Spatial Ultimatum Games, collaborations and the evolution of fairness

Abstract

It is often the case that individuals in a social group can perform certain tasks (such as hunting, for example) more e¤ciently if they collaborate with other individuals than if they act alone. In such situations one is necessarily faced with the problem of how the resource obtained as the result of such a collaboration should be divided among the collaborating individuals. If one of the individuals in the collaboration is in a position (through its dominance rank, for example) to impose a particular division of the resource on the other members of the collaboration then we show that an evolutionary dilemma arises which prevents such collaborations being evolutionarily stable. This dilemma, which is closely related to the well-known Ultimatum Game, results from the fact that in such situations natural selection favours individuals who, if dominant, o¡er smaller and smaller shares of the resource to the others and, if subdominant, will accept lower and lower o¡ers. We also show, however, that this dilemma is naturally resolved in a spatially structured population with selection favouring the evolution of a fair division of the resource and consequently ensuring the evolutionary stability of collaborations of this type.

The spatial Ultimatum game revisited

“…They concluded that large offer levels, around a 34% of the amount to share, emerged and were stable in the ring and the lattice, while evolution converged to the rational solution on a well mixed population. A similar result was later shown for a generalization of the Ultimatum game to describe collaborations by Killingback and Studer (2001). More recently, the effect of complex (non spatial) networks of interactions was addressed by Kuperman and Risau Gusman (2008), Eguíluz andTessone (2009), andSinatra et al (2009), finding again that large offers appeared in the population.…”

Strong reciprocity, social structure, and the evolution of fair allocations in a simulated ultimatum game

“…The authors did briefly discuss implications of a von Neumann neighborhood but the focus of the work was on the effects of varying the population size and the radius of an agent's neighborhood. Another closely related model by Killingback and Studer (2001) produced results not in agreement with those of the current simulation. The authors simulated a The number of generations a single simulation runs 30,000…”

“…It has been well demonstrated that spatial explicitness in computer simulations can lead to outcomes significantly different than when populations are homogenous or well-mixed (Nowak and May 1992;Nowak et al 1994;Killingback and Doebeli 1996;Killingback and Studer 2001). However, there are a number of ways in which a population can be spatially explicit and it is important for researchers to show how different social structures can lead to different results.…”

The Evolution of Fair Offers with Low Rejection Thresholds in the Ultimatum Game

“…A recent review [8] of 36 UG models classified them into six categories: alternating rolebased models [9], reputation-based models [10][11][12], noise-based models [13,14], spite-based models [15][16][17] spatial-population-structure-based models [18][19][20], and empathy-based models [21]. All of these models provide theoretical explanations for large departures from SPNE that are at or close to an even-split Nash equilibrium fairness strategy (i.e., p = q = 0.5).…”