Greece in the penalty box?

I wrote yesterday about the latest moves in the game between the new Greek government and its European creditors. Today I read this excellent piece by Dan Davies. His point is that the ECB has a lot of power and is not afraid to use it, because it can punish Greece without going all the way to kicking it out of the Euro, which would have some costs for the ECB and Europe in general. It comes down to what is the perception of the game the players think they are playing, as I mentioned yesterday. Davies thinks it’s possible that Varoufakis has misunderstood the real nature of the game: he thought it was brinkmanship, but it may be something else, where the ECB can severely punish Greece without going all the way to a Grexit.

Back in 1967-68, John C. Harsanyi formulated, in an epic three-part paper, the concept of Bayesian Nash equilibrium (for which he shared a Nobel prize). In this formulation of a simultaneous-move game, the players may be uncertain about the players who are in the game, the strategies the players can play, and the other players’ payoffs. Yet it is possible to introduce the concept of a type of a player, that encompasses all these elements of uncertainty, resort to a Bayesian framework with a common prior for all players, and create an equilibrium straight out of Nash equilibrium by treating the types of the players as the players in a new, artificial, game that matches with the original one in important (if too technical for this blog post) ways.

I can imagine that Varoufakis thinks he’s got the right conception of the types of the other players he’s facing in the current game he’s in. But if he’s missed some possibilities, by assigning zero probability to certain strategies, for example, as the moves that Dan Davies describes, then while he thinks he’s playing to a Bayesian Nash equilibrium, he may find that the outcome does not match his expectation, because the strategy followed by his opponents has exploited aspects of the game that he did not realize were there. He may be a professor of game theory, but it may be hubristic of him to think he can outmaneuver the game theorists employed by outfits like the ECB.

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