Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner’s dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well.

💡 Research Summary

The paper presents a unified game‑theoretical framework that captures how cooperation, social norms, and revolutionary shifts emerge when multiple populations with differing preferences and unequal power interact. Building on the classic replicator dynamics, the authors extend the model to a multi‑population setting: each group (k) possesses its own payoff matrix (A^{(k)}) for intra‑group encounters and a cross‑payoff matrix (B^{(ij)}) that governs how strategies of group (i) affect the payoffs of group (j). Power asymmetry—whether due to population size, resource endowments, or social capital—is introduced through weight factors (w^{(k)}) that scale each group’s contribution to the average fitness. The resulting system of coupled replicator equations reads
\