Boltzmann weight formalism explains non-Nash equilibrium strategic behavior in experimental games

Conventional game theory assumes that players are perfectly rational. In realistic situations, however, players rarely act perfectly rationally. This so-called bounded rationality is one of the main reasons why the predictions of Nash equilibria in normative game theory often diverge from human behavior in real experiments. Motivated by the Boltzmann weight formalism, we here present a theoretical framework to predict non-Nash equilibrium probabilities of possible outcomes in strategic games by focusing on the differences in expected payoffs of players rather than on traditional utility metrics. In our model, bounded rationality is parameterized by assigning a temperature to each player, reflecting their level of rationality by interpolating between two decision-making regimes that are utility maximization and equiprobable choices. Whether players employ pure or mixed strategies, our framework provides a full description over all possible joint strategies and is able to determine the relative probabilities for different choices as well as for multiple pure or mixed strategy Nash equilibria. To validate model predictions, we also analyze experimental data and show that our framework successfully explains non-Nash equilibrium strategies in experimental games. Our approach offers a new perspective, utilizing a theoretical framework to connect the predictions of normative game theory with findings from behavioral experiments.