The Size of the Stag Determines the Level of Cooperation

Abstract

In the last 12,000 years, human societies have scaled up from small bands to large states of millions and even billions. Many modern societies and even groups of societies cooperate on large-scale projects with relatively low levels of conflict, but the scale and intensity of cooperation varies dramatically between societies. Here we attempt to formalize dynamics that may be driving this rapid increase in cooperation and the differences we see between societies. Our model extends an N-person stag hunt to include population growth dynamics, "stags" with different sized payoffs, and competition for these stags. An increasing number of cooperators is required to access larger stags. The payoff from these stags in turn increases carrying capacity, which increases competition for the stag. As population size increases, new cooperative thresholds are attainable, and as population size shrinks, previously attainable thresholds fall out of reach. Among other predictions, we show that when a new threshold is accessible to a population, the level of cooperation will increase to reach this threshold. However, when the next threshold is out of reach, cooperation decreases as individuals refrain from costly cooperation, preferring a smaller stag. This model offers a framework for understanding the rapid increase in the scale of human cooperation and decline of violence, differences between societies, and challenges to future cooperation.

The Importance of Credo in Multiagent Learning

“…We observe less overall incentive to cooperate as the cost 𝑐 increases (i.e., darker blue and has more area inside the triangles). This pattern resembles findings observed in human behavior, where the amount of cooperation depends on the size of the benefit compared to the cost [49]. Another observation is that defection is incentivized in the presence of any amount of self-focus (right axes), with the exception of one environment (𝑐 = 1 and 𝜈 = 0.5).…”

Paradox of diversity in the collective brain

“…Schnell et al [ 147 ] model the competition between cooperative groups at different scales, revealing the importance of resource availability to cooperation and competition. People cooperate to access resources that they would not be able to access by themselves or in a smaller group.…”

“…Clustered diversity may be optimal for avoiding homogeneity through conformity; dividing a problem to solve it [ 14 ]. By contrast, when the perception or reality of competition is zero-sum or resources are perceived to be limited, people cooperate at the scale needed to best access those limited resources, creating conflict and destructive competition [ 147 ]. This insight has policy implications.…”

Dying to cooperate: the role of environmental harshness in human collaboration

“…Previous modelling work has revealed complex evolutionary dynamics at work when the 2-person Stag–Hunt is generalised to a N-person game, specifically, scenarios of defector dominance, pure coordination, or coexistence may arise simultaneously if the population is assumed to be infinite, but when populations are finite and the population is the same size as the group, the evolutionary dynamics are profoundly affected, inverting the direction of natural selection ( Pacheco et al 2009 ). Building on this work Schnell and colleagues (under review ) showed that the size of the Stag reward further affected the level of cooperation in a N-person game such that when a new cooperation threshold is accessible to a population, the level of cooperation increases to reach this threshold. However, when the next threshold is out of reach, cooperation decreases as individuals refrain from costly cooperation.…”