Tit for tat

Tit for Tat is an English phrase that was first recorded in the 16th century in the form of “tip for tap”. Both words should be understood to mean punch, poke. The idiom can roughly be translated as "Like you to me, so I to you" or an eye for an eye .

In game theory , “Tit for Tat” describes a strategy for iterated prisoner's dilemmas that is based on the principle of reciprocity . A player using the tit-for-tat strategy begins the interaction with a cooperative (“friendly”) play. Then a tit-for-tat player imitates the other player's last move. This strategy was formally developed by Anatol Rapoport in the 1960s . Known as “Tit for Tat”, it became known to the general public through the book The Evolution of Cooperation by Robert Axelrod , in which he describes a great success of this strategy in a two-person competition at a computer tournament .

Definition of terms and properties

In game theory, tit for tat describes the strategy of a player who cooperates in a continued game on the first move (behaves "friendly") and then acts in the same way as the opponent in the previous game round. If the opponent has previously cooperated, the tit-for-tat player will also cooperate . If, on the other hand, the opponent has defective in the preliminary round (a defector reacts "unfriendly"), the tit-for-tat player (in retaliation ) also replies with a defect.

The tit-for-tat strategy formulated by Anatol Rapoport not only includes the principle of reciprocity or the talion " An eye for an eye, a tooth for a tooth: do others as they have done you"), but also the limited one Retaliation to keep penalties low and rewards high, regardless of how the other party behaves. The strategy also has the rule of always acting cooperatively at the beginning of an interaction . Tit for Tat is therefore a friendly strategy. When two tit-for-tat players meet, they always cooperate.

The potential of the tit-for-tat strategy became clear in a widely acclaimed computer experiment by Robert Axelrod . Axelrod asked scientists from various disciplines to inform him of strategies that, in the form of rules of behavior , should determine the decisions within a repeated prisoner's dilemma . Using these strategies, Axelrod simulated a tournament in which each player repeatedly competed against each other. Under various test conditions, Tit for Tat repeatedly prevailed as one of the most successful strategies.

In a repeated prisoner's dilemma over several rounds, a player using the tit-for-tat strategy can never do better than the respective opponent, since his moves are always copied. The maximum deficit on the opponent is relatively small. If the other player also plays tit for tat (or another strategy that always responds to friendliness in a friendly manner), there is no backlog, as both players then reap exactly equal cooperation profits. In a game with several players, on the other hand, you do better in many cases than players with other strategies, because cooperation pays off there, but the tit-for-tat strategy cannot be “exploited” at the same time. The strategy “always cooperate”, on the other hand, does significantly worse with unfriendly opponents or in mixed interaction groups, as it can be exploited.

According to Axelrod, Tit for Tat fulfills four properties that every strategy in the repeated prisoner's dilemma must have in order to be effective:

clarity
Indulgence
Niceness
Provocability

Tit for Tat is clear and simple as it consists of just two very simple rules. The strategy is "nice" in that every interaction starts off nicely. It can be provoked, that is, it does not leave unfriendly behavior of an opponent unpunished. And she is lenient because she does not react resentfully and is ready to resume cooperation.

The tit-for-tat strategy is very susceptible to even the slightest disturbance in the iterated prisoner's dilemma, since a single misunderstanding can reverberate indefinitely. Further developed strategies try to overcome this weakness.

Comparable maxims

"Tit for Tat" goes back to Anatol Rapoport as a game theory strategy. In terms of cultural history, comparable maxims can be found. In the Icelandic Hávamál , part of the Edda , this rule can be found:

“The friend should grant friendship to the friend
and gift counts with gift.
The hero should answer scorn with scorn,
And loosess with lies. "

- Older Edda: Hávámal

The historical Talion seeks to strike a balance between the damage suffered by the victim of a crime and the damage with which the perpetrator is to be punished. The quid-pro-quo rule calls for a balance between performance and consideration .

Tit for Tat in the repeated prisoner's dilemma

Tit for Tat became known as a successful strategy in the repeated prisoner’s dilemma . Two defendants are faced with a difficult decision, because the verdict on their guilt or innocence is made according to strict rules. If only one of the two betrays the other, the betrayed will go behind bars for five years. The traitor, however, is acquitted and receives an additional reward. If both betray each other, they both have to go to jail for three years. And if neither betrays the other, both will be acquitted. However, none of them will then receive a reward.

If one considered just one of these decisions, the matter would be simple: each defendant would assume that the other would choose the greatest possible gain: freedom and money. The result would be clear: Both would betray each other and go to prison.

If the two prisoners are repeatedly confronted with this decision and if both of them know the previous decision of the other, there are different strategies for successfully completing the game. Tit for Tat is one of the most successful.

