63 Pages Posted: 3 Jun 2017 Last revised: 4 Jun 2017
Date Written: June 2, 2017
In coordination games of incomplete information, and in speculative over-the-counter financial markets, agents care about what their counterparties, on average, expect their counterparties to think, and so forth. Higher-order average expectations of a group of agents are formed by starting with their expectations of a random variable, and then repeatedly considering each agent’s expectation of the average of others’ expectations. The averaging is done according to an arbitrary network describing 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 slightly more optimistic than himself. Second, we study the tyranny of the uninformed, in which coordination is determined by the prior beliefs of the agent with the least precise private information, even when there is nearly common certainty of the ex post optimal action to play.
Keywords: networks, incomplete information, centrality, common prior, heterogeneous priors, network game
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