Game Theory: Evolutionary Stable StrategiesConsider the hawk-dove game. In this game, hawks, in interacting with other birds, use a strategy of aggression. Hawks challenge the territory of birds they encounter; doves may make an initial showing of defiance, but back down from actual fighing and run away. In this case, the hawk wins the territory, food, mate, or whatever the reward is. However, if the hawk meets another bird using the hawk strategy, then a fight ensues. The result of that contest is unclear beforehand - perhaps the hawk will be killed or mortally wounded, perhaps it will win. Thus, the expectancy is considerably less than the reward gained after challenging a "dove," a bird that runs away. In our game, hawk versus hawk often entails a significant expected loss, even worse than the dove's loss of some particular territory. Let's assume that this is the case.Suppose we have a lot of birds playing this game. An evolutionary stable strategy (ESS) for a game is a strategy such that, if any player deviates from the strategy, he is worse off (or at least no better off). Looking at our hawk-dove game using these "pure" strategies, let's examine two extreme scenerios. Suppose everyone uses the hawk strategy. Then on every encounter, there is an expected loss, since every encounter results in a fight. Now suppose one player decides to switch to the dove strategy. He is suddenly better off - he has a slight loss in territory, but he avoids the greater loss of possibly getting maimed or killed. This proves that everybody a hawk is unstable; hawkishness is not an ESS. Now suppose everybody uses the dove strategy. When challenged, all are perfect "Gandhis" and avoid violent confrontation. Now what happens if one dove becomes a hawk? He literally eats the others for lunch. Every encounter wins territory, food, or mates, and being the only hawk, there is no risk of negative outcomes. The single hawk tyrannizes the other birds. Thus, an all-dove world is unstable; dovishness is not an ESS.Now let's introduce a new strategy - the rattlesnake strategy. The rattlesnake does not attack, but it will certainly defend and strike back if attacked. Is this an ESS? Upon examination, we see that it is. Suppose all players use the rattlesnake strategy. Then, amazingly enough, no one attacks anyone. To an observer, it may look like a world of doves, as far as behavior goes. |
| Against Authority | page 34 |
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