Player-Compatible Equilibrium

Player-Compatible Equilibrium (PCE) imposes cross-player restrictions on the magnitudes of the players' "trembles" onto different strategies. These restrictions capture the idea that trembles correspond to deliberate experiments by agents who are unsure of the prevailing distribution of play. PCE selects intuitive equilibria in a number of examples where trembling-hand perfect equilibrium (Selten, 1975) and proper equilibrium (Myerson, 1978) have no bite. We show that rational learning and some near-optimal heuristics imply our compatibility restrictions in a steady-state setting.

[1]  Massimo Marinacci,et al.  Learning and self-confirming long-run biases , 2019, J. Econ. Theory.

[2]  Laura Doval,et al.  Whether or not to open Pandora's box , 2018, J. Econ. Theory.

[3]  Drew Fudenberg,et al.  Rationalizable partition-confirmed equilibrium with heterogeneous beliefs , 2018, Games Econ. Behav..

[4]  Roland G. Fryer,et al.  Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability , 2013, Math. Oper. Res..

[5]  Andrzej Skrzypacz,et al.  Learning, Experimentation, and Information Design , 2017 .

[6]  Learning and Equilibrium Refinements in Signalling Games , 2017 .

[7]  D. Fudenberg,et al.  Bayesian posteriors for arbitrarily rare events , 2016, Proceedings of the National Academy of Sciences.

[8]  Peter S. Fader,et al.  Customer Acquisition via Display Advertising Using Multi-Armed Bandit Experiments , 2016, Mark. Sci..

[9]  Joel Watson.  A General , Practicable Definition of Perfect Bayesian Equilibrium , 2017 .

[10]  Pierpaolo Battigalli,et al.  Analysis of information feedback and selfconfirming equilibrium , 2016 .

[11]  Navin Kartik,et al.  Optimal Contracts for Experimentation , 2016 .

[12]  E. Kaufmann.  On Bayesian index policies for sequential resource allocation , 2016, 1601.01190.

[13]  D. Fudenberg,et al.  Rationalizable Partition-Confirmed Equilibrium , 2015 .

[14]  Philipp Strack,et al.  Strategic Experimentation with Private Payoffs , 2015, J. Econ. Theory.

[15]  Y. Ishii,et al.  Innovation Adoption by Forward-Looking Social Learners , 2015 .

[16]  Wtt Wtt.  Tight Regret Bounds for Stochastic Combinatorial Semi-Bandits , 2015 .

[17]  Ignacio Esponda,et al.  Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models , 2014, 1411.1152.

[18]  Deepak Agarwal,et al.  LASER: a scalable response prediction platform for online advertising , 2014, WSDM.

[19]  Wei Chen,et al.  Combinatorial Multi-Armed Bandit: General Framework and Applications , 2013, ICML.

[20]  Aurélien Garivier,et al.  On Bayesian Upper Confidence Bounds for Bandit Problems , 2012, AISTATS.

[21]  Massimo Marinacci,et al.  Selfcon…rming Equilibrium and Model Uncertainty , 2012 .

[22]  Bhaskar Krishnamachari,et al.  Combinatorial Network Optimization With Unknown Variables: Multi-Armed Bandits With Linear Rewards and Individual Observations , 2010, IEEE/ACM Transactions on Networking.

[23]  Lihong Li,et al.  An Empirical Evaluation of Thompson Sampling , 2011, NIPS.

[24]  Akira Okada.  Perfect Bayesian Equilibrium and Sequential Equilibrium , 2011 .

[25]  Bruno H. Strulovici.  Learning While Voting: Determinants of Collective Experimentation , 2010 .

[26]  Sven Rady,et al.  Negatively Correlated Bandits , 2008 .

[27]  Ehud Lehrer,et al.  Partially-Specified Probabilities: Decisions and Games , 2006 .

[28]  D. Fudenberg,et al.  Superstition and Rational Learning , 2006 .

[29]  M. Cripps,et al.  Strategic Experimentation with Exponential Bandits , 2003 .

[30]  Drew Fudenberg,et al.  Subjective Uncertainty over Behavior Strategies: A Correction , 2002, J. Econ. Theory.

[31]  Pierpaolo Battigalli,et al.  Conjectural Equilibria and Rationalizability in a Game with Incomplete Information , 1997 .

[32]  M. Jackson,et al.  A Strategic Model of Social and Economic Networks , 1996 .

[33]  R. Agrawal.  Sample mean based index policies by O(log n) regret for the multi-armed bandit problem , 1995, Advances in Applied Probability.

[34]  H Robbins,et al.  Sequential choice from several populations. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Maxwell B. Stinchcombe,et al.  Equilibrium Refinement for Infinite Normal-Form Games , 1995 .

[36]  A. Rubinstein,et al.  Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability , 1994 .

[37]  J. Banks,et al.  An Experimental Analysis of Nash Refinements in Signaling Games , 1994 .

[38]  L. Shapley,et al.  Potential Games , 1994 .

[39]  David M. Kreps,et al.  Learning Mixed Equilibria , 1993 .

[40]  D. Fudenberg,et al.  Steady state learning and Nash equilibrium , 1993 .

[41]  Jordi Brandts,et al.  An Experimental Test of Equilibrium Dominance in Signaling Games , 1992 .

[42]  J. Huyck,et al.  Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure , 1990 .

[43]  David M. Kreps,et al.  Signaling Games and Stable Equilibria , 1987 .

[44]  E. Vandamme.  Stability and perfection of nash equilibria , 1987 .

[45]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[46]  E. Damme.  Refinements of the Nash Equilibrium Concept , 1983 .

[47]  W. R. Thompson.  ON THE LIKELIHOOD THAT ONE UNKNOWN PROBABILITY EXCEEDS ANOTHER IN VIEW OF THE EVIDENCE OF TWO SAMPLES , 1933 .