Tit for tat is an English saying meaning "equivalent retaliation".
It is also a highly effective 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