Bounded best-response and collective-optimality reasoning in coordination games

We investigate experimentally the conditions under which bounded best-response and collective-optimality reasoning are used in coordination games. Using level-k and team reasoning theories as exemplars, we study games with three pure-strategy equilibria, two of which are mutually isomorphic. The third is always team-optimal, but whether it is predicted by level-k theory differs across games. We find that collective-optimality reasoning is facilitated if the collectively optimal equilibrium gives more equal payoffs than the others, and is inhibited if that equilibrium is Pareto-dominated by the others, considered separately. We suggest that coordination cannot be explained by a single theory.

[1]  Colin Camerer,et al.  A Cognitive Hierarchy Model of Games , 2004 .

[2]  D. Regan,et al.  Utilitarianism and Cooperation , 1980 .

[3]  Andreas Blume,et al.  Cognitive forward induction and coordination without common knowledge: An experimental study , 2010, Games Econ. Behav..

[4]  Michael Bacharach,et al.  Beyond Individual Choice: Teams and Frames in Game Theory , 2006 .

[5]  A. Smerilli.  We-thinking and vacillation between frames: filling a gap in Bacharach’s theory , 2012 .

[6]  Daniel John Zizzo,et al.  Groups, cooperation and conflict in games , 2008 .

[7]  Anders U. Poulsen,et al.  Focal points in tacit bargaining problems: Experimental evidence , 2013 .

[8]  Michael Bacharach,et al.  The Variable Frame Theory of Focal Points: An Experimental Study , 1997 .

[9]  Robert Sugden,et al.  How Portable Is Level-0 Behavior? A Test of Level-k Theory in Games With Non-Neutral Frames , 2014 .

[10]  A. Colman,et al.  Collective rationality in interactive decisions: evidence for team reasoning. , 2008, Acta psychologica.

[11]  R. Sugden.  A Theory of Focal Points , 1995 .

[12]  Dale O. Stahl,et al.  Variable-Frame Level-n Theory , 2000, Games Econ. Behav..

[13]  R. Sugden,et al.  Explaining Focal Points: Cognitive Hierarchy Theory Versus Team Reasoning , 2009 .

[14]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[15]  Robert Sugden,et al.  Nash equilibrium, team reasoning and cognitive hierarchy theory. , 2008, Acta psychologica.

[16]  N. Bardsley,et al.  Focal points revisited: Team reasoning, the principle of insufficient reason and cognitive hierarchy theory , 2014 .

[17]  D. Stahl,et al.  Experimental evidence on players' models of other players , 1994 .

[18]  Briony D. Pulford,et al.  Explaining Strategic Coordination: Cognitive Hierarchy Theory, Strong Stackelberg Reasoning, and Team Reasoning , 2014 .

[19]  M. Bacharach.  Interactive team reasoning: A contribution to the theory of co-operation , 1999 .

[20]  Focal points in tacit bargaining games , 2011 .

[21]  David Lewis.  Convention: A Philosophical Study , 1986 .

[22]  R. Sugden,et al.  The Nature of Salience: An Experimental Investigation of Pure Coordination Games , 1994 .

[23]  E. Fehr.  A Theory of Fairness, Competition and Cooperation , 1998 .

[24]  V. Crawford,et al.  The Power of Focal Points Is Limited: Even Minute Payoff Asymmetry May Yield Large Coordination Failures , 2008 .

[25]  D. Hodgson.  Consequences of Utilitarianism , 1967 .

[26]  Gary E. Bolton,et al.  ERC: A Theory of Equity, Reciprocity, and Competition , 2000 .

[27]  Andreas Blume,et al.  Coordination and Learning with a Partial Language , 2000, J. Econ. Theory.

[28]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

[29]  R. Aumann,et al.  Unraveling in Guessing Games : An Experimental Study , 2007 .

[30]  Miguel A. Costa-Gomes,et al.  Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications , 2013 .

[31]  T. Schelling,et al.  The Strategy of Conflict. , 1961 .

[32]  V. Crawford,et al.  Learning How to Cooperate: Optimal Play in Repeated Coordination Games , 1990 .

[33]  André Casajus,et al.  Focal Points in Framed Strategic Forms , 2000, Games Econ. Behav..

[34]  Anders U. Poulsen,et al.  The focality of dominated compromises in tacit coordination situations: Experimental evidence , 2016 .

[35]  U. Fischbacher.  z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[36]  Ariel Rubinstein,et al.  Naive Strategies in Competitive Games , 1997 .

[37]  R. Sugden.  Thinking as a Team: Towards an Explanation of Nonselfish Behavior , 1993, Social Philosophy and Policy.