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  • Tit for tat is an English saying meaning "equivalent retaliation". It is also a highly effective

  • strategy in game theory for the iterated prisoner's dilemma. The strategy was first introduced

  • by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. Notably, it

  • was both the simplest strategy and the most successful in direct competition.

  • An agent using this strategy will first cooperate, then subsequently replicate an opponent's

  • previous action. If the opponent previously was cooperative, the agent is cooperative.

  • If not, the agent is not. This is similar to superrationality and reciprocal altruism

  • in biology.

  • Implications The success of the tit-for-tat strategy, which

  • is largely cooperative despite that its name emphasizes an adversarial nature, took many

  • by surprise. Arrayed against strategies produced by various teams it won in two competitions.

  • After the first competition, new strategies formulated specifically to combat tit-for-tat

  • failed due to their negative interactions with each other; a successful strategy other

  • than tit-for-tat would have had to be formulated with both tit-for-tat and itself in mind.

  • This result may give insight into how groups of animals have come to live in largely cooperative

  • societies, rather than the individualistic "red in tooth and claw" way that might be

  • expected from individuals engaged in a Hobbesian 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. Moreover, the tit-for-tat strategy has been

  • of beneficial use to social psychologists and sociologists in studying effective techniques

  • to reduce conflict. Research has indicated that when individuals who have been in competition

  • for a period of time no longer trust one another, the most effective competition reverser is

  • the use of the tit-for-tat strategy. Individuals commonly engage in behavioral assimilation,

  • a process in which they tend to match their own behaviors to those displayed by cooperating

  • or competing group members. Therefore, if the tit-for-tat strategy begins with cooperation,

  • then cooperation ensues. On the other hand, if the other party competes, then the tit-for-tat

  • strategy will lead the alternate party to compete as well. Ultimately, each action by

  • the other member is countered with a matching response, competition with competition and

  • cooperation with cooperation. In the case of conflict resolution, the tit-for-tat

  • strategy is effective for several reasons: the technique is recognized as clear, nice,

  • provocable, and forgiving. Firstly, It is a clear and recognizable strategy. Those using

  • it quickly recognize its contingencies and adjust their behavior accordingly. Moreover,

  • it is considered to be nice as it begins with cooperation and only defects in following

  • competitive move. The strategy is also provocable because it provides immediate retaliation

  • for those who compete. Finally, it is forgiving as it immediately produces cooperation should

  • the competitor make a cooperative move. Individuals who employ the tit-for-tat strategy

  • are generally considered to be tough but fair—a disposition that is often respected in the

  • business/organization world. Those who always cooperate with a competitor are often viewed

  • as weak, while those who consistently compete are perceived as unfair. In any case, the

  • implications of the tit-for-tat strategy have been of relevance to conflict research, resolution

  • and many aspects of applied social science. Problems

  • While Axelrod has empirically shown that the strategy is optimal in some cases of direct

  • competition, two agents playing tit for tat remain vulnerable. A one-time, single-bit

  • error in either player's interpretation of events can lead to an unending "death spiral".

  • In this symmetric situation, each side perceives itself as preferring to cooperate, if only

  • the other side would. But each is forced by the strategy into repeatedly punishing an

  • opponent who continues to attack despite being punished in every game cycle. Both sides come

  • to think of themselves as innocent and acting in self-defense, and their opponent as either

  • evil or too stupid to learn to cooperate. This situation frequently arises in real world

  • conflicts, ranging from schoolyard fights to civil and regional wars. Tit for two tats

  • could be used to mitigate this problem; see the description below.

  • "Tit for tat with forgiveness" is sometimes superior. When the opponent defects, the player

  • will occasionally cooperate on the next move anyway. This allows for recovery from getting

  • trapped in a cycle of defections. The exact probability that a player will respond with

  • cooperation depends on the line-up of opponents. The reason for these issues is that tit for

  • tat is not a subgame perfect equilibrium, except under knife-edge conditions on the

  • discount rate. If one agent defects and the opponent cooperates, then both agents will

  • end up alternating cooperate and defect, yielding a lower payoff than if both agents were to

  • continually cooperate. While this subgame is not directly reachable by two agents playing

  • tit for tat strategies, a strategy must be a Nash equilibrium in all subgames to be subgame

  • perfect. Further, this subgame may be reached if any noise is allowed in the agents' signaling.

  • A subgame perfect variant of tit for tat known as "contrite tit for tat" may be created by

  • employing a basic reputation mechanism. Furthermore, the tit-for-tat strategy is not

  • proved optimal in situations short of total competition. For example, when the parties

  • are friends it may be best for the friendship when a player cooperates at every step despite

  • occasional deviations by the other player. Most situations in the real world are less

  • competitive than the total competition in which the tit-for-tat strategy won its competition.

