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.

[edit] See also

• Bishop-Cannings theorem
• Hawk-dove game
• Dollar auction

[edit] 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.

v·d·e Topics in game theory
Definitions	Normal-form game · Extensive-form game · Cooperative game · Information set · Preference
Equilibrium concepts	Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance · Pareto efficiency
Strategies	Dominant strategies · Pure strategy · Mixed strategy · Tit for tat · Grim trigger · Collusion · Backward induction
Classes of games	Symmetric game · Perfect information · Dynamic game · Sequential game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Bargaining problem · Stochastic game · Nontransitive game · Global games
Games	Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock-paper-scissors · Pirate game · Dictator game · Public goods game · Blotto games  ·War of attrition  ·El Farol Bar problem  ·Cake cutting  ·Cournot game  ·Deadlock  ·Diner's dilemma  ·Guess 2/3 of the average  ·Kuhn poker  ·Nash bargaining game  ·Screening game  ·Signaling game  ·Trust game  ·Princess and monster game
Theorems	Minimax theorem · Purification theorem · Folk theorem · Revelation principle · Arrow's impossibility theorem

This page uses content from the English-language version of Wikipedia. The original article was at War of attrition (game). The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.