Social cycling and conditional responses in the Rock-Paper-Scissors game

Abstract

How humans make decisions in non-cooperative strategic interactions is a challenging question. For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium (NE) state with every player randomizing her choices to avoid being exploited, while evolutionary game theory of bounded rationality in general predicts persistent cyclic motions, especially for finite populations. However, as empirical studies on human subjects have been relatively sparse, it is still a controversial issue as to which theoretical framework is more appropriate to describe decision making of human subjects. Here we observe population-level cyclic motions in a laboratory experiment of the discrete-time iterated RPS game under the traditional random pairwise-matching protocol. The cycling direction and frequency are not sensitive to the payoff parameter a. This collective behavior contradicts with the NE theory but it is quantitatively explained by a microscopic model of win-lose-tie conditional response without any adjustable parameter. Our theoretical calculations reveal that this new strategy may offer higher payoffs to individual players in comparison with the NE mixed strategy, suggesting that high social efficiency is achievable through optimized conditional response.

7 pages + 14 pages supplementary information

References in corpus (12)

• Statistical physics of social dynamics
• Evolutionary games on graphs
• Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Human strategy updating in evolutionary games
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
• Cyclic dominance and biodiversity in well-mixed populations
• Entropy production of cyclic population dynamics
• Intrinsic noise in game dynamical learning
• Cycle frequency in standard Rock-Paper-Scissors games: Evidence from experimental economics
• Cyclic game dynamics driven by iterated reasoning
• Test MaxEnt in Social Strategy Transitions with Experimental Two-Person Constant Sum 2$\times$2 Games

Cited by in corpus (7)

• Optimal cooperation-trap strategies for the iterated Rock-Paper-Scissors game
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• The Rock--Paper--Scissors Game
• Market Imitation and Win-Stay Lose-Shift strategies emerge as unintended patterns in market direction guesses
• Synchronization and extinction in cyclic games with mixed strategies
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game