Georg Weizsacker
Business Economics PhD

Dissertation Chair: Prof. A. Roth

Beliefs about Other Players: Experimental Evidence

The thesis combines three articles, asking questions about beliefs that decision makers hold about their opponents in situations of strategic interaction. All three sections use data that are obtained from laboratory experiments, where the action spaces and informational environments can be fully controlled.

In the first section, two behavioral models of two-person normal-form game play are presented and estimated, using three experimental data sets. The models are variants of the Quantal Response Equilibrium model defined by McKelvey and Palfrey (1995, Games and Economic Behavior), but allow a player to hold inaccurate beliefs about the behavior of her opponent. Each model involves two parameters: One captures the player's own level of response rationality, the other the level she attributes to her opponent. In order to allow for type heterogeneity among the subjects in the experiments, parametric distributions of these parameters are assumed. The estimation results indicate that the subjects' choices follow a specific anomalous pattern: On average, subjects play as if they significantly underestimated their opponent's rationality.

Building on this evidence, the other two sections ask further about the belief structure of subjects. In the second section (written jointly with Dorothea Kübler), higher-order beliefs are addressed. To this end, we turn to games in which social learning is possible and predicted by theory. In particular, we examine the robustness of information cascades in experimental settings. Apart from the situation in which each player can obtain a signal for free (as in the experiment by Anderson and Holt, 1997, American Economic Review), the case of costly signals is studied where players decide whether or not to obtain private information, at a small but positive cost. In the equilibrium of this game, only the first player buys a signal and makes a decision based on this information whereas all following players do not buy a signal and herd behind the first player. The experimental results show that too many signals are bought and the equilibrium prediction performs poorly. To explain these observations, the depth of the subjects' reasoning process is estimated, using a statistical error-rate model similar to the one in the first section of the thesis. Allowing for different error rates on different levels of reasoning, we find that the subjects' inferences become significantly noisier on higher levels of the thought process, and that the subjects apply only short chains of reasoning.

In the last section (joint with Miguel Costa Gomes), the focus shifts back to normal-form games. There, we ask whether the deviations from rational expectations that are observe in the first section should be explained by a belief-based decision model at all. I.e., we investigate at a more general level the assumption that players respond to underlying expectations about their opponent's behavior. In our experiments for this section, subjects played a set of 14 two-person 3x3 games, and stated first order beliefs about their opponent's behavior. The experiments allow us to examine the consistency of stated beliefs and observed actions, as well as the effects that asking for such belief statements may have on subsequent actions. The sets of responses in the two tasks are largely inconsistent. Rather, we find evidence that the subjects perceive the games differently when they (i) choose actions, and (ii) state beliefs. On average, they fail to best respond to their own stated beliefs in almost half of the games, and thereby forego additional earnings in the experiments. Subjects appear to pay more attention to the opponent's incentives when they state beliefs than when they play the games themselves. The inconsistency is confirmed by estimates of a unified statistical model that jointly uses the actions and the belief statements. There, we are able to control for noise, and formulate a statistical test that rejects consistency. Effects of the belief elicitation procedure on subsequent actions are mostly insignificant.