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Nick, where did you get your three-fold classification scheme?

Hi Linda: Ummm, I made it up. I couldn't think of any others. There's a limited number of 2x2 symmetric games. There's only so many ways you can rank order 4 squares. I think I counted them once, but I can't remember the answer. Frances and I were discussing Battle of the Sexes and Chicken over lunch, and whether they were really different. But as far as coordination failures go, they aren't really different from Shelling's coordination game.

This point: "And generally, it's just as well that expectations are sticky, because otherwise we would never know which side of the road to drive on, and whether "cat" meant cat or meant dog, so there would be loads of crashes and language would be impossible. Sticky expectations are mostly what prevents Schelling coordination problems."

Reminds me of something Keynes said in A Tract on Monetary Reform about the gold standard. One of the few positive things he had to say about it was that it was slow. That prevented prices from jumping back and forth. The presence of the friction itself contributed to the stability of the system.

Interestingly enough, that was one of the things Hayek DIDN'T like about it in a 1925 essay (I'll have to look up the title) he wrote.

Hmm, 2x2 symmetric game means 2 squares equal? So you need to rank order 3 values? That's factorial 3, or 6. I suspect the other 3 are dull because they are stable good.

Interesting and gutsy post Nick. You cover ground.

The following is for readers with some background in game theory. I barely understand this myself let alone write intelligently for a lay audience. Apologies. -w

The stag-hunt is one type of coordination type game (pure coordination game, Hawk-Dove game, Chicken game. Those looking at a one-shot Nash equilibrium always end up with a single pure Nash equilibrium. Dynamic or multi-player games generally produce multiple pure equilibria. If players deploy evolutionary stable strategies (ESS), replicator dynamics--a crude proxy for social learning--can deliver a unique solution. However, players could adopt a risk-dominated strategy and the social outcome is still Pareto inferior.

A two-player, static, one-shot Prisoners' Dilemma (PD) game has but one pure Nash strategy while dynamic and/or mixed player versions may have multiple pure strategies.

In PD-type games, including continuous-space social dilemmas, not cooperating or defecting typically implies imposing some kind of punishment on the other player. Economic agents and institutions do frequently impose penalties be it Saudi Arabia increasing sales and driving down the price of crude oil to discipline cheating OPEC members or the first-come, first-served exploitation of many public resources and services or Politiburo-style central banks that occasionally slam agents with high real interest rates.

I do not believe the US federal reserve or any other economic players have at any time tried to punish agents before, during and after the last two recessions. (Incidentally, if we examine the US economy before and after these recessions, sticky prices per se never seem to be an issue.)

On the other hand, I see some similarities between the Stag-hunt coordination game and the time inconsistency/commitment technology problem as captured by multi-stage games producing Nash equilibria. Stag hunters would clearly benefit from some kind of credible commitment technology. Similar issues of trust or assurance developed through signalling and reputation all come into play.

I am not sure how Schelling's focal point equilibrium refinement and the related concept of salience can explain macroeconomic fluctuations though I believe they might be more useful for explaining the social conventions and entitlement attitudes that make recessions more likely.

But clearly the USA should look at all the other rich nations that have adopted explicit inflation-targeting and consider a similar move. Growth is the wrong mandate for a central bank. Creating the conditions for stable growth should be the sole mandate and that means stable, informative prices.

Nick, I would just like to say that you are an outstanding blogger and economist. With each of you posts I learn more economics than I did in semester-long courses

Nick, I would just like to say that you are an outstanding blogger and economist. With each of you posts I learn more economics than I did in semester-long courses

+1. This blog really is excellent quality. If I end up back in g school, Nick is at least partially to blame for constantly piquing my interest with these posts.

I would just add that the coordination failure view fits Gary Gorton's analysis of the collapse of the financial system that brought on the crisis: a "run" on the shadow banking system. A bank run is the bad equilibrium in a coordination game. I think that another coordination failure stems from the fact that part of what makes one firm credit-worthy is the ability of its suppliers and customers to get financing. Unless there is One Big Bank, then we have an equilibrium where banks aren't lending because banks aren't lending!

Most S&P stocks aren't publicly owned, they are owned by other big business or banks directly. So if they are cashed in on in the secondary market that money isn't going to be spent because S&P stocks aren't being held by unemployed individuals. It would be the same "rich" people, firms and banks that are currently hoarding cash that would benefit and they most likely will continue hoarding.

