Evolutionary mechanisms that promote cooperation may not promote social welfare

TL;DR

The study investigates whether mechanisms that promote cooperation align with maximizing social welfare in a well-mixed population playing the one-shot Prisoner\'s Dilemma. Using stochastic evolutionary dynamics with mutation and imitation (Fermi update) and a Markov-chain stationary distribution, it quantifies strategy frequencies and net social welfare under peer and institutional incentive schemes. The key finding is a frequent misalignment: peer punishment often raises cooperation but lowers welfare, whereas peer reward improves welfare more reliably; institutional rewards extend welfare benefits across a broader parameter range, with peak welfare occurring at intermediate incentive levels rather than at maximum. The work argues for prioritizing social welfare in the design of incentives for social and collective goods and highlights implications for policy and AI-enabled collective action, suggesting extensions to other mechanisms and networked settings.

Abstract

Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual payoffs, it is however possible that aiming for highest levels of cooperation might be detrimental for social welfare -- the later broadly defined as the total population payoff, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparatively analysing the social welfare and cooperation levels obtained from stochastic evolutionary models of two well-established mechanisms of prosocial behaviour, namely, peer and institutional incentives, we demonstrate exactly that. We show that the objectives of maximising cooperation levels and the objectives of maximising social welfare are often misaligned. We argue for the need of adopting social welfare as the main optimisation objective when designing and implementing evolutionary mechanisms for social and collective goods.

Figures (8)

• Figure 1: Impact of peer reward vs peer punishment for the long-term level of cooperation ($f_C$, see Equation \ref{['eq:frequency']}) and population social welfare ($SW$, see Equation \ref{['eq:SociaWelfare']}), for varying the efficiency of incentive $\delta/\epsilon$, for different values of the intensities of selection $\beta$. We observe that punishment is better than reward for promoting cooperation in most cases, especially for weaker selection and when the impact to cost ratio of incentive is sufficiently high. However, reward leads to higher social welfare than punishment in most cases. Parameters: Population size, $N = 50$, mutation rate $\mu = 0.01$, cost of peer incentive $\epsilon = 1$, Prisoner's Dilemma payoff matrix $R = 1, S = -1, T = 2, P = 0$.
• Figure 2: Impact of institutional reward vs institutional punishment for the long-term level of cooperation and population social welfare. We observe that although both types of incentives lead to the same level of cooperation given the same incentive impact on the incentive recipient $\delta$ (assuming their impact to cost ratios are the same, i.e. $a = b$, see panel d), reward leads to positive social welfare for a much wider range of parameters (compare red areas in panels a and b). Parameters: Population size, $N = 50$, mutation rate $\mu = 0.001$, intensity of selection $\beta = 0.1$, Prisoner's Dilemma with $R = 1, S = -1, T = 2, P = 0$.
• Figure S1: Impact of peer reward vs peer punishment for the long-term level of cooperation and population social welfare, for varying the efficiency of incentive $\delta/\epsilon$, for different values of the intensities of selection $\beta$ and $\mu$. Other parameters as in Figure \ref{['fig:peerincentives_vary_impact']} in the main text.
• Figure S2: Impact of peer reward vs peer punishment for the long-term level of cooperation and population social welfare, for varying the efficiency of incentive $\delta/\epsilon$, for different values of the intensities of selection $\beta$ and payoff scalings of the Prisoner's Dilemma (fixing $T - R =P - S = 1$, while varying $R - P$). Other parameters as in Figure \ref{['fig:peerincentives_vary_impact']} in the main text.
• Figure S3: Impact of peer reward vs peer punishment for the long-term level of cooperation and population social welfare, for the impact to cost ratio up to 100 under strong selection ($\beta = 1.0$). Other parameters as in Figure \ref{['fig:peerincentives_vary_impact']} in the main text.