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Area of Science:

  • Evolutionary game theory
  • Social decision-making
  • Network science

Background:

  • Fairness is crucial in collective decision-making across various domains.
  • The two-player ultimatum game is well-studied, but multiplayer dynamics are less explored.
  • Hypergraphs offer a novel framework for modeling complex group interactions.

Purpose of the Study:

  • To investigate the evolutionary dynamics of collective resource allocation in multiplayer ultimatum games.
  • To explore the impact of group structure and empathy on fairness.
  • To utilize hypergraphs for modeling group interactions.

Main Methods:

  • Adaptive dynamics modeling.
  • Analysis of uniform random hypergraphs and heterogeneous hypergraphs.
  • Simulations of multiplayer ultimatum games within hypergraph structures.

Main Results:

  • In uniform random hypergraphs, strategies evolve towards rational, unfair outcomes.
  • Empathy stabilizes the population with fair allocation schemes.
  • Increasing hypergraph order promotes fairness; heterogeneous networks amplify this effect.

Conclusions:

  • Empathy is a key factor in achieving fairness in multiplayer resource allocation.
  • Group structure, particularly heterogeneity, significantly influences the evolution of fairness.
  • Hypergraph models provide valuable insights into complex social dynamics.