Tit for Tat

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 (shows why two individuals might not cooperate, even if it appears that it is in their best interests to do so). The strategy was first introduced by mathematical psychologist Anatol Rapoport in political scientist Robert Axelrod’s two tournaments, held around 1980. Notably, it was (on both occasions) both the simplest strategy and the most successful.

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. The success of the tit-for-tat (TFT) strategy (which is largely cooperative despite that its name emphasizes an adversarial nature) took many by surprise. In successive competitions various teams produced complex strategies which attempted to ‘cheat’ in a variety of cunning ways, but TFT eventually prevailed in every competition.

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 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 TFT 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 TFT 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 TFT begins with cooperation, then cooperation ensues. On the other hand, if the other party competes, then TFT 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 TFT strategy is effective for several reasons: the technique is recognized as clear, nice, provocable, and forgiving. Also, 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 TFT 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 TFT technique have been of relevance to conflict research, resolution and many aspects of applied social science.

While Axelrod has empirically shown that the strategy is optimal in some cases, 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 avoid this problem. Therefore, ‘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. 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.

‘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 TFT strategy, once an opponent defects, the other 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 (in the game-theory sense) than its predecessor.

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 (unchoke). 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.

Studies in the prosocial behavior 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 formalized by mathematician John von Neumann and economist Oksar Morgenstern (1953), was first devised by geneticist Maynard Smith (1972) and explored further in bird behavior by zoologist Robert Hinde. Their application of game theory to the evolution of animal strategies launched an entirely new way of analyzing animal behavior.

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.

The tit for tat strategy has been detected by analysts in the spontaneous non-violent behavior, 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.

This approach to interactions can be seen as a parallel to the eye for an eye approach from Judeo-Christian-Islamic tradition, where the penalty for taking someone’s eye is to lose one’s own.

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