Tit for tat

Tit for tat is both the simplest strategy and the most successful in direct competition in infinitely repeated prisoners dilemma game.

Tit for tat  is largely cooperative despite that its name emphasizes an adversarial nature.

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 response to competition. 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.

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”: 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.   Tit for two tats could be used to mitigate this problem.

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.

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 cause of many prolonged conflicts throughout history.

https://en.wikipedia.org/wiki/Tit_for_tat

https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation

Some other variations:

  • Generous Tit for Tat:

Similar to Tit for Tat, but occasionally forgives the opponent’s defection and returns to cooperation even if the opponent has defected in the previous round. This generosity can promote cooperation and prevent a cycle of retaliation.

  • Pavlov (Win-Stay, Lose-Shift):

This strategy involves cooperating as long as the outcome is favorable (winning or mutual cooperation) and defecting if the outcome is unfavorable (losing or mutual defection). It’s based on the idea of reinforcing successful strategies.

  • Grim Trigger:

Cooperate initially, and as soon as the opponent defects, switch to a permanent strategy of always defecting. This strategy is designed to punish defection severely and discourage the opponent from betraying trust.

  • Random:

Randomly choose between cooperation and defection in each round. This strategy can be effective in unpredictable environments and may prevent opponents from exploiting a predictable pattern.

  • Forgiving Tit for Tat:

Similar to Generous Tit for Tat, but forgives after a certain number of rounds even if the opponent continues to defect. This forgiveness can prevent a prolonged cycle of retaliation and encourage cooperation.

  • TFT-2 (Tit for Tat with Two Turns Memory):

Takes into account the opponent’s last two moves instead of just the previous one. This can provide a more nuanced response, considering a slightly longer history of interactions.

  • Soft Tit for Tat:

Similar to Tit for Tat but responds with cooperation if the opponent defects only once in a while. This strategy allows for occasional forgiveness and may avoid unnecessary retaliation.

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Logic symbols

Set
Group
Ring
Field
Ideal
Principal Ideal
Galois Field
Lattice
Algebra
Mapping
Other links

https://www.csee.umbc.edu/portal/help/theory/group_def.shtml

List of games in game theory – Wikipedia

GitHub – medvedev1088/game-theory-cheat-sheet: Game Theory Cheat Sheet

RunTheModel – Game Theory Simulation: Repeated and Evolutionary Games – Marketplace & Competition

 

https://en.wikipedia.org/wiki/List_of_games_in_game_theory

1. Cooperative and Non-Cooperative Games:
2. Normal Form and Extensive Form Games:
3. Simultaneous Move Games and Sequential Move Games:
4. Constant Sum, Zero Sum, and Non-Zero Sum Games:
5. Symmetric and Asymmetric Games:

 

Repeated Games and Trust

Game Theory and Trust: Untangling the Role of Repeated Interactions in Trust Building

https://www.gsb.stanford.edu/faculty-research/publications/game-theory-trust-untangling-role-repeated-interactions-trust-building

Game theory and its sociological aspect     https://blog.ipleaders.in/game-theory-and-its-sociological-aspect/

https://blog.ipleaders.in/game-theory-and-its-sociological-aspect/

Sociology and Game Theory: Contemporary and Historical Perspectives

https://www.jstor.org/stable/657964

What Is Game Theory?  An Overview of the Sociological Concept

https://www.thoughtco.com/game-theory-3026626

 

 

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