What is the "Ur-model" of all models of human interaction? I can think of two, and I'm going to talk about them both. The two models are almost the same, and differ in only one respect. [I'm looking at Nash Equilibrium, comparing the "simultaneous" with the "sequential" version of the same game.]

There are two players, call them Adam and Betty. Adam and Betty have one move each, then the game ends. Adam's payoff (profit, utility, whatever) depends both on what he does (he picks a number of apples "a") and on what Betty does (she picks a number of bananas "b"). Same for Betty. Both Adam and Betty know everything about the game (it's "common knowledge").

Here's where the two models differ:

1. In the "Cournot" model, Adam makes his move before observing Betty's move; and Betty makes her move before observing Adam's move.

2. In the "Stackelberg" model, Adam makes his move before observing Betty's move; and Betty makes her move after observing Adam's move.

We sometimes say that in the Cournot game Adam and Betty have to make their moves "at the same time", or "simultaneously". But that isn't strictly accurate. Betty might choose how many bananas to pick before or after Adam has already picked his apples. But if she doesn't observe how many apples Adam has picked, until after she has already picked her bananas, it makes no difference.

Here is how economists (and game theorists) would (usually) solve those two models.

1. In the "Cournot" model, we solve for Adam's reaction function, which tells us how many apples he would pick ("a") to maximise his payoff as a function of how many bananas he expects Betty to pick ("b"). The reaction function is an equation like a=A(b). We do the same for Betty, and get an equation like b=B(a). We then solve the two reaction functions like simultaneous equations for the Nash Equilibrium. Graphically, the Nash Equilibrium is where the two curves cross.

In the Cournot model, it doesn't make sense to ask whether a determines b or b determines a. Both are co-determined simultaneously by the two player's reaction functions, which are in turn determined by the payoff matrix and the structure of the game. Only in degenerate cases, where one reaction function is vertical and the other is horizontal (so each player has a "dominant strategy" that is best for him regardless of what she picks) can we ignore simultaneity.

2. In the "Stackelberg" model, we solve for Betty's reaction function b=B(a) as before. We then find that point on Betty's reaction function that maximises the payoff to Adam. Graphically, the  equilibrium is the point where Betty's reaction function is a tangent to Adam's highest Indifference Curve. It's a little bit more complicated than finding the point where two curves cross, because we need to draw lots of curves for Adam, to make sure we have found the right one for the tangency point.

In the Stackelberg model, it is very tempting to say that Adam's choice determines Betty's choice, but not vice versa. Tempting, but wrong. If Betty had different preferences, or a different productivity on growing bananas, her reaction function would be different, and Adam's choice would have been different too. Even though he moves first, and Betty gets to observe Adam's choice before making her choice, Adam's choice is determined, in part, by his knowledge of how Betty will choose, and especially, by Adam's knowledge of how Betty would choose differently if he were to choose differently.

These are the lessons I draw from these two models:

First, it doesn't matter who moves "first" in calendar time. What matters is who gets to observe the other's choice before making her choice. That's what affects the equilibrium.

Second, In both games, her expectation (or observation) of his choice will affect her choice, and his expectation of her choice will affect his choice. Both games are "simultaneous" in the sense of mutual co-determination. You cannot explain Adam's choice without explaining how Betty will choose, even if Adam chooses first.

The simple "linear", "A causes B causes C causes D" model of a causal chain just does not work, even for these two very simple models of human interaction (except in degenerate cases where one or both person has a dominant strategy).

There are lots of ways you could complicate those two simple models. You could introduce uncertainty by allowing "Nature" to make a move after one or both human players has made a move, so you would be talking about a "Bayes-Nash Equilibrium". You could add more players. You could add more moves, to make the game last longer. I would conjecture that all games, and all models of human interaction, however complex, are just glorified versions of my two simple models above. These two simple models are the building blocks from which all others can be constructed.

You can complicate it all you like. But economics is about human interaction, and you can't avoid simultaneity. (I don't think you can avoid simultaneity generally in non-human interaction either, but that's a different question.)

Comments

[marris]

Can you apply this to the question of whether reserves create deposits or deposits create reserves? That seems to be a source of great confusion for MMTers and mainstream economists alike. I think Artsie non-linearity is a primary cause of the confusion.

[Nick Rowe]

marris: Bingo! I could, but I daren't. It would probably turn into a mare's nest of a confused debate. Partly it depends on your assumptions about elasticities of "supply and demand", which depend on whether you are talking short run or long run, and what you are implicitly holding constant when you do the analysis.

Saving and investment is bad enough.

[tomslee]

So relativistic economics is a non-starter, I guess.

[Nick Rowe]

tomslee: what's "relativistic economics"? I Googled, but I'm not sure I understand what I skimmed, or if it's what you mean by the term. But what I skimmed sounded like the attempt to apply physics to economics. OK. The Newtonian physics I learned in high school had loads of simultaneity in it. Dunno about Einstein, since I never understood that stuff.

[Ritwik]

Nick

If my reading of Leijonhufvud is correct, the simultaneity that you speak of is a static equilibrium concept (move form State A to state B with all variables changing simultaneously and causing one another), while dynamic disequilibrium methods would focus on the process and the sequence of decisions, which makes things quasi-linear (in the artsie sense).

[Nick Rowe]

Ritwik: Lets take a much longer game, which is a sequence of my 2 simple games, following one after the other. So each player has more than one move. The equilibrium is a path, what we would normally call a time-path. And it won't always involve (it usually won't involve) each player doing exactly the same thing twice. But it's still going to involve simultaneity.

[Reverend Moon]

“Well, the game is pretty straightforward. You can choose to spin or you can choose to choose. If you choose to spin, you can land on spin, or choice, or lose a spin, or lose a choice, or free spin, or free choice or spin again.”
-Peggy Hill

Sorry. I know this adds nothing to the conversation but, it's all I could think while I was reading.

[Leigh Caldwell]

I can see that in principle this is true. But is it in practice?

In reality we know very little about the payoff functions, beliefs and information available to other players. We don't even know that much about our own! Therefore we make moves fairly blindly, and (if we are especially sophisticated) use those moves to learn a bit about the other players. Though by the time we've learned much, the game has changed and it might not do us much good.

We could in principle model the possible payoff functions and information sets of the other players as a probabilistic distribution and determine the optimal moves accordingly - but in practice that is neither achievable, nor do people really even try to do it.

