The evolution of cooperation by social exclusion

The exclusion of freeriders from common privileges or public acceptance is widely found in the real world. Current models on the evolution of cooperation with incentives mostly assume peer sanctioning, whereby a punisher imposes penalties on freeriders at a cost to itself. It is well known that such costly punishment has two substantial difficulties. First, a rare punishing cooperator barely subverts the asocial society of freeriders, and second, natural selection often eliminates punishing cooperators in the presence of non-punishing cooperators (namely, “second-order” freeriders). We present a game-theoretical model of social exclusion in which a punishing cooperator can exclude freeriders from benefit sharing. We show that such social exclusion can overcome the above-mentioned difficulties even if it is costly and stochastic. The results do not require a genetic relationship, repeated interaction, reputation, or group selection. Instead, only a limited number of freeriders are required to prevent the second-order freeriders from eroding the social immune system.

💡 Research Summary

The paper tackles a central puzzle in the evolution of cooperation: how can a population of cooperators overcome the invasion of selfish “free‑riders” when the only available sanction is costly peer punishment? Classical models of peer sanctioning suffer from two well‑known drawbacks. First, when punishers are rare they cannot shift the population away from a non‑cooperative equilibrium; the selective advantage of a punisher is too small to spread. Second, punishers are vulnerable to “second‑order free‑riders” – cooperators who enjoy the benefits of a cooperative society but do not incur the cost of punishing. In the presence of such second‑order free‑riders, punishing cooperators are typically eliminated by natural selection.

To address these issues, the authors introduce a novel strategy called social exclusion. Instead of imposing a direct penalty, an excluding cooperator (E) attempts to prevent free‑riders (D) from sharing the public good. The exclusion is stochastic: with probability p the excluder succeeds, incurring a cost c and gaining an additional benefit b (e.g., a larger share of the remaining resource). If exclusion fails, the excluder behaves like a regular cooperator. The population also contains non‑excluding cooperators (C) who share the public good without paying the exclusion cost, and pure free‑riders (D) who receive the benefit only when they are not excluded.

The authors formalize the interaction as an n-player public‑goods game and derive expected payoffs for each strategy as functions of the frequencies of E, C, and D in the group. Using replicator dynamics, they identify fixed points and assess evolutionary stability. The analysis yields several key results:

1. Threshold for Exclusion Success – When the exclusion cost c is modest and the success probability p exceeds a critical value, the expected payoff of D drops below that of both C and E. Consequently, the frequency of free‑riders declines, and the population can move away from the all‑defector equilibrium even when excluders are initially rare.

2. Resistance to Second‑Order Free‑Riders – The presence of C individuals does not automatically undermine the exclusion mechanism. As long as the proportion of D remains below a certain bound, the exclusion advantage of E outweighs the cost advantage of C. In this regime, E can coexist with C in a stable polymorphic equilibrium, or even dominate the population, thereby preventing the erosion of cooperation by second‑order free‑riders.

3. Minimal Assumptions – The model does not rely on kin selection, repeated interactions, reputation, or group selection. The only structural requirement is that the number of free‑riders in any given interaction is limited; this “social immune system” condition is sufficient for exclusion to be an evolutionarily viable sanction.

4. Robustness to Stochasticity – Simulations confirm that the qualitative outcomes persist when exclusion is probabilistic rather than deterministic. Even low success probabilities can sustain cooperation if the exclusion cost is sufficiently low, highlighting the flexibility of the mechanism.

The authors discuss the biological and sociological relevance of social exclusion. Real‑world analogues include ostracism in primate troops, club membership revocation, or online community bans. These practices share the essential feature of denying access to shared benefits rather than inflicting a direct penalty. The theoretical results suggest that such exclusion can be an efficient, low‑cost way to maintain cooperation without the need for elaborate monitoring or reputation systems.

In the concluding section, the paper proposes several avenues for future work. Extending the model to structured populations (networks, spatial lattices) could reveal how local clustering influences the spread of excluders. Incorporating multiple public goods, variable group sizes, or cultural transmission would increase realism. Moreover, empirical tests—e.g., experimental economics studies that manipulate exclusion costs and success rates—could validate the predicted thresholds.

Overall, the study provides a compelling alternative to costly punishment. By showing that a simple exclusion rule can overcome both the rarity problem and the second‑order free‑rider problem, it expands our understanding of how cooperative norms can evolve and persist in societies where direct retaliation is too expensive or impractical.