Cognitive hierarchy theory and two-person games

TL;DR

This paper develops an algorithm for modeling strategic behavior in two-player games using Cognitive Hierarchy Theory, revealing new properties of snowdrift games and proposing an evolutionary dynamics model.

Contribution

It introduces a novel algorithm for analyzing strategies in symmetric two-player games under Cognitive Hierarchy Theory and uncovers new properties of snowdrift games.

Findings

Snowdrift game behavior complexity increases with cognitive levels

Snowdrift games can be characterized by a single parameter

Snowdrift games are anti-symmetric with respect to pay-off space diagonal

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-players-two-actions 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.