Genghis Khan's empire over time

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. Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor. Such actions led in essence to the development of the Hanseatic League for trade and mutual defense following centuries of Viking depredation.^[2] Image File history File links Mongol_Empire_map. ... Image File history File links Mongol_Empire_map. ... In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ... It has been suggested that simulation software be merged into this article or section. ... This article is about cooperation as used in the social sciences. ... In psychology and other social and behavioral sciences, aggression refers to behavior that is intended to cause harm or pain. ... A strategy is a long term plan of action designed to achieve a particular goal, most often winning. Strategy is differentiated from tactics or immediate actions with resources at hand by its nature of being extensively premeditated, and often practically rehearsed. ... This article is about the person. ... A strategy is a long term plan of action designed to achieve a particular goal, most often winning. Strategy is differentiated from tactics or immediate actions with resources at hand by its nature of being extensively premeditated, and often practically rehearsed. ... Carta marina of the Baltic Sea region (1539). ... For other uses, see Viking (disambiguation). ...

Hanseatic trade and defense routes

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 is 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: Image File history File links Download high resolution version (795x609, 174 KB) Beschreibung Vereinfachte Darstellung der Haupthandelsroute der Hanse im Nordeuropäischen Raum, eigene verbesserte Darstellung mit GMT, erstellt von Flo Beck Licensing File links The following pages link to this file: Hanseatic League ... Image File history File links Download high resolution version (795x609, 174 KB) Beschreibung Vereinfachte Darstellung der Haupthandelsroute der Hanse im Nordeuropäischen Raum, eigene verbesserte Darstellung mit GMT, erstellt von Flo Beck Licensing File links The following pages link to this file: Hanseatic League ... Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game. ... This article is about cooperation as used in the social sciences. ... In politics, a defector is a person who gives up allegiance to one state or political entity in exchange for allegiance to another. ... A peace dove, widely known as a symbol for peace, featuring an olive branch in the doves beak. ... For other uses, see War (disambiguation). ... In evolutionary biology, reciprocal altruism is a form of altruism in which one organism provides a benefit to another in the expectation of future reciprocation. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ... In computer science, a deterministic algorithm is an algorithm which, in informal terms, behaves predictably. ... For other uses, see Game (disambiguation). ... Go is a strategic board game for two players. ... It has been suggested that this article or section be merged with normal form game. ... For other uses, see Game (disambiguation). ...

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.^[3] "Provokable nice guy's" optimality depends on iterations. How many are necessary is likely tied to the payoff matrix and probabilities of choosing.^[4] A peace dove, widely known as a symbol for peace, featuring an olive branch in the doves beak. ... For other uses, see War (disambiguation). ... A peace dove, widely known as a symbol for peace, featuring an olive branch in the doves beak. ... For other uses, see War (disambiguation). ... In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. ... The word probability derives from the Latin probare (to prove, or to test). ...

Notes

"He who is skilled in war subdues the enemy without fighting." - Sun Tzu, The Art of War, III.2 Industrial organization is the field of economics that studies the behavior of firms, the structure of markets and of their interactions. ... Mapúa Institute of Technology (MIT, MapúaTech or simply Mapúa) is a private, non-sectarian, Filipino tertiary institute located in Intramuros, Manila. ... John Forbes Nash, Jr. ... A Beautiful Mind by Sylvia Nasar A Beautiful Mind is a biography of Bank of Sweden Prize winning economist and mathematician John Forbes Nash by Sylvia Nasar. ... A Beautiful Mind is a 2001 American biographical film about John Forbes Nash, the Nobel Laureate (Economics) mathematician. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... A peace dove, widely known as a symbol for peace, featuring an olive branch in the doves beak. ... For other uses, see War (disambiguation). ... For other uses, see Game (disambiguation). ... Sun Tzu (孫子 also commonly written in pinyin: Sūn Zǐ) was the author of The Art of War, an influential ancient Chinese book on military strategy (for the most part not dealing directly with tactics). ... For other uses, see The Art of War (disambiguation). ...