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| '''Tit for tat''' is a highly effective strategy in [[game theory]] for the [[Prisoner's dilemma|iterated prisoner's dilemma]]. It was first introduced by [[Anatol Rapoport]] in [[Robert Axelrod]]'s two tournaments, held around 1980. Based on the English saying meaning "equivalent retaliation" ("tit for tat"), an [[Agent (grammar)|agent]] using this strategy will initially cooperate, then respond in kind to a previous opponent's action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is equivalent to the concept of [[reciprocal altruism]] in the context of [[biology]]. | | '''Tit for tat''' is a highly effective strategy in game theory, sometimes called evolutionary theory. |
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| == Overview ==
| | [http://en.wikipedia.org/wiki/Tit_for_tat Wikipedia Entry] |
| This strategy is dependent on four conditions that has allowed it to become the most prevalent strategy for the Prisoner's Dilemma:
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| # Unless provoked, the agent will always cooperate
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| # If provoked, the agent will retaliate
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| # The agent is quick to forgive
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| # The agent must have a 2/3 chance of competing against the opponent more than once.
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| In the last condition, the number 2/3 is arbitrary and depends on the [[payoff matrix]] of the Prisoner's Dilemma. The important thing is that the competition continues long enough for repeated punishment and forgiveness to generate a long-term payoff higher than the possible loss from cooperating initially.
| | ==Description== |
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| A fifth condition applies to make the competition meaningful: if an agent knows that the next play will be the last, it should naturally defect for a higher score. Similarly if it knows that the next two plays will be the last, it should defect twice, and so on. Therefore the number of competitions must not be known in advance to the agents.
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| For several decades Tit-for-Tat was the most effective strategy for playing the game, winning in annual automated tournaments against (generally far more complex) strategies created by teams of computer scientists, economists, and psychologists. Game theorists informally believed the strategy to be optimal (although no proof was presented).
| | Based on the English saying meaning "equivalent retaliation" ("tit for tat"), an Agent using this strategy will initially cooperate, then respond in kind to a previous opponent's action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is equivalent to the concept of reciprocal altruism in the context of biology. It leads to a non zero sum or win win game. Both Richard Dawkins and Robert Wright note that in both animal and human behavior, this simple strategy led to cooperation amongst tribes or collectives. |
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| It is important to know that Tit-for-Tat still is the most effective strategy if you compare the average performance of each competing team. The team which recently won over a pure Tit-for-Tat team only outperformed it with some of their algorithms because they submitted multiple algorithms which would recognize each other and assume a master and slave relationship (one algorithm would "sacrifice" itself and obtain a very poor result in order for the other algorithm to be able to outperform Tit for Tat on an individual basis, but not as a pair or group).
| | In relationship to P2P culture, this strategy can be found in written online dialogue or dialectic, leading users to co-intelligence or synthesis of idea. See also [[OS 0 1 2]] |
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| == Example of play ==
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| Assume there are 4 agents: 2 are Tit for Tat players ("variables") and 2 are simply trying to maximize their own winnings ("controls"). Assume that each player faces the other 3 in a match lasting 6 games. If one player gives evidence against a player who does not, the former gains 5 points and the latter nets 0. If both refrain from giving evidence, both gain 3 points. If both give evidence against each other, both gain 1 point.
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| When a variable faces off against a control, the former refrains from giving evidence in the first game while the control does the opposite, gaining the control 5 points. In the remaining 5 games, both players give evidence against each other, netting 1 point each game. The final score is control, 10; variable, 5.
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| When the variables face off against each other, each refrains from giving evidence in all 6 games. 6 * 3 = 18 points for each variable.
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| When the controls face off, each gives evidence against the other in all 6 games. 6 * 1 = 6 points for both controls.
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| The final score for each variable is 5 + 5 + 18 = 28 points. The final score for each control is 10 + 10 + 6 = 26 points. Despite the fact that the variables never won a match and the controls never lost a match, the variables still came out ahead, because the final score is not determined by the winner of matches, but the scorer of points. Simply put, the variables gained more points tying with each other than they lost to the controls.
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| (This example was taken from [[Piers Anthony]]'s novel, ''[[Golem in the Gears]]''.)
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| == Implications ==
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| The success of the strategy, which is largely cooperative, took many by surprise. In successive competitions various teams produced complex strategies which attempted to "cheat" in a variety of cunning ways, but Tit for Tat eventually prevailed in every competition.
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| Some theorists believe this result may give insight into how groups of animals (and particularly human societies) have come to live in largely (or entirely) cooperative societies, rather than the individualistic "red in tooth and claw" way that might be expected from individual engaged in a [[Hobbes]]ian state of nature. This, and particularly its application to human society and politics, is the subject of [[Robert Axelrod]]'s book ''[[The Evolution of Cooperation]]''. Also the theory can give insight in how technological innovation have taken place in history, and in particular, why the modern age evolved in the many competing kingdoms of Europe, but not for example in China. This is further discussed in [[Robert Wright]]'s book ''[[Nonzero : The Logic of Human Destiny]]''.
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| == External link ==
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| {{wiktionary|tit for tat}}
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| * [http://www.wired.com/news/culture/0,1284,65317,00.html Wired magazine story about Tit for Tat being 'defeated' by a group of collaborating programs]
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| == See also ==
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| * [[Iterated prisoner's dilemma]]
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| * [[Reciprocal altruism]]
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| == References ==
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| * ''[[The Evolution of Cooperation]]'', [[Robert Axelrod]], Basic Books, ISBN 0465021212
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| *''[[The Selfish Gene]]'', [[Richard Dawkins]] (1990), second edition -- includes two chapters about the evolution of cooperation, ISBN 0192860925
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| *''[[The Origins Of Virtue]]'', [[Matt Ridley]], Penguin Books Ltd, ISBN 0140244042
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| *''[[How Are We to Live?]]'', [[Peter Singer]], Prometheus Books, ISBN 0879759666
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| {{game theory}}
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| [[Category:Game theory]]
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| [[de:Tit-for-tat]]
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| [[es:Tit for Tat]]
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| [[fr:Coopération-réciprocité-pardon]]
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| [[pl:Wet za wet]]
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| [[pt:Olho por olho]]
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Tit for tat is a highly effective strategy in game theory, sometimes called evolutionary theory.
Wikipedia Entry
Description
Based on the English saying meaning "equivalent retaliation" ("tit for tat"), an Agent using this strategy will initially cooperate, then respond in kind to a previous opponent's action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is equivalent to the concept of reciprocal altruism in the context of biology. It leads to a non zero sum or win win game. Both Richard Dawkins and Robert Wright note that in both animal and human behavior, this simple strategy led to cooperation amongst tribes or collectives.
In relationship to P2P culture, this strategy can be found in written online dialogue or dialectic, leading users to co-intelligence or synthesis of idea. See also OS 0 1 2