War of attrition (game)
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In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. The model was originally formulated by John Maynard Smith (1974). Strategically, the game is an auction, in which the prize goes to the player with the highest bid, and both players pay the loser's low bid.
The evolutionarily stable strategy when playing this game is a probability density of random persistence times which cannot be predicted by the opponent in any particular contest. This result has led to the prediction that threat displays ought not to evolve, and to the conclusion (e.g. in the The Illuminatus! Trilogy) that optimal military strategy is to behave in a completely unpredictable (ie insane) manner. Neither of these conclusions are truly reasonable applications of the model to realistic conditions.
See also
References
- Bishop, D.T. & Cannings, C. (1978) A generalized war of attrition. Journal of Theoretical Biology 70: 85-124.
- Bishop, D.T., Cannings, C. & Maynard Smith, J. (1978) The war of attrition with random rewards. Journal of Theoretical Biology 74:377-389.
- Maynard Smith, J. (1974) Theory of games and the evolution of animal contests. Journal of Theoretical Biology 47: 209-221.
- Maynard Smith, J. & Parker, G. A. (1976). The logic of asymmetric contests. Animal Behaviour. 24:159-175.
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