On the other hand, from a business perspective, an increase in the market value of those S&P firms would be based on the hopes and dreams of the central bank, who could be seen in the background with fingers crossed, rather than real demand based growth. Everyone (including Tinkerbell) would know this, so why would firms use this as collateral to invest and hire (didn't you just do a post on the #1 reason business is struggling), and why would banks use the extra money they make from an increase in market value of their indexed stock portfolios to finance a "hopeful" expansion? The only way they would is if the central bank were also to guarantee those loans implicitly through the federal government.

I know that you mean well but this amounts to the exact same thing as giving money directly to companies and banks. There is all sorts of reason to believe that they would just sit on it, unless of course they were directed to spend it by the federal government, as a condition, through legislation. But that's the same as fiscal expansion, just brokered by private industry and financed. If that's the plan why channel tax dollars through the banks and corporations, why not just give it directly to the people through fiscal stimulus? It's cheaper and probably more effective.


I agree with Rick, I really struggle to see why a rise in stock prices that everyone attributes to CB buying would have any effect at all on confidence.

I think higher asset prices would help but I think that can be accomplished by the CB buying government bonds. And the mechansim that higher asset prices work through doesn't need to have anything to do with confidence, it could directly lower the cost of capital by lowering real interest rates and at the same time supporting the value of the assets that back the debt issuance.

These are all perfect information games. Does that leave Hamlet out of the play? Is there a place for the market for lemons (which can be phrased as a two-player game) here or does that just confuse the point you are making?

Interesting point tomslee. All the games mentioned in this post have imperfect/incomplete information versions.

The Stag-hunt game has an implicit imperfect information assumption built into it. That is why it is sometimes referred to as an Assurance game. That is why issues of 'trust' and credible commitment are so important.

I was implicitly referring to a context of asymmetric information when I mentioned that signalling and reputation extensions work with both coordination and PD-type games.

Incidentally, experimental lab evidence suggests that authoritative cheap talk or 'credible assignments' can help experimental subjects coordinate on the best strategy. (Ignoring the message carries no direct costs per se.)

In that spirit, I would argue that the US federal reserve is encouraging people to be gloomy.


Wonderful post, as usual.

A question for you. If (say) inflation expectations are "sticky" in the manner you describe, how do you account for Sargent's observation (The End of Four Big Inflations): http://www.minneapolisfed.org/research/WP/WP158.pdf

Sticky expectations.... Isn't that a contradiction?

Agents often adopt policies like rules of thumb behaviour or even contingent-strategy policies. Re-optimization is presumably costly. Policy rules and social conventions can be slow to budge.

Agents can update expectations in response to information shocks. Does incomplete information suggest some kind of stickiness? Or does the possibility that information is time-consuming and expensive to process imply 'stickiness'? Lags yes, stickiness no.

Calling a dated information set 'sticky' grinds the ear. But then I can readily imagine describing sunk-cost-driven behaviour as being 'stuck'. ;-)


I wish the blog had an edit function. I offered two incorrect opinions in a previous post. Contrary to what I wrote:
- Schelling's approach to social coordination offers an explanation of positive inflation targets as opposed to a zero or a slightly negative inflation target. This is not my favourite approach to coordination but many of the social convention theorists seem to think it is important and should be treated seriously.

- Central banks threaten agents with punishing real rate increases if they do not behave. The threat may be veiled but real nonetheless even if punishing rate hikes have not been used for a few decades. PD and social dilemma game theoretic interpretations are realistic.

Terrific post Nick. I just realized that Tinker Bell could be a cheap talking central banker--the source of assignments whose credibility is not necessarily a sure thing.

Incidentally, are you referring to the practice of centrally coordinating information and outlooks from the Bank of Canada versus the American practice of allowing various governors to express their personal, professional views no matter how contradictory? Never thought of dissenting governors as an important issue. Though I see the potential for confusing the public.

Jim: symmetry means you can swap the two players, and the games look the same. So there are 8 payoffs, but 4 are the mirror of the other 4. But you can also swap south with north, and west with east, by just re-naming the two moves. And only the ranking matters. Is one payoff bigger, smaller, or equal to another. I can't remember how to work out how many games there are. But it can't be too hard, for anyone who can keep a straight head.

westslope: thanks!

I wish I had thought of talking about evolutionary stability. The population "learns", even though no individual learns, right? Those with bad strategies die out, and those with better strategies multiply. Of course, evolution is just a metaphor in this context. Strategies breed, not humans. But it's a good metaphor.

