Periodic frequencies of the cycles in $2\times2$ games: evidence from experimental economics

TL;DR

This study provides experimental evidence that the periodic frequency of cycles in 2x2 games is determined by the payoff matrix, confirming a key prediction of evolutionary dynamics through controlled experiments.

Contribution

First experimental validation of the relationship between payoff matrices and cycle frequencies in 2x2 games, using replicator dynamics models to predict observed frequencies.

Findings

Observed cycle frequencies differ significantly across different payoff matrices.

Both standard and adjusted replicator dynamics models accurately predict frequency differences.

Experimental frequencies are linearly and positively related to theoretical predictions, with the adjusted model performing slightly better.

Abstract

Evolutionary dynamics provides an iconic relationship --- the periodic frequency of a game is determined by the payoff matrix of the game. This paper reports the first experimental evidence to demonstrate this relationship. Evidence comes from two populations randomly-matched $2\times2$ games with 12 different payoff matrix parameters. The directions, frequencies and changes in the radius of the cycles are measured definitively. The main finding is that the observed periodic frequencies of the persistent cycles are significantly different in games with different parameters. Two replicator dynamics, standard and adjusted, are employed as predictors for the periodic frequency. Interestingly, both of the models could infer the difference of the observed frequencies well. The experimental frequencies linearly, positively and significantly relate to the theoretical frequencies, but the adjusted model performs slightly better.