Adaptive Punishment in Social Dilemmas

TL;DR

This paper presents a coevolutionary model where adaptive punishment influences cooperation dynamics across various social dilemma games, revealing complex behaviors that support sustained cooperation.

Contribution

It introduces a novel adaptive punishment framework that dynamically adjusts based on cooperation levels, reshaping game dynamics and providing new insights into social and ecological systems.

Findings

Adaptive punishment drives transitions among canonical games.

Rich dynamical behaviors such as coexistence and bistability are observed.

Adaptive punishment effectively sustains cooperation in social dilemmas.

Abstract

We introduce a coevolutionary framework in which punishment intensity dynamically adapts to the fraction of cooperators in the population. Unlike static models, adaptive punishment reshapes the effective payoff landscape, driving transitions among canonical games, including the Prisoner's Dilemma, Harmony, Stag Hunt, and Chicken games. Analytical results reveal rich dynamical behaviors such as coexistence, bistability, limit cycle and Hopf bifurcation. These findings highlight adaptive punishment as a robust mechanism for sustaining cooperation by the coevolutionary feedback and offer insights into institutional design, ecological interactions, and social governance.