In this example, this means that one of the prisoners generally goes into the game cooperatively and helps the other participant by being silent. If the other prisoner does not remain silent, the tit-for-tat player takes revenge in the following round by not being silent either. However, he is ready to forget immediately when the teammate improves and plays cooperatively again. In the next round he will play cooperatively again.

Discussion of practical applications

Communication ban?

The repeated prisoner's dilemma, in which Tit for Tat performs well on average, sets extreme rules in an extreme situation. However, it is not always clear whether a real action situation can be interpreted with sufficient accuracy as a repeated prisoner's dilemma. So the only “ communication ” between the two players is that they know each other's previous decision. The often obvious possibility of explicitly communicating with the other about cooperative behavior is by definition not possible.

Misunderstandings between great powers

Two potential problems with Tit for Tat are the ability to be provoked quickly and the automatic retaliation of the strategy. The rule is therefore dangerous to use in situations in which the reaction of the interaction partner cannot be correctly recognized or interpreted. For example, if an action is wrongly recognized as a defect, a misunderstanding has occurred. But even an action wrongly recognized as unfriendly triggers an unfriendly reaction of its own in a tit-for-tat player. If the other player also plays tit for tat , this one misunderstanding can lead to a complete breakdown of the cooperation.

For example, in 1987 the American embassy in Moscow was bugged and spied on by Soviet agents. The United States then reduced the number of Soviet diplomats admitted to Washington . The Soviets, in turn, withdrew the local aid workers from the US embassy in Moscow and demanded that the American delegation be downsized. As a result, it became more difficult for both sides to pursue their diplomatic activities.

According to this description of the events, the Russians had not "played" tit for tat as they started with an unfriendly "move". The Americans interpreted the "bugging" of their message as an unfriendly act, which they followed up with a retaliation in the sense of the tit for tat . Perhaps, however, there was a misunderstanding: The Russians interpreted the unilateral demand of the USA to reduce the number of Russian diplomats as a (first) defection and punished this behavior of the USA. If such misunderstandings exist, a chain reaction of defective behavior can result, as in the case described. Sociologically, this form of misunderstanding is also described as a vicious circle .

In situations in which such misunderstandings can occur, the win-stay, lose-shift strategy is superior to the "tit for tat" strategy, since the players can come back from a non-cooperation loop and into the cooperation.

Derived strategies

Tit for Tat also punishes interaction partners who have previously behaved cooperatively over a long period of time in the event of a defect. For example, given the possibility of misunderstandings, a strategy that takes this friendly history into account is conceivable. The strategy could be lenient when the defect appears to be an exception and retaliate when it appears to be the rule. Tit for Tat can be used as a punishment when it appears that the other side is trying to take advantage of you.

The following guidelines must be observed:

Start with cooperation.
Keep track of how often the other side acts unkindly as you cooperate.
When the proportion of unkind behavior becomes too high, return to tit for tat .

In order to determine the unreasonable proportion of the unfriendly behavior, short, medium and long-term information about the history of the behavior of the other side is required. This means that you have to know how often the interaction partner has cooperated “recently”. A long-term view alone is not enough. If someone has been cooperative for a long time, that doesn't mean they won't take advantage of you now. An example of such a strategy: Start cooperating until one of the following tests is negative:

First impression: Unfriendly behavior right from the first move. - Get back to tit for tat !
Short term: Unfriendly behavior in two out of three rounds. - Get back to tit for tat !
Medium term: Unfriendly behavior in three of the last 20 rounds. - Get back to tit for tat !
Long term: Unfriendly behavior in five of the last 100 laps. - Get back to tit for tat !

The tit for tat punishment does not have to go on indefinitely. If it is the first violation of one of these four tests, then return to cooperation after about 20 periods of tit-for- tat echo with alternating unfriendly behavior. However, the other side should be put on probation . This means that the thresholds for permitted misconduct in the medium and long-term test should be reduced. If the other side has been suspended for 50 periods, revert to the original standards. If not, then return to tit for tat forever .

The most important principle is not to punish all unfriendly behavior in the same way. Guesswork must be made as to whether there has been a misunderstanding, be it on the opponent's side or on your own. The additional indulgence allows the opponents a little unfriendly behavior, but has the consequence that the trust that has been placed in this opponent is reduced. Unfriendliness of the opponent continues to harm him.

This strategy has one disadvantage: if you face a consistent traitor alone, he will prevail. So in reality it is extremely difficult - for example out of a state of war - to achieve the cessation of opposing punitive actions through a unilateral armistice. The proposed “indulgent” strategy can only win if other friendly partners can also be found who, through cooperative behavior, ensure that the (one-off) disadvantage from the betrayal of the consequent traitor is compensated for after two successful partnerships at the latest.