In certain cases the game is simple enough that we can model the equilibrium outcome rather than the steps to get there (though it can still be instructive to imagine the actual causal chain from, say, a gas pipeline explosion to the ultimate effect on the equilibrium point of the petrol market). But in many other cases, we can't, and these are in fact the cases which never really reach an equilibrium - or not in sensible human timescales anyway.

Maybe sometimes you can move the definition of "simultaneity" up a level. In physics [I can't remember if physics analogies are frowned upon here] there are plenty of problems which do not reach a static equilibrium - eg pendulums or waves on a string. But if instead of saying that the atoms of the string reach equilibrium, we say that the _waves_ reach equilibrium then we can say how the length and tension of the string and the energy of its vibration codetermine the amplitude and frequency of the waves. However, I don't think economics does normally take this explicit step - and even then, I'm not sure that the majority of economic problems can be handled that way either.

So if the point is: are simple microeconomic problems better modelled as simultaneous, non-Artsie-linear systems, then sure. But all of economics? Or the interesting problems of economics? I don't think it's the best philosophy. [as mentioned above, I understand that Leijonhufvud's work is partly based on this argument]

[Scott Sumner]

Now I need to say "Never reason from a price change unless supply is perfectly elastic."

[Nick Rowe]

Rev Moon: King of the Hill? One of my favourites!

Leigh. Suppose Adam doesn't know Betty's preferences. Just to keep it simple, suppose Betty could be one of two "types": a Betty with "Type c preferences", or a Betty with type d preferences. We just add that into the game, where right at the beginning Nature makes a move, to determine Betty's type, but Adam does not observe Betty's type. Adam uses Bayesian reasoning to try to infer Betty's type from observing her moves. But Betty knows Adam is doing this, so that in turn affects Betty's moves, because that can influence how Adam moves, which affects Betty's payoffs. But Adam in turn knows that Betty will be doing this.

Economists have been modelling games like this for a couple of decades. It's a sort of signalling equilibrium. But my point here is not that this can be modelled (it can, but it's hard, and raises some deeper questions about what exactly Nash equilibrium means, that I used to try to keep up with but can't any more); my point here is that this sort of game gets even more simultaneous than a simple game. It's even more Artsie non-linear.

In the olden days (I can just remember them) we used to draw the two reaction functions for the "Cournot" game, then "cobweb" around them, to "explain" how the two players got (or didn't get) to the equilibrium where the two curves cross. "Suppose Adam does a1, then Betty will reply with b1, and Adam in turn will reply with a2, to which Betty will reply with b2,...and draw a cobweb picture around the equilibrium, to see if it converged ("stable") or diverged ("unstable") from that equilibrium. That was a "linear" model.

People are too embarrassed to remember those old cobwebs nowadays, so you never (I think) hear them mentioned. But we weren't that stupid back then. We were trying to see if people could learn the location of the Nash Equilibrium. But, IIRC, we were very unclear on what exactly it was the players were learning. Plus, the sort of learning we were implicitly assuming (a very crude sort of adaptive expectations) didn't necessarily make sense. Why couldn't the players, at least after a couple of rotations round the cobweb, see where it was heading, or even behave strategically? Plus, was this really a one-shot game, or a repeated game, because the two are rather different? You can have players build reputations in repeated games.

[Nick Rowe]

Scott: Yep. Or, unless demand is perfectly elastic!

And the implicit assumption of those who reason from an interest rate change is that the supply curve of reserves is not only always and everywhere perfectly interest-elastic, but has zero elasticity with respect to any other endogenous variable, and will have that zero elasticity forever and ever.

[Greg Ransom]

Or you can blow up the fake science "modeling" paradigm altogether.

Think of the economy as a causal, flowing stream never in equilibrium but constantly exhibiting a coordinated order with many constantly changing elements, some of them relics from the past some of them temporary new novelties -- but not a perfectly coordinated order with constantly replicating identical parts.

Compare Hayek's 50th anniversary paper give at the LSE in 1981 in Hayek's _Monetary Economics, Part II_ or some of his essays on Keynes in Hayek's _New Studies_, or Hayek's discussion of this in his _Pure Theory of Capital_.

[Jeremy Fox]

I note that you tossed in the billiard ball analogy that utterly failed to convince anyone when I argued much the same point over on Oikos Blog. ;-) I can only assume that you're just showing off and proving that your magic touch can turn my leaden analogies to gold. ;-) (just kidding, nice post)

[rsj]

Nick,

Yes, simultaneity is important, but it is a red-herring.

One needs to get the rules of the game right. Those of us who are pushing back are saying that your rules of the game are wrong, and the possible moves available to each player are not what you believe are available.

Without getting the rules right, and without modelling the moves available to each player correctly, then how on earth can you hope to accurately model the simultaneous solution?

Reserve banks don't create "money" as held by the non-financial sector, they create reserves, as held by the financial sector. At the individual level, investment *does* create savings, whereas the individual's decision to save reduces income for someone else.

With a different set of moves available to each player, and a different set of rules, you get a different equilibrium.

Do not slur those of us who disagree about the rules and moves available to each player by arguing that we can't understand equilibrium. It is a trivial.

We understand equilibrium very well, except that we are modeling a completely different game because (we believe) we are doing a better job at modeling the institutions and the options available to each player. Therefore we obtain a much better simultaneous approximation.

All the hand-waving about artists and what-not doesn't reduce the obligation to understand the roles of the institutions in this game, and the possible moves available to each player.

[Nick Rowe]

Greg: OK, let me restate in more Hayekian language (I actually find his language very useful at times):

People have plans for how they will act in future. Even if a person's plan does not change over time, the actions he performs under that plan will (nearly always) change over time. (They don't always plan to do the same thing day after day). (An equilibrium may be, and usually is, a moving equilibrium.)

People's plans depend on their expectations of how other people will plan and act. Their plans are interdependent. My ability to implement my plan usually depends on what others will do. What plan is best for me usually depends on what others will do. (Simultaneity).

If your plan and actions are different from what I expected, I will probably revise my plan. My original plan may or may not have contemplated the possibility that you could do something different. It maybe be a contingent plan. (Here I think is where the trouble starts, because if I am fully "rational" I will be aware of the possibility that my beliefs might change over time, when I observe your moves, and so I will formulate a *contingent* plan, depending on your and Nature's moves. And if so, if you do something different from what I thought your most likely move would be, and implement a different contingency in my own plan, can I really be said to *change* my plan? Is this a "disequilibrium", or not?

