The Tit for Tat strategy that stems out from the Prisoner’s Dilemma
The prisoner’s dilemma is a famous example of a game analyzed through the lens of game theory that shows why two individuals might choose not to cooperate even when it appears that it benefits both of them. Instead of choosing to keep quiet, the two prisoners are given an incentive to snitch on the other as it is their dominant strategy to aim for the lowest amount of jail time. This classic example of the prisoner’s dilemma shows how each prisoner is given an incentive to choose the scenario in which noncooperative equilibrium occurs resulting in both parties suffering consequences.
However, there is a strange solution to this dilemma if given the chance to play this mind game multiple times or be placed in a scenario where each player can observe the decisions of the other, the “Tit for Tat” strategy. The “Tit for Tat” strategy can be seen in a multitude of scenarios both in the human world as well as the animal kingdom.
Let’s say that in a given scenario of the animal kingdom there are a pair of fish that are considered to be a lower part of the food chain. When an unfortunate situation unfolds and a predator shark enters the fish territory the two fish are placed into a game of the prisoner’s dilemma. If both fish decides to make a risky escape the chances of them surviving are 40%. If one fish stays put while the other decides to escape, the fish that decides to attempt to flee will survive, but the fish that stays put will become shark food. However, if both fish decide to hide from the shark the chances of them surviving are 70%. In this scenario, game theory suggests that it is in their best interest to both attempt to flee despite the lower chances of survival due to the fact that each fish are given an incentive to choose an action that, when both fish choose it, makes them both worse off. Each fish is probably thinking about the possibility that they stay put, but the other decides to flee. This high risk and lack of trust in the other individual is what creates the incentive to flee resulting in a noncooperative equilibrium scenario that leaves both parties worse. However, this is how we humans would think about this scenario. Animals, especially fish, do not have a complicated enough brain process power to analyze and act based upon what the other animal might do. Instead, animals have been shown to act unintentionally which presents a solution to this dilemma in the simplest of ways: the “Tit for Tat” strategy.
The “Tit for Tat” strategy basically explains that if one fish simply waits for the other and mimics the strategy/action they take they will always end up in the better-case scenario. Take this fish dilemma for example. If fish A decides to hide and fish B mimics fish A’s actions this means they will both survive with a high chance of 70%. However, if fish A decides to run, fish B decides to run as well obtaining a chance of both surviving at a 40% rate. While these results may not seem like much on the surface, this means that in no scenario is either fish exposed to a situation in which they are going to die 100%. The possibility of survival is always open to both fish in both scenarios, meaning that the worst case, one of the fish dying for sure, is always avoided using this strategy of mimicry. The only limit to this strategy is the fact that in order for it to work and promote cooperative equilibrium that rewards both players for being cooperative is by playing multiple rounds or by having the participants within an observable distance of each other. The fish example is the scenario when the players can see each other’s actions.
The other scenario where the “Tit for Tat” strategy works is when the game is played multiple rounds. This works by having the players play one round first and for the following rounds mimic the other player’s moves/decisions from the previous round. If the prisoners are theoretically given multiple compounding rounds to play the game, this strategy tends to result in a situation where they end up choosing the same course of action and continue to do so once it begins to align. Noncooperative decisions are punished by having one player face the harsh consequences of in the prisoner’s dilemma situation, a lot more jail time. If prisoner A sees that prisoner B decided to stay quiet in the previous round if A decides to stay quiet for round 2, hopefully, prisoner B will continue to go with the decision that he made in the first round and decide to stay quiet as well leading to the scenario where both end up much better by staying quiet despite constantly being given the incentive to defect and choose to snitch. Choosing to mimic the other player and disregarding the incentives thereby taking the “Tit for Tat” strategy solution creates a scenario in the prisoner’s dilemma where both choose to stay quiet and face significantly less jail time.
Source:
https://www.quantamagazine.org/game-theory-explains-how-cooperation-evolved-20150212/
https://www.investopedia.com/terms/t/tit-for-tat.asp
Moffatt, Mike. “Understanding the Tit-for-Tat Strategy.” ThoughtCo, Aug. 27, 2020, thoughtco.com/the-tit-for-tat-game-theory-strategy-1147269.