UC Berkeley

This dissertation consists of three chapters, which study the identification of people's reasoning abilities and belief levels in strategic interactions. The first chapter examines the methodology to identify subjects' reasoning levels in the ring games proposed by Kneeland (2015). In the second chapter, an experiment is designed to identify whether it is limited reasoning ability or incorrect belief that prevents people from playing equilibrium strategies. The experiment builds on a series of ring games similar to the ones analyzed in Chapter 1. The third chapter links people's performance in games to a measure of their cognitive ability, which also validates the findings in Chapter 2.

The ring games are first used by Kneeland (2015) to separate different orders of belief in rationality. Her experiment finds rationality levels higher than those in the literature. The first chapter points out two features in the ring games used by Kneeland (2015) that could potentially bias type classification, and reports the experimental results using two new sets of games with these features removed. Similar type distribution as seen in Kneeland (2015) is reproduced when the rows with the largest sums in the payoff matrices do not coincide with the equilibrium strategies. However, when some rows that have the lowest sums and contain zeros are set to be the best responses, a considerably larger fraction of low types are found. Additionally, the deviation rates from the theoretical prediction are higher in my data, partly due to the lesser performance of the identifying assumption.

The second chapter reports an experiment to identify the decisive factor that prevents people from using more depth of reasoning: their incorrect belief of others' rationality or their limited reasoning ability. The analysis first classifies subjects into different Lk types by the reasoning steps they use in the games. It then distinguishes between the "Lkb" players, who have high ability and best respond to Lk belief, and the "Lka" players, who could use, at most, k steps of reasoning, and thus could not respond to L(k+1) or higher-order belief. The separation utilizes a combination of simultaneous and sequential ring games. In the sequential games it requires more than k reasoning steps to respond to Lk belief, so Lkb players still best respond but Lka would fail. I find that around half of the L2 and L3 subjects are best responding to L2 or L3 belief, while the rest have reached their upper boundaries of reasoning. The findings suggest that both belief and reasoning ability could be the decisive factors of players' observed levels.

The third chapter finds positive relationship between the Cognitive Reflection Test (CRT) scores, an indicator of cognitive ability, and the reasoning levels in the ring games in Chapter 2. The CRT scores increase with levels among the lower types (from L0 to L2b), and but do not differ significantly from L2b to L4. Striking difference is found between the CRT scores of L2a and L2b subjects, which suggests that cognitive ability are strongly related to reasoning skills.