Jeremy: I thought your billiard ball analogy was a very good one, so I stole it! (I gotta do a post on reading Darwin.)

rsj: agreed. Simply saying "it's simultaneous" isn't enough. There are lots of different theories, and it matters which one we use. For example, the "Cournot" game (usually) has a very different prediction from the "Stackelberg" game, even when everything else is the same. (The only time they give the same prediction, IIRC, is when one or both players has a dominant strategy, so causation is no longer simultaneous.)

[nemi]

I don´t understand.

If people want more apples, there will be an increase in the price of apples. The farmers will then increase the production of apples and in the end there might be a higher quantity of apples sold/bought as well as a somewhat higher price,

Sure, in each moment in time price and quantity is determined simultainiously but there is also a lot of cause and effect in the story.

[Nick Rowe]

nemi: it may be that the short run supply curve is perfectly inelastic. It takes time to plant more trees and wait for them to grow, for example. In which case supply alone causes quantity, and supply and demand together cause price. But if there is an increase in demand, and a higher price this year, the producers will ask themselves whether this is a transitory or a permanent shift in demand. Each producer trying to decide how many trees to plant is trying to form expectations about the future price, which depends on expectations of future demand and on how other producers will be responding too ("Will I be the only one planting more trees, or will everyone be planting more?")

In other words, once we start to flesh the story out, and make the simplest model even a bit more like the real world, by bringing in lags, we get even more simultaneous causation.

[Nick Rowe]

rsj: "All the hand-waving about artists and what-not doesn't reduce the obligation to understand the roles of the institutions in this game, and the possible moves available to each player."

I strongly agree. But actually, my two very simple models can be used to illustrate the importance of institutions. Suppose we had a rule that said that Adam must announce in advance how many apples he will pick, and can't change his decision after he has announced it. That rule would change the equilibrium from the Cournot to the Stackelberg. And that's *even though* there is no uncertainty in these games, so that both Adam and Betty can predict with certainty exactly how many each will pick.

It is exactly those sort of institutions that are at the root of (e.g.) central bank commitments to a target path for NGDP (or whatever), for example. That commitment to a target *is* an institution. This stuff really really matters.

[Nick Rowe]

Or, another example of why institutions really matter, and why the stuff I am writing about here *is about institutions*.

Suppose we had a rule which said that Adam and Betty must announce the *price* at which they will sell apples and bananas, rather than the *quantity* they will pick and sell. Even with everything else (all the concrete stuff) exactly the same, and even under full certainty, we get a totally different equalibrium number of apples and bananas. It's the Bertrand equilibrium rather than the Cournot Equilibrium.

Now, see how it matters whether the central bank can announce (say) an NGDP target as opposed to (say) an interest rate target, even if all the concrete stuff is exactly the same?

[JP Koning]

Interesting. This reminds me of the Keynesian beauty contest, although Keynes used the mechanism in a derogatory sense to show that markets are silly. I remember that Irving Fisher built a hydraulic machine to model equilibrium - I wonder how he was able to do so since machines are linear.

[Nick Rowe]

It matters whether duopolistic firms talk in terms of prices or talk in terms of quantities, even if all the concrete stuff is exactly the same. One gives us the Bertrand and the other gives us the Cournot equilibrium, which are very different in terms of the concrete stuff.

See how all the artsie fartsie stuff like "framing" matters? Is this all "confidence fairy" crap? You go tell that to the hard-nosed Industrial Organisation types. They know damned well it matters. They've known that since those two old French economists figured it out hundreds of years ago. Same concrete problem in terms of demand and costs and maximising profits, different framing, and you get a different concrete outcome.

[Nick Rowe]

JP: I disagree with machines being "linear" (Artsie sense).

Take 2 springs, tie them together at one end, pull the other ends apart. How long will each spring be? You write down 2 equations, one for each spring, which tells you the force on that spring as a function of its length. Set the two forces equal, then solve the two equations simultaneously. The length of each spring, and the force on each spring, are co-determined simultaneously by the total length between your hands, and the whatjamacallit of the two springs.

Machines don't have expectations though, which rules out one type of simultaneity.

[Diego Espinosa]

Does simultaneity allow for path dependency?

[Nick Rowe]

Diego: yes. I don't see why it shouldn't. Simultaneity also allows for the possibility of multiple equilibria (if the two curves cross twice or more) which is like an extreme version of path dependency.

[Dan Kervick]

Nick, this is utterly unpersuasive. All you are arguing is that there are decisions whose outcomes depend on the decisions of others, and that are made in the context of imperfect information about what those other decisions will be. This does not alter the fact that those decisions occur in time, and are causal responses - rational or irrational - to information about phenomena that occurred prior to the decision. Decision-making under uncertainty does not mean decision-making independent of time or outside of complex causal chains extending through time.

Consider a typical day at a firm like mine: The people at the firm might make a large number of decisions: whether to make a offer; how to respond to a counter-offer; whether to hire or fire people; how to reorganize a work-flow; how to reorganize a a reporting chain or managerial structure; whether to borrow money; whether to pay a bill; whether to place and order or cancel an order; whether to adjust overtime hours; whether to buy a piece of capital equipment. These decisions take place in in time, in the context of a massive flow of information. They are all responses to events that occurred previously, and about which the decision-makers have accumulated substantial information - sometimes informal anecdotal information, sometimes piles of data on spreadsheets. The information, which was caused by previous events, in turn causally conditions the decision. And the decisions they make today are going to cause various effects tomorrow, next week, next month; next quarter, or next year. And those effects will provide information that is the causal precondition

Even those decisions that can be modeled as multiple-person games in which the players' decisions are based on their uncertain expectations about the decisions of other relevant players are the effects of the past and the causes of the future. Those expectation functions you are talking do not exist in a causal or temporal or epistemic vacuum. They have been built up over time and are based on information about behavior that has occurred previously. For example, if a firm decides whether to hire and train more temporary staff to process an increase in fall orders it expects from various customers, the expectations are based on a large amount of information: how those customers behaved in previous fall season, what can be read in the paper this morning about business conditions, consumer confidence, predictions of transportation costs, etc. This point is particularly relevant here, since part of the debate is about what causes various types of expectations.

The economic world is a flow of events and information through time and history. Decisions are responses to previous events about which one has at least some information, and are in turn the causes of future events.