Another disadvantage is the relatively complex implementation of the strategy compared to the "simple and clear" original version of Tit for Tat . A simpler, "more indulgent" strategy is tit for two tats : only after two defections does one react unfriendly, which avoids mutual punishments in the interaction with other, less indulgent strategies. This strategy would have won against Tit for Tat in the first round of the RAND Corporation's computer tournament, but there were more aggressive strategies in later tournaments that could exploit the good nature of Tit for two Tats . The advantage of the Tit for Two Tats strategy over Tit for Tat is its lower susceptibility to communication errors.

literature

Anatol Rapoport, Albert M. Chammah: Prisoner's Dilemma - A Study in Conflict and Cooperation . 2nd Edition. University of Michigan Press, Ann Arbor 1970.
Avinash K. Dixit, Barry J. Nalebuff: Game Theory for Beginners - Strategic Know-How for Winners . Schäffer-Poeschel-Verlag, Stuttgart 1997, ISBN 3-7910-1239-8 .
Avinash K. Dixit, Susan Skeath: Games of Strategy . 2nd Edition. WW Norton & Company, New York 2004, ISBN 0-393-92499-8 .
Harald Wiese: Decision and game theory . Springer-Verlag, Berlin / Heidelberg 2002, ISBN 3-540-42747-3 .
Robert Axelrod : The evolution of cooperation. Oldenbourg, Munich 2005, ISBN 3-486-53995-7 .
Thomas Riechmann: Game Theory . 2nd edition, Verlag Franz Vahlen, Munich 2008, ISBN 978-3-8006-3505-4 .

Individual evidence

↑ Gernot Sieg: Game Theory. Oldenbourg Verlag , 2005. p. 45

↑ Anatol Rapoport (PDF; 80 kB) Institute for Advanced Studies.

↑ Ernst Fehr: Human behavior: Don't lose your reputation . In: Nature . No. 432 , November 25, 2004, p. 449-450 , doi : 10.1038 / 432449a . read online , (PDF 345 kB, accessed September 15, 2015)

↑ Synonyms and origins
- Origin of defect . Oxford Dictionaries 2015. Retrieved September 19, 2015.
  Quotation: “Late Middle English (as a noun, influenced by Old French defect 'deficiency'): from Latin defectus, past participle of deficere 'desert or fail', from de- (expressing reversal) + facere 'do'. "
  (German late Middle English (as a substance name , influenced by the Old French defect 'deficiency'): from the Latin defectus , past participle from deficere 'desertieren oder schauern ', from de - (as an expression of reversal) + facere 'to do / do'.)
Note: In the German-speaking world, the English term defector is mostly translated or used as a defector. A defector when iterated a Prisoner's Dilemma "corresponds counter poker players" (see FIG. Adversary ).

↑ ^a ^b "Tit-for-Tat" strategy . University of Munster.

↑ ^a ^b ^c ^d ^e ^f Avinash K. Dixit , Barry J. Nalebuff: Game theory for beginners: strategic know-how for winners . Schäffer / Poeschel, Stuttgart 1997, ISBN 3-7910-1239-8 , pp. 105-108.
English Original Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life . 1991 (New edition, Norton, New York 1993, ISBN 0-393-31035-3 )

^ Per Molander: The Optimal Level of Generosity in a Selfish, Uncertain Environment . In: The Journal of Conflict Resolution , Vol. 29, No. 4, December 1985, pp. 611-618. Sage Publications, JSTOR 174244,
quoted from Robert Axelrod: On Six Advances in Cooperation Theory. School of Public Policy, University of Michigan, Ann Arbor (USA), January 2000, p. 27; umich.edu (PDF)
(Quote) It is well known that the Tit for Tat strategy suffers from even small amounts of noise because a single mistaken defection can echo indefinitely.
Suggested translation: It is well known that the Tit for Tat strategy suffers even with low noise, as a single misunderstood defect can reverberate indefinitely.

↑ Older Edda: Hávámal ( Wikisource )

↑ Martin A. Nowak, Roger Highfield: Supercooperators - altruism, evolution, and why we need each other to succeed . Free Press, New York 2011

↑ ^a ^b Avinash K. Dixit, Barry J. Nalebuff: Game theory for beginners, p. 112 ff.

^ ^A ^b Robert M. Axelrod: The evolution of cooperation . 6th edition. Oldenbourg Verlag, 2005, ISBN 3-486-53996-5 , p. 107.

^ Rudolf Kruse et al .: Computational Intelligence . Vieweg + Teubner, Wiesbaden 2011, ISBN 3-8348-1275-7 , p. 240.

[1] Gernot Sieg: Game Theory. Oldenbourg Verlag , 2005. p. 45

[2] Anatol Rapoport (PDF; 80 kB) Institute for Advanced Studies.