I talk about 2-person games, but really i have n-person games at the back of my mind, since it's macro, where n is very large. So if each person is very small, they won't make commitments with all the other players. They play one-shot games. It's different for the monetary and/or fiscal authorities though. They might develop reputations.

JCE and Canuck: thank you both very much for saying that. It matters to me to hear that. But, truthfully, I'm a no-name academic economist. Respectable, just, but no more, and a bit past it. Blogging brought me out, and let me do those things that I can do.

kevin: it does fit right in. But that Gary Gorton stuff, if I understand it correctly, is dynamite! If I've got it right, he says that because of runs on shadow banks, the money supply fell. And by "money" I think he really does mean money, i.e. the medium of exchange, not some B.S. definition of money. In which case, if he's right, it means we have to resurrect old-style monetarism. It wasn't an increased demand for money (or for "safe assets" or other irrelevant crap) that caused the recession. It was a good old fashioned fall in the supply of money. Just like the 1930's bank runs. Just like Milton Friedman. My God! Maybe monetarism is right after all! We just missed out on what was happening to half of the money supply. I've been trying to get my head around it this afternoon.

Rick: "Most S&P stocks aren't publicly owned, they are owned by other big business or banks directly."

I didn't know that. But does that include mutual funds?

Rick and Adam:

One of the main transmission mechanisms I envisage is through Tobin's q. When stock prices rise, it is easier and cheaper for firms to finance new investment by issuing shares. But in general, raising the value of shares, relative to the earnings streams, an increase in P/E ratios, is really the very same thing as a fall in interest rates/yields. Only it's on shares, not bonds.

Ultimately, the big difference between monetary and money-financed fiscal policy is what the government gets in return. The US seems to have a big structural deficit. And I mean "structural" here more in a political sense than any economic sense. That means there's a big difference between printing money to buy shares and printing money to give it away. Plus, if the policy works, those shares rise in value, and the government (or Fed) makes a capital gain. That's one downside with QE to buy bonds, which would fall in value if the policy worked.

tomslee: I don't know. I wanted to keep it simple. It's complex enough as it is. Within those big-picture games, there's lots of important games being played that are imperfect information. But I suppressed that detail here.

And what westslope said: the Fed doesn't seem even to be engaging in "cheap talk" (like an inflation target, which is at least cheap talk, and probably more than that) that could help the players coordinate on the better, "let's all hunt stag" equilibrium.

Plus, they are not even all hunting hare. Expectations of US inflation are all over the place. Some are investing to hunt stag, but nobody else is turning up to join them, so it's a waste. They can't even coordinate on the bad equilibrium. Car crashes all over the place, because they are driving on different sides of the road (to mix metaphors and games). That's what I meant by a smattering of Schelling coordination failures, mixed in with Stag Hunt. There is no clear focal point.

Thanks David!

With difficulty, is the short answer. Sometimes, like in the 1982 recession, there's a lot of inflation inertia. The cold turkey shock therapits were wrong there, and the monetary gradualists were right. And sometimes there isn't. I think that's why it matters that there's a very clear announcement from the Fed as to what its target is. A very loudly announced regime-change, that everyone hears, and everyone knows that everyone hears it....common knowledge. It then becomes a new focal point for expectations. "As of tomorrow morning, we will all drive on the other side of the road", and that advert appears everywhere.

I think Sargent's end of 4 big inflations had a commonly observed regime change, which created a new focal point for prices. Plus, they didn't have the stupid Neo-Wicksellian interest rate instrument to worry about, which means nobody can distinguish monetary tightening from loosening. Simple direct story from deficits to money growth to inflation. When those 4 big inflation people saw the deficits fall, they knew where it would eventually lead.

westslope: we were posting at the same time! If there's a lag for each individual, and the times at which each individual gets the information are staggered, and if there's positive feedback between individuals' actions, the effect at the aggregate level looks very much like stickiness, or inertia.

Imagine a game of 365 agents, each of whom changes his price once a year, on his particular "birthday", and the price he wants to set is always close to the price he expects the others to set (he doesn't want to move his price too far away from the centre of the pack). Like a pack of hounds, where each wants to follow the hare, but not get too far away from the pack. It is very hard for that pack to change direction. Actually, that's the Taylor Price setting model, which generates inflation-inertia.

