Level-k Reasoning and Incentives

Level-k theories are agnostic over whether individuals stop the iterated reasoning because of their own cognitive constraints, or because of their beliefs over the cognitive constraints of their opponents. In practice, individual level of play may be a function both of their own constraints and their beliefs over their opponents’ reasoning process. Moreover, the rounds of introspection that players perform may depend on their incentives to think more deeply. We develop a theory which explicitly models players’ reasoning procedure. The rounds of introspection that individuals perform and their actual level of play both follow endogenously. This model delivers testable implications as payoffs and opponents change, and it allows for comparisons across games. It also disentangles the cognitive bound of players for a given game from their beliefs about the play of their opponents. In conjunction with the framework, we present an experiment designed to test its predictions. We modify the Arad and Rubinstein (2012) ‘11-20’ game to serve this precise purpose, and administer different treatments which vary beliefs over payoffs and opponents. The results of this experiment are consistent with the model, and appear to lend support to our theory. This experiment also confirms the central premise that individuals change their level of play as incentives to think more and beliefs over opponents vary.