Tit For Tat - Problems

Problems

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

"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.