Yep, inflation target is, at the very minimum, cheap talk. And even cheap talk matters, in a coordination game. Tinkerbell is cheap talk.

"Incidentally, are you referring to the practice of centrally coordinating information and outlooks from the Bank of Canada versus the American practice of allowing various governors to express their personal, professional views no matter how contradictory?"

Yes, absolutely. How can anyone believe Tinkerbell, if there's half a dozen fairies, all saying different things? Nothing to coordinate on. Just cheap babble.

Daniel: missed you, sorry!

The gold standard does provide an anchor for expectations, but it also provides a nominal anchor in terms of the payoff matrix. There's only one equilibrium price level. The trouble with using interest rates as the monetary policy instrument, as opposed to the price of gold, is that it only works well if the central bank announces a clear and credible inflation target as a focal point for people's expectations.

Of course, the gold standard had lots of bad points as well.

the 365 agents, sounds like; David Colander/Abba Lerner market anti-inflation plan. Firms auction for the right to raise prices, match with people lowering. "property rights in gross mark-ups"


My non-economics background focuses me on the "stickiness" itself. Take meanings. We know /dog/ (phonetic) means animal/poor quality thing/ugly female person/machine part and the rest because the sound and meaning are embedded in a complex structure, part linguistic, part social, part environmentally referential. And the structure - which imposes the "stickiness" - is essential to understanding the world and surviving in it.

So the signal here (are we hunting stags or rabbits) is not just an isolate - the expectation and behaviour are anchored, tightly or loosely, in larger structures, and are only interpretable in their context. One view of the financial derivatives market was that it was created on a mutual understanding that the inside players were all our people (and so clever, tricky but fundamentally sound) and the outsiders were not our people, probably suckers, and what happened to them didn't matter. And then the insiders realised their people had sold them rubbish. So they all stopped playing with each other.

To get people out of the "hare" equilibrium into the "stag" one, purely material pay-offs are not enough in the absence of a structure that tells them who are appropriate players, how the stag will be divided, who will get the applause and so on. What makes you think the financial elite thinks Central Banks are suitable rule/style-setters? Or that a stag shared with peasants is worth eating?

Also it is an awesome blog. http://www.lulu.com/
Best of.. or Crisis ... or whatever I don't mind spending some money supporting your 'habit'
Basically I use blog books as an explanation to my family as to what I do with my time. eg swpl

"One of the main transmission mechanisms I envisage is through Tobin's q. When stock prices rise, it is easier and cheaper for firms to finance new investment by issuing shares. But in general, raising the value of shares, relative to the earnings streams, an increase in P/E ratios, is really the very same thing as a fall in interest rates/yields. Only it's on shares, not bonds."

Well yes, you're now just repeating my point. But then, if lowering funding costs and thus required returns is the point, why all the talk of tinkerbell and stags?

An interesting post for sure.

Wont raising asset prices simply provide more "work free" income for the owners of the assets? Is that what the prescription for todays malaise is? As was pointed out by someone else, if everyone simply believes the CB is buying stocks to prop the market how does that contribute to out put that generates employment? This sounds like another supply side trick that expects that if you "give" employers enough money eventually they will buy labor with it.

There is no two ways about it, in order to lower unemployment someone needs to spend, labor does cost something, it is another type of good to be purchased. The problem I see is that too many want to simply hope or assume that unemployment will come down as a result of some other action rather than actually making reducing unemployment the primary goal.

Nick, the whole series of Gorton papers on the crisis is really good, and the most recent one with Metrick is the best of the lot. Note that like you, Cowan was struck by the degree to which treasuries and cash are close substitutes and when he linked to the paper on MR he emphasized the observation that this might vitiate the operations of the FOMC, since they are essentially exchanging one form of money for another.

However, although I am not yet persuaded by Delong's categorization, I think your monetarist interpretation is too simplistic. For one thing, it picks up only half of Gorton's story; he asserts not only that demand for collateral has increased, but also that the pressure to supply it. Since, as he observes, repo data is hard to come by, it is difficult to be sure which of these factors dominates. Second, you should not elide the distinction between treasury collateral and privately created collateral such as AAA-rated securitizations.

