Abstract
Conflict occurs throughout the animal world. Such conflicts are often modelled by evolutionary games, where individual animals make a single decision each within the game. These decisions can be sequential, in either order, or simultaneous, and the outcome of the game can depend strongly upon which case is assumed to occur. Real conflicts are generally more complex, however. A fight over a territory, for instance, can involve a succession of different stages and, therefore, choices to be made by the protagonists. In this paper we thus introduce a method of modelling a more complex class of interactions, where each individual can make a sequence of decisions. We show that despite the inherent complexity, under certain assumptions, the resulting game often leads to the case where both animals fight to the fullest extent or where one concedes immediately, thus mirroring the outcomes of simpler single decision games. However, for other cases we see that the outcome is not so simple, and intermediate level contests can occur. This happens principally in cases where the duration of contests is uncertain, and partially governed by external factors which can bring the contest to a sudden end, such as the weather or the appearance of a predator. We thus develop a theory grounded in simple evolutionary models, but extending them in various important ways.
Highlights
Conflict is ubiquitous throughout the animal world, taking many different forms
In this paper we introduce a method of analysing an animal conflict over an indivisible valuable resource, as in the Hawk–Dove game, involving a potentially long sequence of decisions
In this paper we have considered an extension to the modelling of evolutionary contests where contests follow a sequence of decisions, rather that a single instantaneous decision made by each protagonist
Summary
Conflict is ubiquitous throughout the animal world, taking many different forms (see e.g. [22]). Real animal conflicts are often more complex than just involving a single decision by each combatant, and animals may make a sequence of decisions affected by the decisions made by themselves and their opponent, and the outcomes of those decisions, earlier in the contest This is the case in the example of stags competing for a territory considered above. In this paper we introduce a method of analysing an animal conflict over an indivisible valuable resource, as in the Hawk–Dove game, involving a potentially long sequence of decisions. These are binary in form, where individuals choose to persist in the contest (at some additional cost) or concede, concession allowing the opponent to take the resource. We analyse our game under a number of scenarios, and connect it to the dollar auction, a game from economics with some similar features
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