Endogenous Depth of Reasoning

Abstract

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.

Gender Differences and Stereotypes in the Beauty Contest

“…We also highlight the endogeneity of depth of reasoning with respect to incentives (also found in Alaoui and Penta, 2013). Regarding gender, our results show that the combination of incentives and gender priming enhances females'performance.…”

“…In short, it should be natural to expect observed strategic sophistication to depend on both beliefs about the sophistication of others and on incentives. 2 In this paper, we explore the heterogeneity and endogeneity of strategic sophistication in the context of gender. Gender constitutes an obvious source of observable heterogeneity across individuals.…”

Who knows it is a game? On strategic awareness and cognitive ability

“…5 they are playing the BCG against experienced graduate students instead of other undergraduates. In a similar vein Alaoui and Penta (2013) show that subjects' level of reasoning in an 11-20 game varies with their knowledge about the inferred sophistication of opponents. 4 More generally, our findings add to an emerging literature that explores the impact of cognitive ability on economic behavior.…”

“…The CRT is a three-question test that builds upon the presumption that our brain uses two types of cognitive processes, a more intuitive or emotional 4 Alaoui and Penta (2013) show theoretically that their experimental results are consistent with individuals engaging in a cost-benefit analysis of applying additional rounds of reasoning. See also Strzalecki (2010) for an alternative theoretical approach in which behavior also depends on own bounded rationality and beliefs about opponents' bounds.…”

Rational attitude change by reference cues when information elaboration requires effort

“…In the literature on k-level reasoning, Alaoui and Penta (2015a) introduce costs to access higher levels of reasoning, and perform a cost-benefit analysis that allows to endogenize the level of reasoning; pursuing this line, Alaoui and Penta (2015b) test this model in the lab and find evidence that supports the idea that players weigh the value of thinking deeper against the cost of reasoning. Our model resembles theirs in that there are explicit cognitive costs but in our model the costly activity is only about information processing.…”