One request: your unusual use of "linear" is only confusing matters. There are few causal systems of interest in which all events in question are part of a totally ordered "chain". The events in the causal systems comprising the economic world all have multiple causal antecedents and multiple consequent effects. That's not the issue.

Please note that the kinds of situations you are describing in your toy examples do not involve simultaneous causation. All you are talking about are cases in which some effect C is the causal consequence of events A and B, where neither A causally influences B nor B causally influences C. I fail to see the relevance of this point to any of the contested issues under discussion, or any violation of temporarily of causation in the economic sphere.

Also, your earlier invocation of feedback is a red herring. The price I set on Monday might influence the behavior of customers on Tuesday in a way that causes me to adjust my price on Wednesday. So the price-setting mechanism involves feedback loops, in which my subsequent price-setting decisions are the causal consequences of antecedent events that include my own earlier price-setting decisions. But clearly my Monday decision and Wednesday decision are different events. The Wednesday decision was causally influenced by the Monday decision, but the Wednesday decision was not causally influenced by the Monday decision. So again, no violation of the temporality of causation in the economic realm.

[Nick Rowe]

Dan: "Nick, this is utterly unpersuasive. All you are arguing is that there are decisions whose outcomes depend on the decisions of others, and that are made in the context of imperfect information about what those other decisions will be."

Actually, in my two toy models, the decisions are made in the context of perfect information about what those other decisions will be.

I can add in imperfect information if you like, (I said in the post how), but it doesn't affect my argument.

And it's not just the outcomes of my decisions that depend on the decisions of others; my decisions too will depend on what I expect those decisions of others will be.

[vimothy]

http://gregmankiw.blogspot.co.uk/2009/03/identification-problem.html

[Dan Kervick]

"my decisions too will depend on what I expect those decisions of others will be."

Sure, but your expectations are based on information you have about the past. Your expectations do not spontaneously generate. They are psychological states caused by your things that happened in the past.

I don't think I understand what you mean when you say your examples involve perfect information. Don't they involve reaction functions that encode lack of certainty about the behavior of the other the other player.

Anyway, you are just describing setups that allow a priori for the existence of equilibrium outcomes. They say nothing about actual behavior and have no predictive or explanatory use.

[Diego Espinosa]

Nick,
Agreed. However, alternate equilibria are a function of initial conditions. Chuck Norris only allows for one state of the world to exist regardless of initial conditions. After all, the "Chuck Postulate" is that a central bank's ability to control the price level in the future completely informs expectations in the present. Therefore the existence of inertia/momentum in expectations is impossible, regardless of such initial factors as financial frictions. The debate over multiple equilibria is therefore over before it starts.

[JR Hulls]

Fisher is not the one who came up with the hydromechanical economic simulator. It was Phillips, whose '50's model showed how a really good analog simulation can give insights into complex interactions. See the OECD Insights piece celebrating Turing's centenary, to which I made a modest contribution entitled "Going with the Flow: Can Analog Simulation make Economics an Experimental Science. at:
http://tinyurl.com/busy3nu

The piece discusses Phillips 'Moniac', and it's worth the time to watch Allan McRobie's video of experimenting with Cambridge's restored Phillips machine. Best quote, "Lets turn off the banking sector for a moment"

The Reiss paper on simulations in economics, mentioned in the article, is worth reading but here's a direct link. http://www.jreiss.org/papers/S%26G_42(2)_2011.pdf

The following piece in the Insights series is on supercomputers and the flash crash from Dr. David Lienweber of Lawrence Berkeley National Labs, and makes interesting reading.

[Frances Woolley]

Nick - if everything is simultaneous, are we reduced to potato theories of history, where the few shocks that are truly exogenous to the system (like the discovery of the potato) are the only explanatory variables, and all the rest is fancy modelling? What is exogenous?

[Nick Rowe]

JR: Phillips certainly made a machine, but didn't Fisher make one too? I seem to remember reading about Fisher's machine only a couple of weeks back. Wish my memory worked.

Diego: "After all, the "Chuck Postulate" is that a central bank's ability to control the price level in the future completely informs expectations in the present. Therefore the existence of inertia/momentum in expectations is impossible, regardless of such initial factors as financial frictions. The debate over multiple equilibria is therefore over before it starts."

I don't think I would go that far. Reality might look like a 'Y'. There is only one equilibrium path at present, but then we come to a fork in the road, and could go either way, simply depending on which way everybody expects everybody else to go. But there could still be history dependence, in that once we have taken the left branch, we cannot go back to the right. It depends.

vimothy: I love it!

[Nick Rowe]

Dan: "I don't think I understand what you mean when you say your examples involve perfect information. Don't they involve reaction functions that encode lack of certainty about the behavior of the other the other player."

There's a short answer and a long answer:

Short answer (most economists' answer):
It's easy. Nick assumed that the payoff matrix and the structure of the game were common knowledge between Adam and Betty, so if Nick can solve for the Nash Equilibrium of the game then so can Adam and Betty, who are just as smart as Nick. So if Nick knows what the outcome is, so do Adam and Betty.

Long answer (for game theorists, philosophers, and other people who want their brains to hurt, and really beyond my pay-scale to give more than a rough inaccurate sketch of some of the issues):
Hang on. What about Adam and Betty's free will? How can there possibly be common knowledge of rationality, let alone the subjective evaluation of any payoff matrix? What does common knowledge of rationality even mean in this context anyway? Does it include common knowledge that Adam and betty will play the Nash strategy? And doesn't that rather beg the question that Nash is the right equilibrium? (Especially since empirical experiments like the ultimatum game show that real people often don't play Nash? And while we are on the subject of free will, how come you get a different outcome when Betty actually observes how Adam played compared to when she simply can predict with certainty how Adam will play? In fact, that raises a really big question in games with multiple moves for each player. The standard line from the Nash guys is that the equilibrium must also be "subgame perfect". But that raises a problem. Suppose Adam did in fact make a move away from the subgame perfect equilibrium path. Hey, Adam's got free will, so he can do that! What would Betty think if she saw Adam do that? By assumption, Betty has just been confronted with a logical contradiction, since she is assumed to know with certainty that Adam will follow the equilibrium path, so if she does observe him off the equilibrium path her only rational response is not some Bayesian updating of her priors, but instead to calmly think: "WTF?!!!". And how can we, the theorists, possibly figure out what Betty will do next, after she has just observed a logical contradiction? And if we can't figure out what betty will do next, neither can Adam. So, who knows, maybe it would be in Adam's self-interest to make that crazy move, because Betty might just react in a way that benefits Adam. But in which case, maybe the move wasn't so crazy after all. But, in which case, we can't even figure out what the equilibrium path is, without answering how a player would react in such a "WTF?!!!" case. And maybe, just maybe, the whole of civilisation rests on exactly how people would update their beliefs and react in such situations, like keeping promises, and punishing transgressions, etc. And targeting NGDP ;-) Etc.

