A coordination failure is when rational individual behaviour leads to a bad outcome. Some other outcome would be preferred by all. Keynesians especially emphasise coordination failures, though nearly all macroeconomists say that coordination failures sometimes happen, and say the US economy is in one right now. That makes us optimists. Maybe this isn't the best we can do.
But there are three types of coordination failure: Prisoners' Dilemma; Stag Hunt; and Schelling. Unlike previous recessions, this one is mostly Stag Hunt, with maybe a smattering of Schelling. The 1982 recession was more Prisoners' Dilemma.
Stag Hunt has two Nash Equilibria, a bad one (hunt hare) and a good one (hunt stag). Each can catch a hare by himself, but it takes both players to catch a stag. Half a stag is better than a whole hare. If he expects the other player to hunt hare, it will be individually rational for each to hunt hare too. And if he expects the other to hunt stag, it will be individually rational to join him in hunting stag.
Schelling has two Nash Equilibria, both equally good. It doesn't matter if everyone drives on the right or if everyone drives on the left. And both are Nash Equilibria, because you always want to drive on the same side as everyone else. But if you don't know which of the two equilibria the other player will pick, you might pick the other one, and both players will crash.
The simple Keynesian Cross Income-Expenditure model is a Prisoners' Dilemma coordination failure. There is one equilibrium, but it is usually a bad one. Or, at least, only by sheer fluke would the equilibrium be the best one, called "full-employment". Flukes aside, you need a big player, the government, to either force people to play differently (spending the money they won't spend themselves) or change the payoff matrix (do something to change individuals' incentive to consume or invest) to move the Nash Equilibrium to the good outcome.
The second year textbook model, ISLM with downward-sloping AD curve and sticky prices in the short run, is also Prisoners' Dilemma in the short run. But in the long run, prices adjust to change the real money supply M/P to slowly move the Nash Equilibrium to the right outcome, on the LRAS curve. Monetary policy can help it get there more quickly, by changing M to change M/P, rather than waiting for P to change M/P. The underlying reason for the coordination failure of low employment and output is that M/P is too small.
But if we start asking why prices are slow to adjust, that same model starts to look a bit more like Stag Hunt. Maybe each firm would cut its price, if all the other firms cut theirs too; but it won't be the first to cut. If each thought the others would halve their prices, each would halve its price too. But everybody hunts hare, because if you go out to hunt stag, and nobody else shows up, you catch nothing.
If that's the underlying reason for price-stickiness, then the macroeconomic model is Prisoners' Dilemma in quantity-space, given prices, but is Stag Hunt in price-space. How you see it depends on the strategy space you are looking at.
That seems to work well for the 1982 recession. M fell (or increased more slowly than previously), and it took time for P to fall (or stop rising as quickly). Central banks wanted inflation to fall, but it took time to happen.
The recent (cross fingers) Canadian recession, and the current (never mind the NBER) US recession are different. M/P is higher than normal, and I think higher than it would be if confidence recovered and people expected higher inflation and higher real growth. We are not playing Prisoners' Dilemma any more; we are playing Stag Hunt. With a bit of Schelling thrown in, because different people have very different views on where the economy is headed. Some of them will be very wrong, and will crash. Many just stay off the roads.
It's no good making Happy Faces in Prisoners' Dilemma; it won't work. You have to do something real, like change the payoff matrix. Tinkerbell can't do it. Even if everyone believes her, and thought that everyone else would start spending at the "full employment" level, each would spend more than now, but less than what would be required for full employment. Reality wouldn't quite meet Tinkerbell's optimistic forecast, and her credibility would fall as people learned that, and the economy would slowly converge back on the Nash Equilibrium.
But Stag Hunt is very different. Happy faces, Tinkerbell, sunspots, whatever, could work, at least in principle. There are two Nash Equilibria, and nothing to pick which of the two is the actual outcome. Might as well be Tinkerbell who chooses.
Trouble is, for Tinkerbell, even if there is nothing to anchor people's expectations, they don't change overnight. Some people don't always listen, and the ones who do listen know there are others who don't. And nobody, except the economist who builds the model, knows where the other Nash Equilibrium is anyway. People's expectations get stuck at where we are now. It takes some real force to get them moving. Game theory, which normally assumes players go straight to a Nash Equilibrium, typically ignores all that.
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.
So we can't just rely on Tinkerbell alone, though we certainly need her. All the forces of inertia in expectations, that normally keep us in the good equilibrium, are now keeping us in the bad equilibrium. We need to do something real, and change the payoff matrix to change peoples' behaviour, which will change expectations, and boost Tinkerbell's credibility. My vote is for the Fed to buy some index of stocks, like the S&P500. Raising stock prices would increase demand directly, and seeing stock prices move in the direction of the good equilibrium would raise Tinkerbell's credibility. We get a positive feedback loop.
In the olden days, about 50 years ago, economists used to do a sort of "dynamics" around a Nash Equilibria. They (I nearly said "we") would draw the two firms' reaction curves in a Cournot duopoly game, for example. And then draw a cobweb picture, by supposing the first firm set output at Q1, and the second replied to that with Q2, and the first replied again with Q3, and so on. And they would ask whether the equilibrium were stable or unstable.
Later economists didn't like that stability analysis, with its implicit assumption of adaptive expectations, and assumed players jumped immediately to the Nash equilibrium. But how do players know where the Nash equilibrium is? Can they solve for it? Do they even understand the concept? Why should they believe in it, even if they do understand it? It is not a daft idea to suppose that people have to learn where the Nash Equilibrium is, and learn it by some sort of trial-and-error gradient-climbing process, rather than jumping straight to the top of the hill.
The bad equilibrium is probably locally stable, in other words, given sticky expectations. Locally it looks like a Prisoners' Dilemma. But it's not globally stable. Kick the ball hard enough and it won't roll back to where it started; it will roll to the good equilibrium. The old "pump-priming" metaphor ("kick-starting" is hardly more modern) is another way of saying this. You don't need to change the payoff matrix permanently; only long enough to break out of the bad equilibrium and into the good equilibrium.
The Bank of Canada was better at playing Tinkerbell than the Fed, because it had an explicit inflation target, and a reputation for sticking to it. The Fed seems to have half a dozen Tinkerbells, all saying something different.
(This post is sort of a response to David Andolfatto.)