The Hawk-Dove Game is a fundamental model in evolutionary game theory. It examines how individuals choose between aggressive and peaceful strategies when competing for limited resources. Hawks represent aggressive players who always fight, while Doves represent peaceful players who prefer to avoid conflict.
The game is represented by a payoff matrix. When both players choose Hawk, they fight and each gets V minus C over 2, where V is the resource value and C is the fighting cost. When a Hawk meets a Dove, the Hawk gets the full resource V while the Dove gets nothing. When both choose Dove, they share the resource peacefully, each getting V over 2.
The Nash equilibrium analysis reveals different outcomes based on parameter values. When the resource value V exceeds the fighting cost C, pure strategies emerge as equilibria. However, when V is less than C, fighting becomes too costly, leading to a mixed strategy equilibrium where players randomize between Hawk and Dove strategies with equal probability.
The Evolutionary Stable Strategy represents the long-term equilibrium in a population. When the proportion of Hawks equals V over C, the population reaches stability. If there are too many Hawks, Doves have an advantage and increase. If there are too many Doves, Hawks can invade successfully. This creates a dynamic balance that maintains the ESS ratio.