[Nick Rowe]

Frances: that's a question I always duck, by saying "it depends on the theory". Which depends on what you want to do with it. Some stuff you choose to ignore. Some stuff is so small it can be ignored, for some questions. So we don't try to explain everything at once. Almost all models are partial equilibrium in some sense. And that's OK.

Best I can do!

[JP Koning]

Are the people from the concrete steppes engaging in partial equilibrium analysis?

[JR Hulls]

Turns out you're right...Fisher did make a machine, and more interestingly, a Mathlab model of the machine was made to see if it would have worked. Interesting paper here. http://cowles.econ.yale.edu/P/cd/d12b/d1272.pdf The paper points out that Fisher had deescribed a fully developed equilibrium model and the hydromechanical device in his 1891 thesis.

Once again the advantage of a good hydromechanical simulation is that errors in assumptions and faulty logic about equilibrium etc. tend to cause puddles on the floor.

[JR Hulls]

However, Fisher's machine is essentially a hydraulic calculator and it was in no way a 'flyable' simulator in the sense of the Phillips 'Moniac'

[J.V. Dubois]

Nick: I found that last comment about Economists and Philosopher point of view hilarious. And it is actually something I thought about recently. I would even make a distinction of the two approaches, the first one - the economist - thinks that people play something like a game of chess. With correct information (like knowing all possible board developments) you could play a "perfect move". Every move is contingent on what opponent's counter-move will be, so you have your simultaneity, but ultimately it is theoretically possible to solve the game an devise optimal strategy at every step. You just reduced the human aspect of the interaction to the interaction to static environment. You do not really play with other humans with their "free will" but you turned it into contained "my mind against environment with complex rules", or in your speech "linear" problem. You really play the game against yourself.

The second approach is that of the game of No Limit Poker. There is no optimal strategy, there is no perfect move that can be discerned from information available to a player. What is the best strategy for any player depends on what strategy other players have, and since these strategies can change dynamically you cannot simply solve it. The game can be "rational", every player wants to win a pot, but it does not have to be "solvable".

To be honest I do not know exactly know what all this means, I just find it interesting.

[Metatone]

I don't think I understand, even after all the comments.

It's a lot to ask, but could you put this into systems theory language instead of this odd analogy with film-making?

This sentence: "You cannot explain Adam's choice without explaining how Betty will choose, even if Adam chooses first." seems to be miswritten. Surely, following from the previous statement it should say "You cannot explain Adam's choice without explaining how Adam thinks Betty will choose, even if Adam chooses first."

Now of course, it's true that there is an infinite recursion possible here, because what Adam thinks Betty will choose depends on what Adam thinks Betty thinks Adam will choose, and so on. But this highlights in the end that apart from very rare cases, things are not particularly simultaneous. Rather what is the case is that action is predicated on a much wider sweep of "information" than just "the price signal" or "the negotiation position taken".

And this brings us back to Frances point and your response.

Which for me says most of the time things are realistically multi-caused and multi-effecting. And some people hate that, because they want to pretend (a la Hayek) that you can reduce it all one thing - like price and do fancy math.

Is it wrong to do this? Not necessarily, as in your response to Frances. What's wrong is to do it without examining the causal assumption in the collapse to a lower number of variables. Examine it for accuracy and precision. Because the message is, sometimes you collapse everything to price and it'll give you a good prediction - but other times you'd get a better prediction by collapsing everything back to e.g. cultural norms.

[Peter N]

I think you're oversimplifying a bit. You always have to consider the model's necessary conditions and domain of applicability.

"I would conjecture that all games, and all models of human interaction, however complex, are just glorified versions of my two simple models above. These two simple models are the building blocks from which all others can be constructed."

From your references:

"In game theory terms, the players of this game are a leader and a follower and they compete on quantity. The Stackelberg leader is sometimes referred to as the Market Leader.

There are some further constraints upon the sustaining of a Stackelberg equilibrium. The leader must know ex ante that the follower observes his action. The follower must have no means of committing to a future non-Stackelberg follower action and the leader must know this. Indeed, if the 'follower' could commit to a Stackelberg leader action and the 'leader' knew this, the leader's best response would be to play a Stackelberg follower action."

These are quite restrictive conditions to apply to a supposedly universal model. likewise for Cournot:

"Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot[1] (1801–1877) who was inspired by observing competition in a spring water duopoly. It has the following features:

There is more than one firm and all firms produce a homogeneous product, i.e. there is no product differentiation;
Firms do not cooperate, i.e. there is no collusion;
Firms have market power, i.e. each firm's output decision affects the good's price;
The number of firms is fixed;
Firms compete in quantities, and choose quantities simultaneously;
The firms are economically rational and act strategically, usually seeking to maximize profit given their competitors' decisions.
"

So it is impossible that

"all models of human interaction, however complex, are just glorified versions of my two simple models above."

For example look at BSDE models in finance

http://www.maths.univ-evry.fr/prepubli/326.pdf

or the work of Mertens

http://en.wikipedia.org/wiki/Jean-Fran%C3%A7ois_Mertens#Stochastic_Games

You're also being rather free with the word "equilibrium". A sequence of moves using Nash strategy does not imply an equilibrium or a sequence of equilibria without additional constraints. For instance Imperfect information and disinformation are problems. Unstable or intransitive preferences, information delays, collusion and coercion also come to mind.

There are, however, useful special case solutions with restrictions like:

ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-254-game-theory-with-engineering-applications-spring-2010/lecture-notes/MIT6_254S10_lec18.pdf

You might take a look at More Heat than Light: Economics as Social Physics, Physics as Nature's Economics (Historical Perspectives on Modern Economics):

http://www.amazon.com/More-Heat-than-Light-Perspectives/dp/0521426898/ref=sr_1_1?ie=UTF8&qid=1341496585&sr=8-1&keywords=more+heat+than+light

As for causality, the original subject, it's not a problem if you handle it the way physics does. Objects interact and the interactions can be modeled to various degrees of accuracy. You'd get the same problem if you said the earth caused the moon's orbit, since you would also have to say that the moon caused the earths orbit. However you can discuss their orbits without talking about causality. You always get problems when you apply paradigms to systems for which they aren't appropriate. The issue with causality is whether they are inside each others' light cones. Causality is a useful as a restriction, but not as much so as a mechanism.

