Hawk versus Dove.

The general payoff matrix for the ‘hawk vs. dove’ game (a). The payoffs are for player 1 employing the strategies in the rows against player 2 employing the strategy in the columns. The symbol B represents the benefit of acquiring the resource, and the symbol C is the cost of combative interaction. In the upper left quadrant, an encounter of hawk-vs.-hawk, the payoff to player 1 is ½ the benefit minus the cost, and assumes an equal payoff for both hawks. A hawk encountering a dove obtains the entirety of the benefit, while the dove receives none, as shown in the upper right and lower left quadrant, respectively. If both players adopt the dove strategy, the mutual payoff is the highest, with both players evenly dividing the benefit without cost of conflict (bottom right quadrant). Shown in (b) are the values of the benefit (4) and the cost of combat (3) used for the simulation for a population of 1000 individuals (c). Although the highest mutual payoff occurs when both players are doves, the dove strategy is not an evolutionary stable strategy. The hawk strategy will invade and displace the dove strategy in a population even if the initial number of hawks is very low relative to the doves if the cost of the combat does not exceed the reward of the benefit. The likelihood of a dove encountering a hawk is initially very low, but as hawks increase in number, that likelihood increases. The population-level outcome at any encounter depends on the population makeup resulting from previous encounters.