3 - Global Games: Theory and Applications

Summary

INTRODUCTION

Many economic problems are naturally modeled as a game of incomplete information, where a player's payoff depends on his own action, the actions of others, and some unknown economic fundamentals. For example, many accounts of currency attacks, bank runs, and liquidity crises give a central role to players' uncertainty about other players' actions. Because other players' actions in such situations are motivated by their beliefs, the decision maker must take account of the beliefs held by other players. We know from the classic contribution of Harsanyi (1967–1968) that rational behavior in such environments not only depends on economic agents' beliefs about economic fundamentals, but also depends on beliefs of higher-order – i.e., players' beliefs about other players' beliefs, players' beliefs about other players' beliefs about other players' beliefs, and so on. Indeed, Mertens and Zamir (1985) have shown how one can give a complete description of the “type” of a player in an incomplete information game in terms of a full hierarchy of beliefs at all levels.

In principle, optimal strategic behavior should be analyzed in the space of all possible infinite hierarchies of beliefs; however, such analysis is highly complex for players and analysts alike and is likely to prove intractable in general. It is therefore useful to identify strategic environments with incomplete information that are rich enough to capture the important role of higher-order beliefs in economic settings, but simple enough to allow tractable analysis. Global games, first studied by Carlsson and van Damme (1993a), represent one such environment.