Evolving righteousness in a corrupt world

Abstract

Punishment offers a powerful mechanism for the maintenance of cooperation in human and animal societies, but the maintenance of costly punishment itself remains problematic. Game theory has shown that corruption, where punishers can defect without being punished themselves, may sustain cooperation. However, in many human societies and some insect ones, high levels of cooperation coexist with low levels of corruption, and such societies show greater wellbeing than societies with high corruption. Here we show that small payments from cooperators to punishers can destabilize corrupt societies and lead to the spread of punishment without corruption (righteousness). Righteousness can prevail even in the face of persistent power inequalities. The resultant righteous societies are highly stable and have higher wellbeing than corrupt ones. This result may help to explain the persistence of costly punishing behavior, and indicates that corruption is a sub-optimal tool for maintaining cooperation in human societies.

Figure 1. Conditions for stability of the four corners of the simplex.

If the condition is satisfied, then the direction pointed by the arrow behaves as a local attractor. is always stable, denoted by the filled circle, while is always unstable, denoted by the open circle. While many equilibria at the edges of the simplex may be stable in the reduced games, we reserve filled circles to indicate globally stable equilibria (i.e. equilibria that are stable in the full game with the four strategies.).

Figure 2. Stability of the three main equilibria on the system as a function of parameters and .

The white area corresponds to the cases in which defection is the only globally stable equilibrium. Notice that there is an area where righteousness and corruption intersect, in this region, all three main equilibria are stable. Depicted are representative cases for each of the four areas. While the position of the main equilibria might change and existence of other (unstable) internal equilibria in some edges might exist for specific parameter combinations, the qualitative dynamics are captured by these depicted cases. For simplicity, internal equilibria in the faces of the simplex are not drawn. All internal equilibria in the faces are unstable (see Appendix).

Figure 3. Dynamics of the system in the vicinity of (top), (middle) and (bottom).

The horizontal axis corresponds to the value of . The vertical axis corresponds to the value of . Isoclines represent the proportion of runs converging to corruption (red) and righteousness (blue). All runs that do not converge to either corruption or righteousness end up in defection (white).