Abstract
Arad and Rubinstein (2012, AER) proposed the 11–20 money request game as an alternative to the P beauty contest game for measuring the depth of thinking. In this paper, we show theoretically that in the Nash equilibrium of the 11–20 game players are more likely to choose high numbers if they are risk-averse rather than risk neutral. Hence, the depth of thinking measured in the 11–20 game is biased by risk aversion. Based on a lab experiment, we confirm this hypothesis empirically.
Highlights
Game theory models often make assumptions about the rationality of decision makers.One common form of rationality assumed is that decision makers have the ability to perform strategic reasoning such as iterative reasoning
Arad and Rubinstein (2012) [3] found that the choices in the 11–20 game cannot be explained by a mixed strategy Nash equilibrium
First, we theoretically show that when players are risk averse, players will choose large numbers with larger probabilities than the risk-neutral case
Summary
Game theory models often make assumptions about the rationality of decision makers. One common form of rationality assumed is that decision makers have the ability to perform strategic reasoning such as iterative reasoning. Arad and Rubinstein (2012) [3] proposed the 11–20 money request game as a more effective alternative to the P beauty contest game for measuring the depth of thinking. We elicit the subjects’ risk attitudes using the Holt and Laury (2002) [4] task With this information in hand, we can test our main hypothesis that, in the 11–20 game, the subjects’ choices are mainly influenced by risk aversion rather than strategic reasoning and that, in the P beauty contest game, the subjects’ choices are not influenced by risk aversion. Risk-averse subjects are much more likely to choose high numbers (i.e., exhibiting low depths of thinking if one literally uses the chosen number to infer the level of strategic reasoning) in the 11–20 game. We find that choices in the P beauty contest game are not correlated with risk aversion
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