Bimatrix games that include interaction times alter the evolutionary outcome: The Owner–Intruder game

•A new approach to the theory of two-player bimatrix evolutionary games where pairs are formed by the mass action principle is developed and compared to models with instantaneous pair formation.•This theory explicitly considers the duration of interactions between the two players and their status as singles between interactions.•When applied to the bimatrix Hawk-Dove game (called the Owner-Intruder game), this theory shows that differences in interaction times lead to new interior and boundary Nash equilibria.•Existence and stability of these Nash equilibria depend on whether pairing is instantaneous or not. Classic bimatrix games, that are based on pair-wise interactions between two opponents in two different roles, do not consider the effect that interaction duration has on payoffs. However, interactions between different strategies often take different amounts of time. In this article, we further develop a new approach to an old idea that opportunity costs lost while engaged in an interaction affect individual fitness. We consider two scenarios: (i) individuals pair instantaneously so that there are no searchers, and (ii) searching for a partner takes positive time and populations consist of a mixture of singles and pairs. We describe pair dynamics and calculate fitnesses of each strategy for a two-strategy bimatrix game that includes interaction times. Assuming that distribution of pairs (and singles) evolves on a faster time scale than evolutionary dynamics described by the replicator equation, we analyze the Nash equilibria (NE) of the time-constrained game. This general approach is then applied to the Owner–Intruder bimatrix game where the two strategies are Hawk and Dove in both roles. While the classic Owner–Intruder game has at most one interior NE and it is unstable with respect to replicator dynamics, differences in pair duration change this prediction in that up to four interior NE may exist with their stability depending on whether pairing is instantaneous or not. The classic game has either one (all Hawk) or two ((Hawk,Dove) and (Dove,Hawk)) stable boundary NE. When interaction times are included, other combinations of stable boundary NE are possible. For example, (Dove,Dove), (Dove,Hawk), or (Hawk,Dove) can be the unique (stable) NE if interaction time between two Doves is short compared to some other interactions involving Doves.