No payoff, no game

If you are not willing to even consider a clash, you’re not negotiating.
Varoufakis

I am not ready to make nice, I am not ready to back down.
Dixie Chicks

What is the payoff structure in the Greece versus Euro Area (EA) game? Games are defined by payoffs. No payoffs, no game. As we do not know the payoff structure, we need to infer it from the strategy of the players. One possibility is this: Greece expects the best result if it does not cooperate and the EA cooperates. If both do not cooperate, that is the worst outcome for Greece, because it is committed to staying in the monetary union and the EU, a cooperative structure. The EA does better if cooperating than if not cooperating, but its worst outcome is if it cooperates while Greece does not. This is not exactly a prisoners’ dilemma (PD), because the EA gets its third best outcome, while Greece its worst, if failure to cooperate is the outcome of the game. For Greece, lack of cooperation being the strategy, failure to agree is better than cooperating on EA uncooperative terms. The game differs from prisoners’ dilemma (PD): in the PD joint uncooperative solution would be the third best for both, while the cooperative solution would be the second best, as here.

Not cooperating for EA means sticking to the existing Troika programme; for Greece it means scraping the Thoika programme; cooperating for EA means postponing and rescheduling the Troika programme; for Greece, cooperating means renegotiating a new programme the EA, the EU, the ECB, and the IMF separately. The game as defined by this pay-off structure has one pure strategy Nash equilibrium (2, 2, or alternative y) and no mixed strategy Nash equilibrium. How could the game be played?

The dominant strategy for EA is not to cooperate. With that, Greece is better off cooperating rather than not cooperating. Greece, indeed, would want eventually to get to the cooperative outcome. That is the weakness in its position, as the interest in eventually cooperating is not enough to move the EA to be cooperative. Because, if Greece were rational, once EA declares its willingness to cooperate, it does better by not cooperating. So, assuming both players are rational, EA sticks to the strategy of not cooperating and waits for Greece to give up or shoot itself in the foot.

So, Greece signals that it is irrational. It is preferring clash over cooperation. That could work in the following way. Greece is convincing as an irrational player: e.g. people are on the streets, the prime minister mobilises the support of the parliament, the finance minister declines all offers in negotiations. It will go, it is irrevocably committed to go, for the worst outcome rather than cooperate with the uncooperative EA, but it will also cooperate if EA cooperates. Why? Because it is irrational, and being irrational it will cooperate, even though in that case it is better, rationally, for Greece not to cooperate when EA is cooperative.

So, Greece needs to project the image of rather thorough irrationality, not of cleverness or cunningness. Not to be intransigent only as long as the other player is not ready to cooperate and then switch back to the rational choice of not cooperating. It needs to play the uncooperative move until the EA decides to cooperate, then indeed cooperate, even though that is the inferior move.

That is the best that the rational EA can get by playing with the irrational Greece and vice versa. The result is the Nash equilibrium.

Decision making rules (P=strict preference; R=preference. i.e. at least as good as; I=clash or joint indifference):

Voting count:

EA: x(1) P y(2), y(2) P z(3), z(3) P w(4).

Greece: w(1) P y(2), y(2) P x(3), x(3) P z(4).

Both: xPz and yPz, clash over all other choices.

The way to choose y: yPz, zIw, wIx, by transitivity of preference R (at least as good as) yRx.

Borda count:

x and y share the first place (4 points), w is second best (5 points), while z is the worst (7 points).

The way to choose y is to add the breaking rule, by rank or by strength, which would both favour y as the second best choice for both players.

Expected payoff for both players: 2 (Nash equilibrium in pure strategies; there is no Nash equilibrium in mixed strategies).

Peščanik.net, 13.02.2015.

The game theory in Vladimir Gligorov’s book Why do countries break up – The case of Yugoslavia