Learning to coordinate in a beauty contest game

Abstract

We study a dynamic game in which a group of players attempt to coordinate on a desired, but only partially known, outcome. The desired outcome is represented by an unknown state of the world. Agents' stage payoffs are represented by a quadratic utility function that captures the kind of tradeoff exemplified by the Keynesian beauty contest: each agent's stage payoff is decreasing in the distance between her action and the unknown state; it is also decreasing in the distance between her action and the average action taken by other agents. The agents thus have the incentive to correctly estimate the state while trying to coordinate with and learn from others. We show that myopic, but Bayesian, agents who repeatedly play this game and observe the actions of their neighbors in a connected network eventually succeed in coordinating on a single action. However, as we show through an example, the consensus action is not necessarily optimal given all the available information.

Information aggregation in a beauty contest game

“…We remark that these results extend beyond the beauty contest game payoffs to quadratic symmetric payoffs with strategic complementarities [1]. Next, we show that consensus in actions implies that agents agree on their individual estimates on the state of the world [2,3]. However, this does not necessarily mean that the agreed estimate is optimal.…”

“…4,5] for a discussion of different equilibrium concepts. In Section 3, we survey some of the results presented in [1][2][3] that show consensus in actions and ex-ante payoffs. We remark that these results extend beyond the beauty contest game payoffs to quadratic symmetric payoffs with strategic complementarities [1].…”

“…The agents thus can benefit from learning from others. This paper provides a survey of results from [1][2][3][4]. We first present a recent result that states repeated play of the game by myopic but Bayesian agents, who observe the actions of their neighbors over a connected network, eventually yield coordination on a single action.…”