You can say one thing causes another one dominates its interaction with the other. If we drop a glass and break it, we don't invoke the earth's orbit around their common center of mass, even though it must exist. It's negligible, and physics is all about finding the right things to neglect to make a model useful.

[Nick Rowe]

Peter N: "...and physics is all about finding the right things to neglect to make a model useful."

I really like that. So is economics.

(I wasn't talking about the Cournot and Stackelberg models in their literal historical senses. E.g you can have a "Cournot"-like model in which one firm produces apples and the other bananas, which are not perfect substitutes, even if it's not the model that Cournot himself wrote down. These are just names for the order of moves in my post; don't take them literally.)

[Dan Kervick]

I am finding this whole discussion somewhat bizarre. Doesn't economics strive to be an empirical science anymore? Certainly we can describe models of hypothetical interactions where some outcome is the effect of multiple decisions, no one of which is causally influenced by the other. And just as certainly we can describe models of interactions in which some outcome is the effect of decisions which are in turn the effects of previous decisions. What does this have to do with anything important?

[Nick Rowe]

Dan: "Certainly we can describe models of hypothetical interactions where some outcome is the effect of multiple decisions, no one of which is causally influenced by the other."

Which is not what I am talking about here. Those are what I called the "special" or "degenerate cases, where by fluke each player has a dominant strategy. I am talking about multiple decisions, each one of which is influenced by the others.

[Nick Rowe]

Sorry I haven't responded to all comments. I'm reading a fascinating David Glasner article.

[Dan Kervick]

Which is not what I am talking about here. Those are what I called the "special" or "degenerate cases, where by fluke each player has a dominant strategy. I am talking about multiple decisions, each one of which is influenced by the others.

That's inconsistent with what you said about the Cournot game, Nick. You described that as a game in which each player's decision is influenced by that player's expectations of the other player's decision, but in which neither player actually receives information about the other player's decision prior to making her own decision. In that case, neither player's decision causally influences the other player's decision, but the two decisions jointly causally determine the outcome of the game.

And again, no body doubts that there are many situations in the actual world that are like this; just as no one doubts that there many situations in the world that are not like this. But describing toy models of the many varieties of human decision-making and policy-making contexts, by sketching small possible worlds in which those contexts are exemplified, doesn't answer any empirical questions about what any specific context in the actual world are like.

[Nick Rowe]

Dan: unless someone else physically grabs my hand and moves it (in which case it is not really my decision to move my hand) it is always my expectation/belief/information about someone else's decision that influences my decision. In the Stackelberg game, when Betty's eyes give her information that leads her to form an expectation of how many apples Adam picked, you could always say it is her information on Adam's past decision that influenced her decision, and not Adam's decision itself.

[Dan Kervick]

Nick, based on your last comments, it appears to me that there might be some confusion here between causal dependency and other forms of dependency. Suppose my goal at Friday noon is to meet my son for lunch, but my son and I can't communicate, and I have no direct information about his own lunch decision. Based on my knowledge of his previous behavior, I expect that he will either be at the Camembert Cafe or the Green Grille. I drive to the Green Grille. The whether my decision turns out to be optimal depends on the present decision my son makes. And my decision is causally influenced by my expectations about his present decision, which are in turn causally influenced by his actual previous decisions. But my Friday decision itself is not causally influenced by my son's actual Friday decision, since no information about that decision flows to me before I have to make my decision.

On the other hand, if we imagine an alternative situation in which my son decides where to go first, and then sends me a text message about the choice he made, then my Friday decision is causally influenced by my son's Friday decision. It is immediately influenced by my expectations about where he will be. But is this second case, my expectations are not just a causal outcome of knowledge I have about his previous decisions, but have been causally influenced by my receipt of the text message, which in turn was causally influenced by my son's actual Friday decision.

So in the second case, there is a channel of causal influence running from my son's Friday decision to my Friday decision. In the first case, there is no channel of causal influence running from my son's Friday decision to my Friday decision.

[Nick Rowe]

Dan: yep. (And, the two examples you give are parallel to my two toy models. Except in the Stackelberg model equilibrium, your son goes to a really expensive restaurant, and texts you from there, because he knows you will be paying the bill, and he's just presented you with a fait accompli. While in the Cournot model he goes to the Green Grille, because he knows that's where you will be going. The analogy isn't perfect.)

[Nick Rowe]

Metatone: "It's a lot to ask, but could you put this into systems theory language instead of this odd analogy with film-making?"

Hmm. I don't think I would know how.

"Now of course, it's true that there is an infinite recursion possible here, because what Adam thinks Betty will choose depends on what Adam thinks Betty thinks Adam will choose, and so on."

Yes. But there may be a fixed point, which is what we call a "Nash equilibrium".

Remember back when you first learned simultaneous equations. Suppose a=A(b) and b=B(a). Solve for a and b. There were three ways to solve them:

1. The way(s) the teacher taught you.

2. Infinite recursion. Guess an answer for a, plug it into b=B(.) to get a guess for b, then plug that guess into a=A(.) to get a second guess for a, and so on, hoping it will eventually converge, which it may or may not. That's what you are talking about, and what I was talking about when I mentioned "cobwebs" in a comment above.

3. Brute force trial and error. Consider all the zillions of possible answers {a,b}. See which answer(s) fits both equations.

[Dan Kervick]

OK, so getting back to my point: If economics strives to be an empirical science, a social and behavioral science that describes, explains and predicts actual human behavior in the actual social circumstances we inhabit - and not just an a priori normative study that appraises the rationality or optimality or sub-optimality of hypothetical decisions in toy possible worlds, then it really matters quite a bit what kinds of channels of causal influence actually exist, and how causal influence is and is not propagated in the kind of world we actually live in.

If an economist says, "Policy maker X should make policy decision A at time t, because that decision will have outcome B", then the onus falls on the economist to defend that claim and explain how A will cause B. It is not enough to describe a possible world in which A causes B. One should provide empirical evidence that our world is a world of that kind.

