Adaptive dynamics of eco-evolutionary repeated games: Effect of reward and punishment

TL;DR

This paper develops an eco-evolutionary model of repeated games with reward and punishment, analyzing how incentives influence resource conservation and the emergence of stable oscillations in strategies and resource levels.

Contribution

It introduces a coupled eco-evolutionary framework with adaptive dynamics for repeated games, exploring the effects of incentives on preventing resource depletion.

Findings

Incentives can effectively prevent the Tragedy of the Commons.

Stable oscillations in strategies and resources can emerge via Hopf bifurcation.

Institutional rewards and punishments influence long-term resource sustainability.

Abstract

Long-term evolutionary processes can strongly influence common-pool resource conservation by generating new traits or behaviours that modify the feedback between population strategies and the resource state. Here we develop an eco-evolutionary framework in which individuals repeatedly interact with the same opponent and follow direct reciprocity through reactive strategies. The strategic dynamics is coupled to a renewable common resource and analyzed using adaptive dynamics. After our exhaustive non-linear dynamical analysis of $2\times2$ strategic games, we focus on comparative and combined usefulness of institutional incentives in the form of rewards and punishments in preventing the Tragedy of the Commons even when defection dominates in the replete resource state. We also report possibility of robust stable oscillations -- emerging via Hopf bifurcation -- in resource state and population strategies.