Econ 618: Topic 10 Introduction to Global Games

The term ”global games” was introduced by Carlson and Van Damme in their classic 1993 Econometrica paper to describe a type of Bayesian game. In this type of game, the players’ payoffs for a given strategy profile also depends on the realization of a fundamental ”state of the economy”, which is unobserved.The fundamental has a prior distribution which is common knowledge. At the start of the play, Nature picks a value for the fundamental which players cannot observe. Each player receives a noisy private signal about the realized fundamental. The distribution of the noise is iid across players and also common knowledge. Based on one’s own signal, players form posteriors about the fundamental state and about the signals received by other players. As in the previously discussed Bayesian games, players must pick a strategy map that tells them which action to pick from a set of actions, for each signal. The description ”global” is supposed to convey the idea that each player observes the game selected by Nature with some noise implying, the observed game belongs to a larger class of games any one of which is possible. An optimal strategy has to be optimal for the entire larger class of games, not only for the observed one. It is as if the players are playing a ”global” game rather than the observed one. The difference between this type of game and the previous types of Bayesian games discussed in class, is that in all the previous cases, the uncertainty related to the type of each player. But the types were independently distributed. Hence, at the beginning of the game when a player learnt his own type, this information conveyed no further information about the types of the other players.