The Iterated Prisoner's Dilemma

The opponent 

Cooperate 
Defect 

You 
Cooperate 
(R, R) 
(T, S) 
Defect 
(S, T) 
(P, P) 
If two players play prisoners' dilemma more than once in
succession and they remember previous actions of their opponent and change
their strategy accordingly, the game is called Iterated Prisoners' Dilemma
(IPD).
Two conditions must be hold for the above general matrix of PD. Firstly,
the order of the payoffs is important. The best a player can do is T
(temptation to defect). The worst a player can do is to get the sucker payoff,
S. If the two players cooperate then the reward for that mutual cooperation, R,
should be better than the punishment for mutual defection, P. Therefore, the
following must hold.
T > R > P > S
Secondly, players should not be allowed to get out of the dilemma by taking it
in turns to exploit each other. Or, to be a little more pedantic, the players
should not play the game so that they end up with half the time being exploited
and the other half of the time exploiting their opponent. In other words, an
even chance of being exploited or doing the exploiting is not as good an
outcome as both players mutually cooperating. Therefore, the reward for mutual
cooperation should be greater than the average of the payoff for the temptation
and the sucker. That is, the following must hold.
R > (S + T) / 2
IPD is fundamental to certain theories of human
cooperation and trust. On the assumption that the game can model transactions
between two people requiring trust, cooperative behaviour
in populations may be modeled by a multiplayer, iterated, version of the game.
It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles
devoted to it at over 2,000. The iterated prisoners' dilemma has also been
referred to as the "PeaceWar game".
·
An IPD is finite if it repeats exactly n rounds. Mutual defection is the only
Nash equilibrium in this situation according to classic game theory. The proof
is inductive by means of the so called backward induction. Both players might as well defect in the
last round, since they will not have a chance to punish the opponent. Thus,
they might as well defect in the secondtolast round since both will defect in
the last round no matter what is done. The same induction applies till the
first round, and therefore both will defect throughout the game.
·
An IPD is infinite if its iteration n→∞. Under this circumstance, mutual cooperation is
equilibrium as well. A series of Folk Theorems
in game theory contains theoretical explanation of it.
·
An IPD is indefinite if its iteration is stochastic. A
discount factor w is the probability
that the next round will be played. For example, the expect length of an IPD
with discount factor w=0.98 is 50.
Mutual cooperation is equilibrium of indefinite IPD according to Folk Theorems.