Peace war game

Genghis Khan's empire over time

Peace war game is an iterated game originally 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 gain resources. This led to the development of the "provokable nice guy" strategy, a peace-maker until attacked.^[2] Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor.^[2] The Hanseatic League for trade and mutual defense appears to have originated from just such concerns about seaborne raiders.

The peace war game is a variation 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 an escape from wasting cycles of retribution, a motivation similar to the Rule of Ko in the game of Go. "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. "Provokable nice guy's" optimality depends on iterations. How many are necessary is likely tied to the payoff matrix and probabilities of choosing.^[3] A subgame perfect version of this strategy is "Contrite Tit-for-Tat" which is to make peace unless one is in "good standing" and one's opponent is not. Good ("standing" assumed) means to make peace with good opponents, make peace when bad, or make war when good and opponent is not.^[4]

He who is skilled in war subdues the enemy without fighting.
—Sun Tzu, The Art of War, III.2

Notes

↑ Shy, O., 1996, Industrial Organization: Theory and Applications, Cambridge, Mass.: The MIT Press.
↑ ^2.0 ^2.1 N.R. Miller, "Nice Strategies Finish First: A Review of The Evolution of Cooperation", Politics and the Life Sciences, Association for Politics and the Life Sciences, 1985.
↑ Industrial Organization - economics lecture in which the Peace War Game is an example.
↑ Herbert Gintis, Game Theory Evolving: A Problem-centered Introduction to Modeling Strategic Behavior, Princeton University Press, 2000, p. 133

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Peace war game. Read more

[1] Shy, O., 1996, Industrial Organization: Theory and Applications, Cambridge, Mass.: The MIT Press.

[Miller-2] 2.0 ^2.1 N.R. Miller, "Nice Strategies Finish First: A Review of The Evolution of Cooperation", Politics and the Life Sciences, Association for Politics and the Life Sciences, 1985.

[3] Industrial Organization - economics lecture in which the Peace War Game is an example.

[4] Herbert Gintis, Game Theory Evolving: A Problem-centered Introduction to Modeling Strategic Behavior, Princeton University Press, 2000, p. 133

[1]

[2]

[3]

[4]

v t e Topics in game theory
Definitions	Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game
Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium
Strategies	Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy
Classes of games	Symmetric game Perfect information Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global game Strictly determined game Potential game
Games	Go Chess Infinite chess Checkers Tic-tac-toe Prisoner's dilemma Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and Monster game Rendezvous problem
Theorems	Arrow's impossibility theorem Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Purification theorem Revelation principle Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith Antoine Augustin Cournot John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition First-move advantage in chess Game mechanics Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions

Peace war game

Topic: Philosophy

See also

Notes