  • Tit for two tats Tit for two tats is similar to tit for tat

  • in that it is nice, retaliating, forgiving and non-envious, the only difference between

  • the two being how forgiving the strategy is. In a tit for tat strategy, once an opponent

  • defects, the tit for tat player immediately responds by defecting on the next move. This

  • has the unfortunate consequence of causing two retaliatory strategies to continuously

  • defect against one another resulting in a poor outcome for both players. A tit for two

  • tats player will let the first defection go unchallenged as a means to avoid the "death

  • spiral" of the previous example. If the opponent defects twice in a row, the tit for two tats

  • player will respond by defecting. This strategy was put forward by Robert Axelrod

  • during his second round of computer simulations at RAND. After analyzing the results of the

  • first experiment, he determined that had a participant entered the tit for two tats strategy

  • it would have emerged with a higher cumulative score than any other program. As a result,

  • he himself entered it with high expectations in the second tournament. Unfortunately, owing

  • to the more aggressive nature of the programs entered in the second round, which were able

  • to take advantage of its highly forgiving nature, tit for two tats did significantly

  • worse than tit for tat. Real world use

  • Peer-to-peer file sharing

  • BitTorrent peers use tit-for-tat strategy to optimize their download speed. More specifically,

  • most BitTorrent peers use a variant of Tit for two Tats which is called regular unchoking

  • in BitTorrent terminology. BitTorrent peers have a limited number of upload slots to allocate

  • to other peers. Consequently, when a peer's upload bandwidth is saturated, it will use

  • a tit-for-tat strategy. Cooperation is achieved when upload bandwidth is exchanged for download

  • bandwidth. Therefore, when a peer is not uploading in return to our own peer uploading, the BitTorrent

  • program will choke the connection with the uncooperative peer and allocate this upload

  • slot to a hopefully more cooperating peer. Regular unchoking corresponds very strongly

  • to always cooperating on the first move in prisoner’s dilemma. Periodically, a peer

  • will allocate an upload slot to a randomly chosen uncooperative peer. This is called

  • optimistic unchoking. This behavior allows searching for more cooperating peers and gives

  • a second chance to previously non-cooperating peers. The optimal threshold values of this

  • strategy are still the subject of research. Explaining reciprocal altruism in animal communities

  • Studies in the prosocial behaviour of animals, have led many ethologists and evolutionary

  • psychologists to apply tit-for-tat strategies to explain why altruism evolves in many animal

  • communities. Evolutionary game theory, derived from the mathematical theories formalised

  • by von Neumann and Morgenstern, was first devised by Maynard Smith and explored further

  • in bird behaviour by Robert Hinde. Their application of game theory to the evolution of animal

  • strategies launched an entirely new way of analysing animal behaviour.

  • Reciprocal altruism works in animal communities where the cost to the benefactor in any transaction

  • of food, mating rights, nesting or territory is less than the gains to the beneficiary.

  • The theory also holds that the act of altruism should be reciprocated if the balance of needs

  • reverse. Mechanisms to identify and punish "cheaters" who fail to reciprocate, in effect

  • a form of tit for tat, are important to regulate reciprocal altruism. For example, tit-for-tat

  • is suggested to be the mechanism of cooperative predator inspection behavior in guppies.

  • War The tit-for-tat inability of either side to

  • back away from conflict, for fear of being perceived as weak or as cooperating with the

  • enemy, has been the source of many conflicts throughout history.

  • However, the tit for tat strategy has also been detected by analysts in the spontaneous

  • non-violent behaviour, called "live and let live" that arose during trench warfare in

  • the First World War. Troops dug in only a few hundred feet from each other would evolve

  • an unspoken understanding. If a sniper killed a soldier on one side, the other could expect

  • an equal retaliation. Conversely, if no one was killed for a time, the other side would

  • acknowledge this implied "truce" and act accordingly. This created a "separate peace" between the

  • trenches. See also

  • An eye for an eye Attitude polarization

  • Chicken Christmas truce

  • Deterrence theory Golden Rule

  • Mutual assured destruction Nice Guys Finish First, a documentary by Richard

  • Dawkins that discusses tit for tat. Quid pro quo

  • Trigger strategy, a set of strategies of which tit for tat is a member.

  • Virtuous circle and vicious circle Zero-sum game

  • References

  • External links Wired magazine story about tit for tat being

  • 'defeated' by a group of collaborating programs Explanation of Tit for tat on Australian Broadcasting

  • Corporation

Tit for tat is an English saying meaning "equivalent retaliation". It is also a highly effective

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