Expectations, Networks, and Conventions

Abstract

In coordination games of incomplete information, as well as in speculative over-the-counter financial markets, agents care about what their counterparties, on average, expect their counterparties to think, and so forth. Iterated average expectations of a group of agents are formed by starting with their expectations of a random variable, and then repeatedly considering their expectations of the average of others' expectations. The averaging is done according to an arbitrary network that captures whom each agent cares about. We offer a unified analysis of these objects and their limits. Special cases include beauty contests under a common prior and the network centrality analysis of network games. Two leading applications illustrate the results. First, we describe a contagion in which asset values are driven to extremes if almost everyone expects his average counterparty to be just slightly more optimistic than himself. Second, we study the tyranny of the uninformed, in which coordination is determined by the prior beliefs of the player with the least precise information, even when the environment features nearly common certainty of the ex post optimal action to play. Joint work with Stephen Morris (Princeton)