Spatial Evolution of Social Norms in a Common-Pool Resource Game

Abstract

Abstract. We study the conditions for the emergence of cooperation in a spatial common-pool resource (CPR) game. We consider three types of agents: cooperators, defectors and enforcers. The role of enforcers is to punish defectors for overharvesting the resource. Agents are located on a circle and they only observe the actions of their two nearest neighbors. Their payoffs are determined by both local and global interactions and they modify their actions by imitating the strategy in their neighborhood with the highest average payoffs on average. Using theoretical and numerical analysis, we find a large diversity of equilibria to be the outcome of the game. In particular, we find conditions for the occurrence of equilibria in which the three strategies coexist. We also derive the stability of these equilibria. Finally, we show that introducing resource dynamics in the system favors the occurrence of cooperative equilibria.

Local and Global Interactions in an Evolutionary Resource Game

“…For most parts of the present paper, we assume that agents are more 'naive' and simply imitate their most successful neighbor. We find that changing the learning rule does not qualitatively affect the results found in Noailly et al (2007). We also find the emergence of equilibria in which cooperators and enforcers coexist in our settings.…”

“…Eshel et al (1998) instead impose a learning rule in which the on average best performing strategy in the observed neighbourhood is imitated. This rule is examined with a spatial evolutionary analysis in another paper (Noailly et al 2007). When the best strategy in the neighborhood is identical to the player's current strategy, the player sticks to his current strategy.…”

“…5 In this case, we find that on average 56% (out of 495000) of the simulation runs converge to a D-equilibrium, 29% to a DE-equilibrium, 14% to a CDE-equilibrium and 0% to CE-and E-equilbria. In order to compare our results with the ones obtained by Noailly et al (2007), we perform additional simulations on the torus using their 'sophisticated' learning rule. This rule states that agents imitate the strategy that is the most successful on average.…”

“…The problem of local interaction in a common-pool resource game is also studied by Noailly et al (2007). But its setup differs substantially from the present one, in two respects.…”

“…Most real world interactions, like in agriculture or in fisheries, occur in two-dimensional space. Second, Noailly et al (2007) employ a different learning rule. In their setting, agents imitate the strategy yielding the highest average payoffs.…”