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asymmetric games


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A type of evolutionarily stable strategy, usually analysed in terms of game theory. In a symmetric game, such as the hawk–dove game, the two contestants start in identical situations, and have the same choice of strategies and the same prospective payoffs. There may be a difference in strength or size between them, but if this is not known to the contestants, it cannot affect their choice of strategies.

In an asymmetric game there is usually a perceived difference between the contestants which affects their choice of strategies. The contestants may differ in sex, size, age, or a resource such as territory. For example, an individual could behave like a hawk when it is the owner of a territory and like a dove when it is an intruder into the territory of another. That is, when holding a territory, it fights to kill or injure the opponent, even though there is a risk of injury to itself. When an intruder, it threatens its opponent but avoids serious fighting. This is called a bourgeois strategy.

We now assign fitness–increment payoffs to the consequences of encounters involving hawks and doves. Let the winner of the contest score +50 and the loser, zero. Let the cost of wasting time in a display be −10 and the cost of injury be −100. When a bourgeois meets either hawk or dove, we assume it is an owner half the time and therefore plays hawk, and an intruder half the time and therefore plays dove. Its payoffs are therefore the average of hawk and dove. When bourgeois meets bourgeois, on half the occasions it is an owner and wins, while on half the occasions it is an intruder and retreats. There is never any cost of display or injury. When two bourgeois meet the average payoff is +25, more than could be gained by invading doves or hawks, who would get +7.5 and +12.5 respectively.The bourgeois strategy is an evolutionarily stable strategy. Asymmetry of ownership is used as a convention to settle contests even when ownership alters neither the payoffs nor success in fighting. The same is true for any other asymmetry, provided it is unambiguously perceived by both contestants.

Opponent

Attacker

Hawk

Dove

Bourgeois

Hawk

½ (50) + ½ (−100) = −25

+ 50

+12.5

Dove

Zero

½ (50 − 10) + (−10) = +15

+7.5

Bourgeois

−12.5

+32.5

+25

The formulae indicate the average payoffs to the attacker.

Subjects: Zoology and Animal Sciences.


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