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.
Read more about this topic: Tit For Tat
Famous quotes containing the word problems:
“There are nowadays professors of philosophy, but not philosophers. Yet it is admirable to profess because it was once admirable to live. To be a philosopher is not merely to have subtle thoughts, nor even to found a school, but so to love wisdom as to live according to its dictates, a life of simplicity, independence, magnanimity, and trust. It is to solve some of the problems of life, not only theoretically, but practically.”
—Henry David Thoreau (1817–1862)
“Our young people are diseased with the theological problems of original sin, origin of evil, predestination, and the like. These never presented a practical difficulty to any man,—never darkened across any man’s road, who did not go out of his way to seek them. These are the soul’s mumps, and measles, and whooping- coughs, and those who have not caught them cannot describe their health or prescribe a cure. A simple mind will not know these enemies.”
—Ralph Waldo Emerson (1803–1882)
“The question of place and climate is most closely related to the question of nutrition. Nobody is free to live everywhere; and whoever has to solve great problems that challenge all his strength actually has a very restricted choice in this matter. The influence of climate on our metabolism, its retardation, its acceleration, goes so far that a mistaken choice of place and climate can not only estrange a man from his task but can actually keep it from him: he never gets to see it.”
—Friedrich Nietzsche (1844–1900)