[Nick Rowe]

Dan: yep. Which is why we build models, like supply and demand, which are supposed to tell us what happens to price and quantity when (say) the government puts a tax on apples in a competitive market. And why we build models like Cournot, Bertrand, and Stackelberg, which are supposed to tell us what happens if the market isn't competitive. And have econometricians etc. who go off and try to test those predictions. And why (nearly) all of us, and not just the applied econometricians, always try to keep one eye on the world to see if our models seem to at least roughly fit with what we see and hear. And try to figure out what we need to change or add or do differently when things don't seem to go the way we thought they would. Like, to take a recent trivial example, my post about a week back when I wondered why we didn't get as much deflation as I would have predicted if I had known the length and depth of the recession in many countries, and wondered if financing problems might have had a supply-side effect that really needed to be included in my "model", and wondered if that hypothesis fitted the cross country data.

[Greg Ransom]

The Austrians, starting with Hans Mayer, have been working out a billard ball or stream view of economic causation since the 1930s:

http://www.cgl.uwaterloo.ca/~racowan/cause.html

economics is a "non-linear" discipline, in the "Artsie" sense of that word. Most (all?) economic models involve simultaneous causation. They don't say that A causes B causes C causes D in a "linear" (Artsie sense) sequence like billiard balls.

[Greg Ransom]

The beginning of wisdom here is to junk the modelers background assumption of a complete God's eye view of what is going on in the head of every individual, ie drop the idea that you have a full survey of all knowledge and -- related -- that each individual has a complete model of what he thinks is in the head of everyone else.

We live in a world of billions. We don't pretend to model all of those individual judgers and planners in our own head.

We count on some -- _some_ (not complete) -- stability in the network of price relations and in the patterned doings of know, and most importantly, unknown countless others.

That is how we understand the real causal world.

What we are doing or what we can possibly gain from God's eye view models with completely stipulated elements all in the single head of a single modeler is a different and wider issue.

Nick writes,

"If your plan and actions are different from what I expected, I will probably revise my plan. My original plan may or may not have contemplated the possibility that you could do something different. It maybe be a contingent plan. (Here I think is where the trouble starts, because if I am fully "rational" I will be aware of the possibility that my beliefs might change over time, when I observe your moves, and so I will formulate a *contingent* plan, depending on your and Nature's moves. And if so, if you do something different from what I thought your most likely move would be, and implement a different contingency in my own plan, can I really be said to *change* my plan? Is this a "disequilibrium", or not?"

[Greg Ransom]

Nick, most importantly, we don't understand and anticipate most of the patterned behavior of others by modeling a set "given" beliefs & desires we ascribe to others.

This is one of the lessons of Wittgenstein & Ryle & Hayek on rule governed behavior.

The point is a form of the "knowing how" vs "knowing that" distinction.

We simply understand and pair ourselves with the patterned behavior of others -- and this is the deep background even to language (see Searle, who partially gets it, but works his hardest to get everything back in the 'given' boxes of believe / desire intentions).

The belief/desire model on cognition / language is a parallel mistake to the mistake of modeling the socialist economy as a product of 'givens" in a mathematical equilibrium construct.

[Dan Kervick]

Nick, I must be missing something. Earlier you said, "I am talking about multiple decisions, each one of which is influenced by the others." But I don't see any example in the hypothetical cases you have described of some decisions A and B where it is bot the case that A influences B and also the case that B influences A.

[Nick Rowe]

Dan: I meant "multiple *people's* decisions". Yes, in my toy examples each person only makes one decision, but there are multiple (OK, two) people, and hence multiple decisions in that sense.

Greg: We (I mean as people, not as economists) observe other people's patterns/rules of behaviour without enquiring into the reasons why people do what they do? Up to a point. I think we also have a "theory of mind", so we have some idea how others would respond differently if we were to act differently. And this is important in explaining why we don't act differently.

[Dan Kervick]

Yes, in my toy examples each person only makes one decision, but there are multiple (OK, two) people, and hence multiple decisions in that sense.

I understand that. But in the Cournot model, neither decision depends causally on the other decision. They are causally independent.

[Metatone]

Nick: Regarding simultaneity, the Nash equilibrium is a red herring. The key point is that whatever simplification you use for the infinite recursion, real people use a simplification - if they actually did an infinite recursion they'd never act. As such, the simultaneity requirement is not meaningful regarding the causality of their decision making.

And this is the actual case in bigger examples. What people do is they take a point in time, assemble some form of assumption about the state of the system at that moment and make a choice/decision. The outcome of large systems is governed by simultaneity, but that's different to saying that the actors decisions are.

Now we may or may not be in agreement, I can't really get precision out of your terminology so far.

[Greg Ransom]

I'm talking about humans learning & adjusting their judgments in the context of the relative prices of the multi-billion person market economy.

It's simply empirically not reality to claim that people are observing & modeling all these billions of minds.

Lets move to language and such things as background, unspoken negative rules of behavior.

The extent that we are modeling "beetles in the head" of other people, as Wittgenstein describes the Russell / atomistic model of "meanings in the head" is a scratch of the surface of what is going on -- this is the point of all of the work of the later Wittgenstein.

See also Hayek's papers in his _Studies in Philosophy_ on unarticulated imitated ways of going on together or patterns of doings that constitute the practices and codes of behavior of groups of people.

The atomistic elements of meanings strung together in explicitly articulated codes are only the surface phenomena of a background of shared and unarticulated practices and 'expectations' of shared shared ways of going on together.

Bottom line -- the lesson of Wittgenstein & Hayek is that the degree to which we build "theories of other minds" in terms of atomic beliefs & desires made possible by a much deeper, non-articulated shared structure of practices and mind that cannot be limned in terms of "given" atomic elements of "meaning" and relations between them.

If you read the literature of the philosophy of language and mind you will see nothing but failure and intractable pathology in the program which seeks to vindicate the "given" meanings & logical relations picture of language and the "given" beliefs & desires model of mind.

See, for example, the work of top philosopher of economics Alex Rosenberg on this topic, which has direct relevance as he shows to economic choice theory as imagined by main stream economists.

"Greg: We (I mean as people, not as economists) observe other people's patterns/rules of behaviour without enquiring into the reasons why people do what they do? Up to a point. I think we also have a "theory of mind", so we have some idea how others would respond differently if we were to act differently. And this is important in explaining why we don't act differently.

