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Direct reciprocity and model-predictive rationality explain network reciprocity over social ties.

Fabio Dercole1, Fabio Della Rossa2, Carlo Piccardi2

  • 1Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy. fabio.dercole@polimi.it.

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Cooperation evolves in networks when agents use rational prediction and reciprocity, not just imitation. This requires the benefit of cooperation to outweigh network connectivity costs for stable, evolving cooperation.

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Area of Science:

  • Evolutionary Game Theory
  • Network Science
  • Behavioral Economics

Background:

  • Network reciprocity, where cooperation evolves through clustered interactions, is a key concept in evolutionary game theory.
  • Traditional models assume imitation for strategy updates, but human experiments show mood-based reciprocal cooperation and limited imitation.
  • This creates a controversy regarding the mechanisms driving cooperation in networked systems.

Purpose of the Study:

  • To resolve the controversy surrounding the evolution of cooperation in networks by proposing a new model.
  • To investigate the role of rational strategy updates and reciprocal cooperation in networked prisoner's dilemma games.
  • To identify the conditions necessary and sufficient for the stabilization and fixation of cooperation.

Main Methods:

  • Developed a model of the networked prisoner's dilemma incorporating rational, predictive strategy updates.
  • Contrasted reciprocal cooperation with unconditional defection within the network structure.
  • Introduced bounded rationality through a predictive rule for strategy updates.

Main Results:

  • Cooperation is stabilized and fixed when agents employ both reciprocity and a multi-step predictive horizon.
  • These factors are sufficient for cooperation's fixation if the benefit-to-cost ratio exceeds network connectivity.
  • The study re-establishes network reciprocity but through a novel evolutionary mechanism based on rational prediction.

Conclusions:

  • Rational prediction and reciprocal cooperation are crucial for the evolution of cooperation in networks.
  • The findings support a new evolutionary mechanism for network reciprocity, moving beyond simple imitation.
  • The benefit-to-cost ratio and network structure critically influence the success of cooperation.