Strategy dependent mortality in life history games

In games such as the war of attrition and parental care games the length of time spent in a realisation of the game is dependent on the strategy used. Hence, there is a trade off between the mean reward obtained per realisation of the game and the mean number of games played per unit time. Such a game should not be modelled using the standard two-player form, but should be defined as a game against the field (a large population game). In parental care games, such an approach also enables us to define a more consistent model, which takes into account, for example, the obvious fact that each individual has one parent of both sexes and that the ease with which a male deserter can find a new partner depends on the strategy profile used in the population. If the mortality rate is independent of strategy, then each individual should simply maximise the rate of producing offspring. However, if mortality rates depend on strategy, then at equilibrium an individual should maximise the number of offspring produced during their lifetime. This paper considers pure equilibria in a parental care game, in which the mortality rate depends on an individual's strategy.