[Greg Ransom]

Hayek's argument against the "God's eye view" of using economic math constructs to 'imagine' the economy or imagine socialist planning directly parallel's Wittgenstein's "private language argument" against using what Wittgenstein calls "a bird's eye view" of language or 'meanings', and Hayek's rejection of and then attack upon the "war economics" & math socialism of Rathenau/ Neurath / Lange / Lerner is paralleled by Wittgenstein's attack on Russell's & his own Tractarian atomistic/associationist/phenomenological & formal logical construct "cashing out" of language.

Here's how.

Both reject the idea that the "givens" and given formal relations of the math / logical construct is a thing which captures the significance of the social human world of the economy or of language.

On the contrary.

Whatever significance we can give these elements from a "God's eye view" as a formal stipulator of a construction made up of "given" elements & relations is made possible by our prior situated goings on in the real world of shared practices having a great deal of overlapping shared significance, i.e. the world of shared language practices and shared judgments within the net of moving signals of the relative price structure.

This is a "flip", a turning of the picture on its head, you can see both men doing.

And Hayek does it twice, first in his understanding of the economic world, then in his understanding of the ethical and legal and shared practices realm. Hayek even seems in the end seems to be moving toward doing it with his global brain science, going the Wittgenstein practices route in langauge, which had already already been "flipped" from Machian atomic phenomenalism to a structured brain network theory (the famous Hayek/Hebb synaptical learning model of memory, mind, learning and categorization).

[Peter T]

As someone with a bit of background in the practical applications of figuring out what others are going to do, I'd support the contentions in Nick's post - human interaction is an affair of multiple causation, multiply interacting. Where the humanities differ is that they mostly refuse to formalise the possibilities. Because the essential point is that Adam and Bettie are human - they arrive with whole universes of understandings in their heads, many of them shared, most of them invisible even to themselves, some open to conscious manipulation. So the first rule is to understand what the participants think the rules are, who they think makes the rules, what freedom they think they have to bend or break the rules, who they think are the participants and so on. Example from travels in Asia in the 70s - when bargaining, in Indonesia high status people paid more, so the question is what status do you want to claim? In India, goods were bargainable or non-bargainable, and there were upper limits to asking prices - so you had to sort those categories first. In Iran, bargaining too hard was vulgar, and the transgressor had to pay to avoid shame. In Afghanistan, it seemed to depend on perceptions of how much firepower you had (I was too nervous to test this too hard). As Nick says, institutions matter, but that's only the start. The conditions that make for equilibria are narrow, socially constructed and maintained, and subject to change without notice.

[Peter T]

Just to add that Ronald Coase for one seems to have also arrived at the conclusion that formalising the matter does not add much:

http://coase.org/coaseinterview.htm

[Greg Ransom]

Academics attempting to make sense of the significance of words & logical implication had a framework for doing so exactly parallel to that of economists attempting to make sense of the significance of prices & the implication of prices for distribution.

In fact, both modern programs in their mature form came out the the same city -- Vienna. In the word & logic domain the key figures were Wittgenstein and Carnap. And you can connect a direct line from Wittgenstein & Carnap to Abraham Wald's formal existence proof of equilibrium.

BOTH of these programs sought to limn words & logic (language) and prices & distribution (the economy) by mapping these into formal models.

In the first case, by stipulating a mapping of semantics to particular meaning entities & then mapping the formal relation of these in propositional logic, a system of axioms.

In the second case, by stipulating a mapping of values to particular price entities & then mapping the formal value relations of these into an axiomatic system.

These are the "God's eye view" constructs pretending to limn language and the economy that Wittgenstein & Hayek rejected -- rejected because they actually deceive us into misapprehending where the significance we acribe as the modeler "God" to the elements of our constructs actually derive their purchase and significance -- from the social phenomena in which we move and are embedded. We are embodied within language and within a social pricing system and we never have a synoptic God's eye or bird's eye purchase on semantic or price "entities" connected in formal relations -- THE WORLD DOES _NOT_ COME THAT WAY.

Prices are signals, imperfectly perceived and imperfect as instruments for orienting ourselves in coordination with others.

Language, ditto, although much more tightly bound in shared practices and successful common ways of going on together (read some Wittgenstein).

[Min]

Nick Rowe: "Most (all?) economic models involve simultaneous causation. . . .

"Economics is about human interaction."

I have a little trouble reconciling those two statements. Human interaction takes place over time. (OC, it may yield a system of simultaneous equations, but that is using "simultaneous" in a different sense.)

Nick Rowe: "I am trying to think of the model of human interaction that is the simplest possible model, and the most fundamental possible model."

Mother-infant symbiosis comes to mind. :)

Nick Rowe: "I'm looking at Nash Equilibrium, comparing the "simultaneous" with the "sequential" version of the same game."

By sequential version I suppose that you mean one in which the players use behavioral strategies. We know that behavioral strategies are potentially inferior, but easier to process cognitively. People tend to use behavioral strategies, possibly because they are easier to process. :)

Nick Rowe: "1. In the "Cournot" model, Adam makes his move before observing Betty's move; and Betty makes her move before observing Adam's move.

"2. In the "Stackelberg" model, Adam makes his move before observing Betty's move; and Betty makes her move after observing Adam's move.

"We sometimes say that in the Cournot game Adam and Betty have to make their moves "at the same time", or "simultaneously". But that isn't strictly accurate. Betty might choose how many bananas to pick before or after Adam has already picked his apples. But if she doesn't observe how many apples Adam has picked, until after she has already picked her bananas, it makes no difference."

Addressing the latter point first, you are right. Simultaneity in this context is not about time per se, but about knowledge. We consider the moves to be simultaneous if the players do not know what the other's move is before making their move.

As for the first point, these are not, repeat, not the same game. Knowledge states are part of the game.

Nick Rowe: "In the Stackelberg model, it is very tempting to say that Adam's choice determines Betty's choice, but not vice versa. Tempting, but wrong. If Betty had different preferences, or a different productivity on growing bananas, her reaction function would be different, and Adam's choice would have been different too."

If Betty's reaction function were different, we would have a different game. In the game we actually have, it is OK to say that Adam's choice determines Betty's (in part, OC). Otherwise we end up with a very strange notion of causality. To repeat, knowledge states are part of the game.

Nick Rowe: "The simple "linear", "A causes B causes C causes D" model of a causal chain just does not work, even for these two very simple models of human interaction (except in degenerate cases where one or both person has a dominant strategy)."

By "work" I suppose you mean that it will converge to an equilibrium. That is true. However, if what we are interested in is human interaction, if it does not converge, doesn't that say a lot?