As I have mentioned before on this blog, treasuries are actually better money than cash precisely because they have the same surety but they can be posted as collateral. Repo transactions are protected from chapter 11 in a style similar to the safe harbor provisions for bilateral derivatives. The legal claim on cash collateral is not so secure. In this context, it is clear why short-term treasury rates might dip into negative territory when nominal rates are low. But it does not follow as a logical necessity that AAA-securitizations were created in order to supply a demand for collateral. And in fact, I think it is not true. AAA-securitizations were used as collateral to create more AAA-securitizations, not as general collateral. This is the familiar bubble dynamic of self-reinforcing leverage, no different in principle from buying stocks on margin in the '20's.

The characteristic aspects of the crunch had to do with the price of credit, not the price of money. How can the explosion of the basis between 1M and 12M LIBOR to the 200bp level be explained in monetary terms? It is true that the shadow banking system was supplying about 2/3 of credit in the US, but the collapse of this supply seems to have been matched by a collapse in demand.

The two big papers are essentially reproduced in Gorton's brillian book "Slapped by the Invisible Hand".

Phil: I'm still trying to get my head around this. It's the "rehypotheting" thingy that's the biggie, from the medium of exchange point of view. In some places, in the olden days, if you bought something with a cheque, the seller could countersign that cheque, and buy something else with it, and the second seller could countersign it again, buy something, and so on. At that point, the cheques themselves, not just the balance in people's chequing accounts (demand deposits), are money, in the full-blown sense of the word. They circulate like cash.

And I'm trying to get my head clear on the relation between rehypotheting T-bills (and other private AAA securities) and that old story of circulating cheques.

I'm trying to (mentally) simplify it. So I can understand it.

Adam: if it were a pure Stag Hunt, Tinkerbell would be enough to jump the economy from the bad Nash equilibrium to the other. All it takes is the slightest breath to blow a ping pong ball across a flat table. But if there's some sort of friction, or stickiness, or intertia in the ball (it's a tennis ball) you have to blow it a bit harder to get it moving. But it's not like blowing a ball uphill, where you have to keep on blowing.

On Tinkerbell and Stag-Hunts:In practice (in situations which abstractly considered seem to fit the conditions of the game) most stag-hunt situations require more than just Tinkerbell to move from the bad to the Pareto-superior equilibrium. Moving from the bad equilibrium of the bank run game to the good equilibrium requires rebuilding the financial system. Or we may have some non-temporal analogue to "lock-in": Moving from the QWERTY equilibrium to a better one (I know, the QWERTY story may be a fable) would have real costs. And Hume (channeled through Sugden) points out the tendency we humans have of putting a normative gloss on an arbitrary equilibrium reached in a stag-hunt game: "We just aren't the sort of people who play Stag - it's just not done around here, that's all." And just by the way and tangentially, I find Pareto coordination games fascinating ways of explicating what Marx called reification: attributing the effects of our own action to external forces. So, for example, we think that we don't walk the streets because they aren't safe, while in fact -perhaps - the streets aren't safe because we don't walk them.

One of the problems is there is no such thing as Tinkerbell and everyone knows it. Many cling to the idea that they just have to be optimistic and all will get better but in reality those who have a more positive view of the future are those who are doing well in the present. Businesses that are still getting customers (health care, funeral homes) are more positive and looking to expand, those that arent are pretty negative.

We dont have crystal balls, we simply have what we've recently experienced to tell us what to expect. Even the filthy rich cant buy a crystal ball.

Pardon me, Nick, I wasn't disputing that repo creates money exactly as you say. And of course, it is necessary to start with a simple story before elaborating. But ideally, one would like that simple story to be essentially "right." I just meant that I would be cautious about attributing too much to the demand for collateral. It's not that I am positive that Gorton is wrong, it's just that by his own admission, the evidence for this is weak. I can't help but think: the collapse of the asset-backed paper market caused an enormous withdrawal of collateral and contraction of credit - on the order of half. If this credit was underpinning vital economic activity, then our current troubles seem inexplicably mild.

However that may be, the repo market is enormously important and has been for decades, long before the dramatic expansion seen this decade. It is a source of frustration to me that so many people think there is something evil about re-hypothecation. But it is in fact vital to the operation of repo and to financial markets generally; I hope the Gorton papers make that clear.

As it happens, Yves Smith has posted about repo today, in response to a plan for government support advocated by Gillian Tett of the FT: http://www.nakedcapitalism.com/2010/09/why-backstopping-repo-is-a-bad-idea.html. She writes:

"... we need to go back and look hard at why the need for repo has risen since 2001, and how much is related to legitimate activity. The fact that it grew much more rapidly than the economy overall suggests not."

I have my differences with Smith, but in this case our views coincide.

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