Learning with repeated-game strategies.

Christos A Ioannou,Julian Romero

doi:10.3389/fnins.2014.00212

Abstract

We use the self-tuning Experience Weighted Attraction model with repeated-game strategies as a computer testbed to examine the relative frequency, speed of convergence and progression of a set of repeated-game strategies in four symmetric 2 × 2 games: Prisoner's Dilemma, Battle of the Sexes, Stag-Hunt, and Chicken. In the Prisoner's Dilemma game, we find that the strategy with the most occurrences is the “Grim-Trigger.” In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences. In the Stag-Hunt and Chicken games, the “Win-Stay, Lose-Shift” and “Grim-Trigger” strategies are the ones with the most occurrences. Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

Highlights

Robert Axelrod pioneered the area of computational simulations with the tournaments in which game-playing algorithms were submitted to determine the best strategy in the repeated Prisoner’s Dilemma game (Axelrod, 1984). Axelrod and Dion (1988) went on to model the evolutionary process of the repeated Prisoner’s Dilemma game with a genetic algorithm (Holland, 1975)
Similar to Ioannou and Romero (2014), in the computational simulations, we chose to limit the number of potential strategies considered so as to reflect elements of bounded rationality and complexity as envisioned by Simon (1947)
We study the relative frequency, speed of convergence and progression of a set of repeated-game strategies in four symmetric 2 × 2 games: Prisoner’s Dilemma, Battle of the Sexes, Stag-Hunt, and Chicken

Summary

Introduction

Robert Axelrod pioneered the area of computational simulations with the tournaments in which game-playing algorithms were submitted to determine the best strategy in the repeated Prisoner’s Dilemma game (Axelrod, 1984). Axelrod and Dion (1988) went on to model the evolutionary process of the repeated Prisoner’s Dilemma game with a genetic algorithm (Holland, 1975). Robert Axelrod pioneered the area of computational simulations with the tournaments in which game-playing algorithms were submitted to determine the best strategy in the repeated Prisoner’s Dilemma game (Axelrod, 1984). Despite its originality in combining elements from both beliefbased and reinforcement-based models, EWA was criticized for carrying “too” many free parameters. Labeled, the self-tuning EWA, the model does exceptionally well in predicting subjects’ behavior in a multitude of games, yet has been noticeably constrained by its inability to accommodate repeated-game strategies. As Camerer and Ho (1999) acknowledge in their conclusion, the model will have to be upgraded to cope with repeated-game strategies “because stage-game strategies (actions) are not always the most natural candidates for the strategies that players learn about” As Camerer and Ho (1999) acknowledge in their conclusion, the model will have to be upgraded to cope with repeated-game strategies “because stage-game strategies (actions) are not always the most natural candidates for the strategies that players learn about” (p. 871)

Objectives

Results

Conclusion