A Game-Theoretical Winner and Loser Model of Dominance Hierarchy Formation

Abstract

Many animals spend large parts of their lives in groups. Within such groups, they need to find efficient ways of dividing available resources between them. This is often achieved by means of a dominance hierarchy, which in its most extreme linear form allocates a strict priority order to the individuals. Once a hierarchy is formed, it is often stable over long periods, but the formation of hierarchies among individuals with little or no knowledge of each other can involve aggressive contests. The outcome of such contests can have significant effects on later contests, with previous winners more likely to win (winner effects) and previous losers more likely to lose (loser effects). This scenario has been modelled by a number of authors, in particular by Dugatkin. In his model, individuals engage in aggressive contests if the assessment of their fighting ability relative to their opponent is above a threshold . Here we present a model where each individual can choose its own value . This enables us to address questions such as how aggressive should individuals be in order to take up one of the first places in the hierarchy? We find that a unique strategy evolves, as opposed to a mixture of strategies. Thus, in any scenario there exists a unique best level of aggression, and individuals should not switch between strategies. We find that for optimal strategy choice, the hierarchy forms quickly, after which there are no mutually aggressive contests.

The Evolution of Social Dominance through Reinforcement Learning

“…Because of the modeling complexities introduced by aggressive interactions between individuals that may differ in their fighting ability and in previous experience, both of which are likely to be important for social dominance interactions, it has proven difficult to achieve evolutionary analyses of mechanistic models. For instance, for the situation analyzed by Kura et al (2016), which was inspired by the model of Dugatkin (1997), there is variation in an individual's perception of its fighting ability, arising from experiences of wins and losses, but there is no variation between individuals in actual fighting ability, and this limits the realism of the model. Nevertheless, winner and loser effects have been found in game theory models by looking at simplified situations for groups of three individuals (Mesterton-Gibbons 1999; van Doorn et al 2003avan Doorn et al , 2003b.…”

Dominance, sharing, and assessment in an iterated Hawk–Dove game

“…Building on the foundational work of Trivers (1971), Maynard Smith and Price (1973), and Maynard Smith (1979), a wide variety of game-theoretic models have been developed to describe the ways in which animals resolve conflicts (Sandholm, 2012;Weibull, 1995). These include models with conditional strategies in which animals assess individual differences (e.g., in strength or fighting ability) with displays or signals before deciding whether or when to attack (Parker, 1974;Parker and Rubenstein, 1981); sequential assessment with escalation (Enquist et al, 1990;Enquist and Leimar, 1983;Payne and Pagel, 1996); iterated games, in which animals repeatedly encounter the same individuals (Axelrod and Hamilton, 1981); models based on simple learning rules (Fawcett and Johnstone, 2010;Grewal et al, 2013); and models that include winner and loser effects (where winners are likely to keep winning and losers are likely to keep losing) (Goessmann et al, 2000;Hsu et al, 2005;Kura et al, 2015Kura et al, , 2016Mesterton-Gibbons and Sherratt, 2016).…”

Chris Cannings: A Life in Games

“…In Dugatkin [48] individuals could assess the relative fighting ability of their opponent and concede if it was above a certain threshold. Kura et al [90] considered an explicitly game-theoretic model where individuals could select their concession threshold strategically. Here a pure strategy solution was found, and this corresponded with fast establishment of a linear hierarchy.…”