Defense mechanisms of empathetic players in the spatial ultimatum game

Abstract

Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount of money, unfair offers are rare and their acceptance rate small. While empathy and spatiality may lead to the evolution of fairness, thus far considered continuous strategies have precluded the observation of solutions that would be driven by pattern formation. Here we introduce a spatial ultimatum game with discrete strategies, and we show that this simple alteration opens the gate to fascinatingly rich dynamical behavior. Besides mixed stationary states, we report the occurrence of traveling waves and cyclic dominance, where one strategy in the cycle can be an alliance of two strategies. The highly webbed phase diagram, entailing continuous and discontinuous phase transitions, reveals hidden complexity in the pursuit of human fair play.

arXiv comment4 two-column pages, 5 figures; accepted for publication in Physical Review Letters

References in corpus (6)

• Evolutionary games on graphs
• Phase diagrams for the spatial public goods game with pool-punishment
• The Ultimatum Game in Complex Networks
• The effect of the topology on the spatial ultimatum game
• Vortex dynamics in a three-state model under cyclic dominance
• Critical behavior in an evolutionary Ultimatum Game

Cited by in corpus (48)

• Statistical physics of human cooperation
• Evolutionary games on multilayer networks: A colloquium
• Cyclic dominance in evolutionary games: A review
• Interdependent network reciprocity in evolutionary games
• Mathematical foundations of moral preferences
• Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: Phase transitions to elementary strategies
• Robust Reconstruction of Complex Networks from Sparse Data
• Effectiveness of conditional punishment for the evolution of public cooperation
• Collective behavior and evolutionary games - An introduction
• Grand challenges in social physics: In pursuit of moral behavior
• The evolution of trust and trustworthiness
• Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas
• Zealots tame oscillations in the spatial rock-paper-scissors game
• Accuracy in strategy imitations promotes the evolution of fairness in the spatial ultimatum game
• A novel route to cyclic dominance in voluntary social dilemmas
• Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates
• Bargaining with entropy and energy
• Predominance of the weakest species in Lotka-Volterra and May-Leonard implementations of the rock-paper-scissors model
• Costly hide and seek pays: Unexpected consequences of deceit in a social dilemma
• The evolution of lying in well-mixed populations
• Lying on networks: The role of structure and topology in promoting honesty
• Binary birth-death dynamics and the expansion of cooperation by means of self-organized growth
• Evolution of cooperation in spatial traveler's dilemma game
• Aggregation as an antipredator strategy in the rock-paper-scissors model
• Evolution of favoritism and group fairness in a co-evolving three-person ultimatum game
• Non-Hermitian topology in rock-paper-scissors games
• Strategy intervention for the evolution of fairness
• Dynamically generated hierarchies in games of competition
• When greediness and self-confidence meet in a social dilemma
• Coupled dynamics of mobility and pattern formation in optional public goods games
• Small Fraction of Selective Cooperators Can Elevate General Wellbeing Significantly
• Emergence of Fairness Behavior Driven by Reputation-Based Voluntary Participation in Evolutionary Dictator Games
• Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system
• Weak species in rock-paper-scissors models
• A reversed form of public goods game: equivalence and difference
• Interactive diversity disrupts cyclic dominance but maintains cooperation in spatial social dilemma games
• How multiple weak species jeopardise biodiversity in spatial rock-paper-scissors models
• Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems
• Qualitative aspects of the phase diagram of J1-J2 model on the cubic lattice
• Status maximization as a source of fairness in a networked dictator game
• Rock-paper-scissors models with a preferred mobility direction
• Decoding fairness: a reinforcement learning perspective
• Co-action provides rational basis for the evolutionary success of Pavlovian strategies
• Randomness and Arbitrary Coordination in the Reactive Ultimatum Game
• Imitation of Success Leads to Cost of Living Mediated Fairness in the Ultimatum Game
• Locally adaptive aggregation of organisms under death risk in rock-paper-scissors models
• Prejudice driven spite: A discontinuous phase transition in ultimatum game
• Monitoring biodiversity on highly reactive rock-paper-scissors models