Abstract
The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory.
Highlights
Many real-life situations in human societies imply interactions in which the results of one person’s choices depend on his/her own behavior, and on the choices of the other individuals involved
Symmetric two-player-two-action games can be expressed by means of the payoff matrix, where rows represent focal player’s actions, columns represent opponent’s actions and the corresponding matrix element is the payoff received by the focal player: C
While for the Harmony Game (HG), Prisoner’s Dilemma (PD) and Stag Hunt (SH) games, the results are straightforward and universal, i.e., independent of the specific distribution of cognitive levels assumed by the agents, for the Snowdrift Game (SG) game, the analysis shows an increasing complexity with cognitive levels, with results that are non-universal, in the sense that the actions taken by the high cognitive level agents depend on the specificities of the assumed distribution
Summary
Many real-life situations in human societies imply interactions in which the results of one person’s choices depend on his/her own behavior, and on the choices of the other individuals involved. Socially-relevant situations usually involve social dilemmas where individuals profit from selfishness at the expense of collective welfare [15,16,17], as well as coordination and anti-coordination quandaries where all parties can maximize their benefits by making mutually consistent decisions [18,19,20,21,22] These situations have been widely studied in different disciplines ranging from economics, sociology, political science to psychology, by using the framework of game theory to understand how people approach conflict and cooperation under modeling conditions [23,24,25,26]. We numerically solve the model using Monte Carlo simulations, finding patterns of behavior compatible with our theoretical predictions
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