Incentive and stability in the Rock-Paper-Scissors game: an experimental investigation

Abstract

In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a representative mathematical model to illustrate the game dynamics, appearing widely in textbook. However, how actual motions in these games depend on the incentive has never been report quantitatively. Using the data from 7 games with different incentives, including 84 groups of 6 subjects playing the game in 300-round, with random-pair tournaments and local information recorded, we find that, both on social and individual level, the actual motions are changing continuously with the incentive. More expressively, some representative findings are, (1) in social collective strategy transit views, the forward transition vector field is more and more centripetal as the stability of the system increasing; (2) In the individual behavior of strategy transit view, there exists a phase transformation as the stability of the systems increasing, and the phase transformation point being near the standard RPS;(3) Conditional response behaviors are structurally changing accompanied by the controlled incentive. As a whole, the best response behavior increases and the win-stay lose-shift (WSLS) behavior declines with the incentive. Further, the outcome of win, tie, and lose influence the best response behavior and WSLS behavior. Both as the best response behavior, the win-stay behavior declines with the incentive while the lose-left-shift behavior increase with the incentive. And both as the WSLS behavior, the lose-left-shift behavior increase with the incentive, but the lose-right-shift behaviors declines with the incentive. We hope to learn which one in tens of learning models can interpret the empirical observation above.

Testability of evolutionary game dynamics based on experimental economics data

“…That is, the deterministic motions are faster in the social state close to the simplex edge than those close to the rest point. This result was previously unknown; moreover, such clear and high-precision empirical patterns have not been seen [23,26,24,17]. We use the observed values in each patch to evaluate the theoretical models.…”

“…Naturally, the reality of evolutionary dynamics models have been widely considered [27,28,29,30]. In recent decades, social scientists have continued to investigate and improve upon the commonalities between models and experiments [18,19,11,20,21,22,17,23,24,25,26]. However, there is still a significant gap between evolutionary outcomes from models and empirical results.…”

“…However, there is still a significant gap between evolutionary outcomes from models and empirical results. Without loss of generality, the gap can be seen in representative RPS game experiments [23,26,17,24,31,32]. Scientists have clearly illustrated how to distinguish various games with models in experiments [31,23,26,17,24]; however, distinguishing various models associated with games in experiments has only rarely been achieved.…”

“…Without loss of generality, the gap can be seen in representative RPS game experiments [23,26,17,24,31,32]. Scientists have clearly illustrated how to distinguish various games with models in experiments [31,23,26,17,24]; however, distinguishing various models associated with games in experiments has only rarely been achieved. For a given game experiment, it seems that the dynamics model could be arbitrarily chosen because various models have similar expectations regarding existing observations, which is unsatisfying.…”

The rock–paper–scissors game

“…In the experiment each population plays with a fixed reward parameter a whose value ranging from a = 1.1 to a = 100. The empirical results demonstrated that the precise value of a does not affect the qualitative dynamical behaviour of this finite-population system [20,30].…”