Laboratory RPS Game Experimental Evaluations of the Evolutionary Dynamics Theories

Abstract

The evolution equation determines how frequencies of strategies in the population change (Traulsen & Hauert (2009)), where the change indicates velocities (Bowles (2004),Weibull (1997),Sigmund (2010)). In this paper, based on the laboratory Rock-Paper-Scissors (RPS) game experiments and from the velocity vector fields perspective, we empirically study the five most popular evolutionary dynamics theories (Sandholm (2009)), i.e., replicator(Taylor & Jonker (1978)), logit (Fudenberg & Levine (1998)), Brown-von Neumann-Nash (Brown & Von Neumann (1950)) (BNN), best responde (Gilboa & Matsui (1991)) and Smith (Smith (1984)), respectively, which describe different theoretical patterns of the velocity vector fields in strategy space. We conduct a standard Rock-Paper-Scissors (RPS) game in an experimental economics laboratory. The experiments include 12 independent sessions and each session involves 6 human subjects. Each session consists of 300 rounds of the game repeatedly with a random matching for each round. Since we have 6 human subjects in the RPS game experiments, we have 28 possible states. With the data collected from the experiments, we measure the velocity vector at all of the 28 measurable states x(i; j;k) in the strategy space of the game. Three metrics are employed to measure the difference between the experimental result and each specific mode. Main result and conclusion: This is the first time in the literature of experimental economics to reveal the global dynamic patterns in the strategy space using laboratory RPS game study. This is also the first time in the literature to apply the velocity vector fields to study the comparison between the experimental data and the classic evolutionary dynamics theories, which for the first time to show that none of the classic theories completely confirms the experimental data.