strategy in game theory for the iterated prisoner's dilemma. The strategy was first introduced

by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. Notably, it

was both the simplest strategy and the most successful in direct competition.

An agent using this strategy will first cooperate, then subsequently replicate an opponent's

previous action. If the opponent previously was cooperative, the agent is cooperative.

If not, the agent is not. This is similar to superrationality and reciprocal altruism

in biology.

Implications The success of the tit-for-tat strategy, which

is largely cooperative despite that its name emphasizes an adversarial nature, took many

by surprise. Arrayed against strategies produced by various teams it won in two competitions.

After the first competition, new strategies formulated specifically to combat tit-for-tat

failed due to their negative interactions with each other; a successful strategy other

than tit-for-tat would have had to be formulated with both tit-for-tat and itself in mind.

This result may give insight into how groups of animals have come to live in largely cooperative

societies, rather than the individualistic "red in tooth and claw" way that might be

expected from individuals engaged in a Hobbesian state of nature. This, and particularly its

application to human society and politics, is the subject of Robert Axelrod's book The

Evolution of Cooperation. Moreover, the tit-for-tat strategy has been

of beneficial use to social psychologists and sociologists in studying effective techniques

to reduce conflict. 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 following

competitive move. 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. Individuals who employ the tit-for-tat strategy

are generally considered to be tough but fair—a disposition that is often respected in the

business/organization world. Those who always cooperate with a competitor are often viewed

as weak, while those who consistently compete are perceived as unfair. In any case, the

implications of the tit-for-tat strategy have been of relevance to conflict research, resolution

and many aspects of applied social science. Problems

While Axelrod has empirically shown that the strategy is optimal in some cases of direct

competition, 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 mitigate this problem; see the description below.

"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, except under knife-edge conditions on the

discount rate. 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. Furthermore, the 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.

Tit for two tats Tit for two tats is similar to tit for tat

in that it is nice, retaliating, forgiving and non-envious, the only difference between

the two being how forgiving the strategy is. In a tit for tat strategy, once an opponent

defects, the tit for tat player immediately responds by defecting on the next move. This

has the unfortunate consequence of causing two retaliatory strategies to continuously

defect against one another resulting in a poor outcome for both players. A tit for two

tats player will let the first defection go unchallenged as a means to avoid the "death

spiral" of the previous example. If the opponent defects twice in a row, the tit for two tats

player will respond by defecting. This strategy was put forward by Robert Axelrod

during his second round of computer simulations at RAND. After analyzing the results of the

first experiment, he determined that had a participant entered the tit for two tats strategy

it would have emerged with a higher cumulative score than any other program. As a result,

he himself entered it with high expectations in the second tournament. Unfortunately, owing

to the more aggressive nature of the programs entered in the second round, which were able

to take advantage of its highly forgiving nature, tit for two tats did significantly

worse than tit for tat. Real world use

Peer-to-peer file sharing

BitTorrent peers use tit-for-tat strategy to optimize their download speed. More specifically,

most BitTorrent peers use a variant of Tit for two Tats which is called regular unchoking

in BitTorrent terminology. BitTorrent peers have a limited number of upload slots to allocate

to other peers. Consequently, when a peer's upload bandwidth is saturated, it will use

a tit-for-tat strategy. Cooperation is achieved when upload bandwidth is exchanged for download

bandwidth. Therefore, when a peer is not uploading in return to our own peer uploading, the BitTorrent

program will choke the connection with the uncooperative peer and allocate this upload

slot to a hopefully more cooperating peer. Regular unchoking corresponds very strongly

to always cooperating on the first move in prisoner’s dilemma. Periodically, a peer

will allocate an upload slot to a randomly chosen uncooperative peer. This is called

optimistic unchoking. This behavior allows searching for more cooperating peers and gives

a second chance to previously non-cooperating peers. The optimal threshold values of this

strategy are still the subject of research. Explaining reciprocal altruism in animal communities

Studies in the prosocial behaviour of animals, have led many ethologists and evolutionary

psychologists to apply tit-for-tat strategies to explain why altruism evolves in many animal

communities. Evolutionary game theory, derived from the mathematical theories formalised

by von Neumann and Morgenstern, was first devised by Maynard Smith and explored further

in bird behaviour by Robert Hinde. Their application of game theory to the evolution of animal

strategies launched an entirely new way of analysing animal behaviour.

Reciprocal altruism works in animal communities where the cost to the benefactor in any transaction

of food, mating rights, nesting or territory is less than the gains to the beneficiary.

The theory also holds that the act of altruism should be reciprocated if the balance of needs

reverse. Mechanisms to identify and punish "cheaters" who fail to reciprocate, in effect

a form of tit for tat, are important to regulate reciprocal altruism. For example, tit-for-tat

is suggested to be the mechanism of cooperative predator inspection behavior in guppies.

War 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 source of many conflicts throughout history.

However, the tit for tat strategy has also been detected by analysts in the spontaneous

non-violent behaviour, called "live and let live" that arose during trench warfare in

the First World War. Troops dug in only a few hundred feet from each other would evolve

an unspoken understanding. If a sniper killed a soldier on one side, the other could expect

an equal retaliation. Conversely, if no one was killed for a time, the other side would

acknowledge this implied "truce" and act accordingly. This created a "separate peace" between the

trenches. See also

An eye for an eye Attitude polarization

Chicken Christmas truce

Deterrence theory Golden Rule

Mutual assured destruction Nice Guys Finish First, a documentary by Richard

Dawkins that discusses tit for tat. Quid pro quo

Trigger strategy, a set of strategies of which tit for tat is a member.

Virtuous circle and vicious circle Zero-sum game

References

External links Wired magazine story about tit for tat being

'defeated' by a group of collaborating programs Explanation of Tit for tat on Australian Broadcasting

Corporation