Experimental analysis of the role of higher-order beliefs about the cognitive abilities of others in coordination games

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With this project we aim to provide a better understanding of the possible reasons of coordination failure in strategic situations such as financial markets or bank runs.John Maynard Keynes (1936) in his famous beauty contest analogy argues that a good investment strategy not so much depends on having the correct assessment of the fundamental value of the various assets, but more so on what one believes others believe what the fundamental value is and what one believes others believe what others believe the fundamental value is, and so on, possibly ad infinitum. In short, the game investors play is foremost a coordination game and in such games "higher order beliefs" play a crucial role.There is a literature (cited in the proposal) that shows, in theory, how fragile the outcome of coordination games is with respect to small changes in individuals' higher order beliefs. On the other hand there is also an experimental literature (cited in the proposal) that demonstrates that most players in real life do not employ beliefs of high order. This latter literature focuses on two aspects, the tradeoff between risk-dominance ("less risky") and Pareto-dominance ("higher payoffs") and the role of imperfect information about the payoffs in the game.We want to add to the understanding of this problem by investigating a third source of strategic uncertainty based on imperfect cognition: not every player necessarily fully grasps all the possible choices at her disposal. Theoretically, a rational player's behavior then depends on all her higher-order belief about her opponents' cognitive ability (including her opponent's higher order beliefs about her own cognitive ability). In order to test whether players have higher-order beliefs of this nature, we propose to run an experiment tailored for this purpose that builds on the work by Blume and Gneezy (2000, 2010). In their experimental design subjects play coordination games, in which the optimal way to coordinate is not immediately obvious. They have two treatments: 1) a single player plays the coordination game against herself, 2) two players play the coordination game. They find that many subjects play optimally in 1) but not in 2). Their explanation is that subjects are overly pessimistic about their opponents' cognitive ability.We plan to add a third treatment 3) while her opponent plays the game against himself (as in treatment 1), the player of interest is asked to bet on her opponent's choices.A player with pessimistic beliefs about his opponents' cognitive ability will choose the suboptimal strategy in 2) and 3), while a player with non-trivial higher-order beliefs may choose the suboptimal strategy in 2) but bet that her opponent will choose optimally in 3). We can, thus, experimentally identify whether the main reason for coordination failure is that players have pessimistic simple beliefs, or whether it is because of their higher-order beliefs.