Asymmetry Spectrum of Cycle Amplitude in Rock-Paper-Scissor Game of Experimental Economics
3 Pages Posted: 18 Jun 2012
Date Written: June 17, 2012
In a finite population game, the strategy space should fall into a strategy lattice. In a stochastic evolutionary trajectory (Fig. 1), many cycles (generalized Shapley loop) could be filtered out (Table 1). The cycles associated with the stochastic process describe the time evolution. Referring to the direction of the path and the unit size of the lattice (Fig. 1), the amplitude of a cycle must be an integer. The cycles and their amplitudes and then the probability spectrum of the amplitude can be obtained.
Data comes from Standard RPS population games. Subjects are random matching paired each round. 300 rounds are repeated in each of the 12 sessions in each treatment whose population size is 4, 6 and 8 respectively. In these games, Nash random and independent inference is the spectrum should be symmetry but Shapley inference is asymmetry.
Results are (1) We provide, firstly, the spectrum of cycle amplitude (Fig. 2) from RPS population game; (2) Observed the spectrum is asymmetry (unbalance in /- amplitude and Tab. 2) rejects Nash prediction and supports Shapley prediction significant; (3) Interesting is that the characters of the observed spectrum consists with - the extended second law of thermodynamics - fluctuation theorems.
In Summary, in the trajectories, even thought the cycles are erratic, but the distribution of the cycles amplitudes has its own regularity. With this finding, also supported from the observations in the experiments, we suggest that the so called erratic processes of the laboratory social evolution is intrinsic and obey fluctuation theorems.
Keywords: experimental economics, fluctuation theorem, rock-paper-scissors game, mixed strategy Nash equilibrium, evolutionary game theory, stochastic processes
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