Stated Beliefs and Play in Normal-Form Games

Abstract

Using data on one-shot games, we investigate the assumption that players respond to underlying expectations about their opponent's behavior. In our laboratory experiments, subjects play a set of 14 two-person 3x3 games, and state first order beliefs about their opponent's behavior. 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 -they appear to pay more attention to the opponent's incentives when they state beliefs than when they play the games. On average, they fail to best respond to their own stated beliefs in almost half of the games. The inconsistency is confirmed by estimates of a unified statistical model that jointly uses the actions and the belief statements. There, we can control for noise, and formulate a statistical test that rejects consistency. Effects of the belief elicitation procedure on subsequent actions are mostly insignificant.

Equilibrium play and best response to (stated) beliefs in normal form games

“…2 Most closely related to our paper, Costa-Gomes and Weizsäcker (2006) found low rates of compliance with equilibrium predictions (35%), low frequency assigned to equilibrium beliefs (32.2%) and low percentages of best response behavior (50.5%) in a very similar experiment with variable sum games. We here discuss some reasons why in our experiment the predictions of Game Theory may be more successful and in particular, we compare our results in constant sum (CS) and variable sum (VS) games.…”

“…14 NE performs similarly as the other models in the VS treatments, although D1 is the best predictor. It is noticeable that L1 and L2, which were two of the most successful models in Costa- Gomes & Weizsäcker (2006), perform worse than NE, even in the VS treatment. Notice that L2 predicts the same outcome as NE in six games, while L1 does not predict the same outcome as NE in any game.…”

An Experimental Study of Information Revelation Policies in Sequential Auctions

“…Monetary incentives are provided for making accurate guesses. Specifically, for eliciting the beliefs, we applied a quadratic scoring rule, which is incentive compatible for players to state their true their beliefs (Selten, 1998, Nyarko and Schotter, 2002, Costa-Gomes and Weizsacker, 2008. To reduce the likelihood that the belief elicitation reward significantly affects bidding behavior, the maximum reward for the beliefs (20 experimental Francs) is kept low relative to the difference in c h and c l .…”

Measuring Attention and Strategic Behavior in Games with Private Information

“…of the cells and click-and-hold to reveal the payoff. 18 Subjects had to pass a short comprehension quiz as well as go through a practice trial to ensure that they understood the rules before proceeding to the paid trials. A survey including demographic questions, questions about experience with game theory, poker and bridge, as well as the three-question Cognitive Reflection Test (CRT: Frederick, 2005) was administered at the end of each session.…”