Peace war game

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An iterated game played in academic groups and by computer simulation for years to study possible strategies of cooperation and aggression.^[1] As peace makers became richer over time it became clear that making war had greater costs than initially anticipated. The only strategy that acquired wealth more rapidly was a "Genghis Khan", a constant aggressor making war continually to grab everyone else's resources. This led to the development of the "provokable nice guy" strategy, a peace-maker until attacked. Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor. Such a strategy led to the development of the Hanseatic League in response to centuries of Viking depredation.

It is a variation, also called Hawk and Dove, of the iterated prisoner's dilemma in which the decisions (Cooperate, Defect) are replaced by (Peace, War). Strategies remain the same with reciprocal altruism, "Tit for Tat", or "provokable nice guy" as the best deterministic one. This strategy is simply to make peace on the first iteration of the game; after that, the player does what his opponent did on the previous move. A slightly better strategy is "Tit for Tat with forgiveness". When the opponent makes war, on the next move, the player sometimes makes peace anyway, with a small probability. This allows for occasional escape from wasting cycles of retribution. "Tit for Tat with forgiveness" is best when miscommunication is introduced, when one's move is incorrectly reported to the opponent. A typical payoff matrix for two players (A, B) of one iteration of this game is:

A.. B:	Peace	War
Peace	( 2, 2)	( 0, 3)
War	( 3, 0)	( 1, 1)

Here a player's resources have a value of 2, half of which must be spent to wage war. In this case, there exists a Nash equilibrium, a mutually best response for a single iteration, here (War, War), by definition heedless of consequences in later iterations. The concept is named for its originator, John Forbes Nash, about whom a book and popular film were produced. "Provokable nice guy's" optimality depends on iterations. How many are necessary is likely tied to the payoff matrix and probabilities of choosing.