On the evolution of heuristics and bounded rational behavior in random games

Abstract

The emergence of heuristics, sophisticated behavior—such as higher levels of Theory of Mind—and substantive rationality in strategic situations can be studied using evolutionary game theory to jointly account for the interactions between players and their environments. Research thus far has been relatively constrained by limiting analyses to a small number of simple games and by focusing on selection operating over actions rather than rules or policies that prescribe behavior in a wide range of games. As a result, the existing literature has not adequately reconciled the significant evidence amassed in the behavioral game theory literature that people use bounded-rational strategies, rather than the normative prescription (Nash equilibrium). I systematically explore the differential costs of implementing decision policies and how evolution is influenced by key environmental characteristics. Detailed maps linking the performance of policies to 3,060 environments are presented demonstrating that the steady state distribution of policies under replicator dynamics is strongly dependent on: a) complexity costs, derived from the opportunity cost associated with the decision time to execute the policies at a process-level and b) the environmental characteristics such as the size of the game, the degree of payoff uncertainty and the degree of mutual interests or conflict between players. Evolution rarely selects for substantive rationality (Nash equilibrium), favoring instead a plethora of bounded-rational policies with varying levels of theory of mind (Level-k models), and in some environmental niches other heuristics such as maxmin or maximization of joint payoffs to players. An intriguing finding is that there exist non-trivial environmental niches with moderate to high complexity costs, where random behavior can be selected for in conjunction with a policy that best-responds to randomness (Level-1). I conclude that while bounded-rational policies do not conform to the standards of substantive rationality, they exhibit both procedural and ecological rationality once the complexity of decision processes and interactions with environmental characteristics are accounted for.