An empirical model of non-equilibrium behavior in games

Abstract

This paper studies the identification and estimation of the decision rules that individuals use to determine their actions in games, based on a structural econometric model of non-equilibrium behavior in games. The model is based primarily on various notions of limited strategic reasoning, allowing multiple modes of strategic reasoning and heterogeneity in strategic reasoning across individuals and within individuals. The paper proposes the model and provides sufficient conditions for point identification of the model. Then the model is estimated on data from an experiment involving two-player guessing games. The application illustrates the empirical relevance of the main features of the model.

Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games

“…However, given the low levels of k 2 play we find and the econometric difficulties of including own history in the logit, we only analyze the first iteration of reasoning. 36 This suggests that players do respond to expected payoffs calculated from historical opponent play; whereas in the reduced-form results (Table 4) we showed that players did not respond to the expected payoff calculated from predicted opponent play-predicted based on the coefficients from Table 3 and players' histories. 37 We multiply by 100 to convert to percentages and by 2/9 to evaluate the margin at the mean: 0.232…”

“…This is a similar approach to papers that identify player strategies in other settings. Kline [36] presents a method for identification under a continuous action space and applies this method to two-person guessing games. Hahn et al [37] present a method for a setting with a continuous action space where the parameters of the game evolve over time.…”

“…The mean coefficient for the baseline (naive) model is 1.42 (2.47). 36 The expected return is the probability of winning minus the probability of losing (probability of winning), so it ranges from −1 to 1 (0 to 1). The standard deviation is 0.232 (0.137), so, on average, a standard deviation increase in the expected return to an action, increases the percent chance it is played by approximately 7.3 percentage points (7.5 percentage points).…”

Identification of firms’ beliefs in structural models of market competition

“…In the econometrics of games, several papers have studied identification of models that allow for biased beliefs but impose other restrictions, such as level‐k rationality (An 2017), cognitive hierarchy (Brown et al. 2013) or rationalizability (Aradillas‐Lopez and Tamer 2008, Kline 2018). In this paper, I do not impose these restrictions and show that they are testable.…”