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
