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.

EB00000002870K

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• Evolutionary Games with Sequential Decisions and Dollar Auctions