Periodic frequencies of the cycles in 2 × 2 games: evidence from experimental economics

Eur. Phys. J. B (2014) 87: 46

Bin Xu1,2,3, Shuang Wang1,4,5 ,   Zhijian Wang1,3a


1 Experimental Social Science Laboratory, Zhejiang University, Hangzhou 310058, P.R. China and
2 Public Administration College, Zhejiang Gongshang University, Hangzhou 310018, P.R. China and
3 State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China and
4 Chu Kochen College, Zhejiang University, Hangzhou 310058, P.R. China and
5 Department of Economics, Duke University, Durham, NC 27708-0097, USA.




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 × 2 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.

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