Learning to coordinate in a beauty contest game

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 trade-off 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.

[1]  Matthew O. Jackson,et al.  Naïve Learning in Social Networks and the Wisdom of Crowds , 2010 .

[2]  Alejandro Ribeiro,et al.  Bayesian Quadratic Network Game filters , 2013, ICASSP.

[3]  Antoni Calvó-Armengol,et al.  Information Gathering in Organizations: Equilibrium, Welfare, and Optimal Network Structure , 2009 .

[4]  N. Pimlott.  Learning from the neighbours. , 2012, Canadian family physician Medecin de famille canadien.

[5]  Marie Laclau,et al.  A folk theorem for repeated games played on a network , 2012, Games Econ. Behav..

[6]  Alejandro Ribeiro,et al.  Learning in linear games over networks , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[7]  Douglas Gale,et al.  Bayesian learning in social networks , 2003, Games Econ. Behav..

[8]  John Nachbar.  Prediction, optimization, and learning in repeated games , 1997 .

[9]  E. Kalai,et al.  Rational Learning Leads to Nash Equilibrium , 1993 .

[10]  R. Durrett.  Probability: Theory and Examples , 1993 .

[11]  E. Stacchetti,et al.  Towards a Theory of Discounted Repeated Games with Imperfect Monitoring , 1990 .

[12]  S. Morris,et al.  Social Value of Public Information , 2002 .

[13]  P. DeMarzo,et al.  Persuasion Bias, Social Influence, and Uni-Dimensional Opinions , 2001 .

[14]  Jason R. Marden,et al.  Cooperative Control and Potential Games , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Rachel Kranton,et al.  Strategic Interaction and Networks , 2010 .

[16]  Nicolas Vieille,et al.  Informational externalities and emergence of consensus , 2009, Games Econ. Behav..

[17]  J. Jordan.  Bayesian Learning in Repeated Games , 1995 .

[18]  Ali Jadbabaie,et al.  Non-Bayesian Social Learning , 2011, Games Econ. Behav..

[19]  Alejandro Ribeiro,et al.  Dynamic games with side information in economic networks , 2012, 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[20]  H. Peyton Young,et al.  Learning, hypothesis testing, and Nash equilibrium , 2003, Games Econ. Behav..

[21]  J. Jordan,et al.  Bayesian learning in normal form games , 1991 .

[22]  Alessandro Pavan,et al.  Efficient Use of Information and Social Value of Information , 2007 .