Prisoner's Dilemma

the prisoners dilemma game (game theory)

In this game, each player can either cooperate or defect.

To cooperate is to refuse to testify; to defect is to testify.

For the matrix to qualify as a prisoner’s dilemma game, it must be true that *T* > *R* > *P* > *S*,

* *T* is “temptation to defect” payoff,
* *R* is “reward for mutual cooperation” payoff,
* *P* is “punishment for mutual defection” payoff
* *S* is “sucker’s” payoff.

Each cell shows the payoff to suspect 1 (above the dashed diagonal line) and the payoff to suspect 2 (below the dashed diagonal line).

For example, in the lower left cell, when suspect 1 defects and suspect 2 cooperates, the former gets no time in jail, while the latter gets 5 years in jail.

Technically, in order for the game to be a prisoner’s dilemma, it must also be true that the payoff for mutual cooperation (2*R*) is greater than the sum of the payoffs received by two players in a cooperator–defector interaction— that is, 2*R* > *T* + *S*

Kin selection is

**Reciprocal Altruism (Prisoner’s Dilemma & Game Theory)**

punishment

both defect

sucker

B - defects

A - cooperates

temptation

B - cooperates

A - defects

Reward

both prisoners cooperate

Prisoners Dilemma anaylsis

***TFT “tit for tat” is an Evolutionarily Stable Strategy (it resists “mutant” behaviors***)

**A Single Round of Prisoners Dilemma Yields a**

**“Nash Equilibrium” (no player benefits by a change of strategy [from defection to cooperation])**

**In an Iterated Prisoners Dilemma**…

**Strategies are Fluid…** 



**Reciprocal Altruistic Behaviors Can Emerge**

Crows mobbing an owl

Evidence from some species suggests that this sort of antipredator behavior may involve reciprocity among the mobbers.

* not always kin
* Cooperation that protects all

**Reciprocal Mobbing in Pied Flycatchers**

Three nestboxes were placed on a triangular grid spaced roughly 50 m apart.

* non kin

(**A**) Phase one: A stuffed predator (owl) was placed near nestbox 1. Birds from nestboxes 1 and 3 mobbed the predator at nestbox 1, but birds in pair 2 could not join this mob.

(**B**) Phase two (conducted 1 hour after phase one): A stuffed predator was placed at nestboxes 2 and 3. Pair 1 joined the mob at nestbox 3, but not at nestbox 2.

**Reciprocal Altruism (Non-Kin Interactions)**

***Trivers (1971):***



1\.***Stable groups of interaction (often around each other)***



2\.***Multiple opportunities for altruistic behavior***



3\.***Memory abilities***



4\.***Interactors (altruists) give and receive the same benefits***



* ***Natural selection favors an altruistic behavior if it is reciprocated.*** 
* ***(Helps) Explain cooperative behavior in primates.***

**Garret Hardin: The Tragedy of The Commons**

essay

shared village/ground with people



***Benefits accrue to the individual***

* ***“One more cow directly benefits me”***



***Costs are shared by all users***

* ***“Because I don’t own the commons, the cost of my cow (in terms of land usage) is dispersed across all users”***
* water and plants

\
but temptation to take advantage by not helping (cheating)