The Prisoner's Dilemma

by Serge Helfrich

This page is obsolete (and only here for historical reasons). You may want to check out the Java application or the Android app.

The spatial variant of the iterated prisoner's dilemma is a simple yet powerful model for the problem of cooperation versus conflict in groups. The applet below demonstrates the spread of 'altruism' and 'exploitation for personal gain' in an interacting population of individuals learning from each other by experience. Initially the population consists of cooperators and a certain amount of defectors (a fraction represented by p). The advantage of defection is determined by the the value of b in the 'payoff matrix' (see below) which is used to calculate the payoff after each round for each 'player' on the basis of its strategy. For the next round a player determines its new strategy by selecting the most favourable strategy from itself and its direct neighbours.

You can use the links below to learn more about this fascinating topic in 'game theory':

The iterated prisoner's dilemma - A very brief introduction to the problem as studied by Axelrod
The prisoner's dilemma: A Fable - Bonnie and Clyde
Prisoner's dilemma (Stanford Encyclopedia of Philosophy)
The Prisoner's Dilemma (Principia Cybernetica Web)
The Ethical Spectacle - About movies, love, holocausts and more...
Prisoner's dilemma - A list of links by the Constitution site
Undecidability in the spatialized prisoner's dilemma - some philosophical implications (recommended)
Prisoner's Dilemma - Alife Database
Game Theory .net - A resource for educators and students of game theory
Biological basis for human cooperation - Functional MRI scans have revealed a "biologically embedded" basis for altruistic behaviour. (Emory University.)
Reintroducing group selection to the human behavioral sciences - A preprint of the article by Wilson and Sober in BBS (1994, 17, 585-654). Groups as levels of selection? Could group-interest dominate self-interest in evolution? And what does game theory have to do with this?

demonstration applet

BTW I stole the idea for this applet from A.L. Lloyd (Sci. Amer., June 1995, 80-83).

the payoff matrix
opponent

cooperate defect

player cooperate 1 0

defect b 0

the payoff matrix
	opponent
	cooperate	defect
player	cooperate	1	0
defect	b	0

Legend

is cooperating, did cooperate

is defecting, did defect

is cooperating, did defect

is defecting, did cooperate

b: advantage for defection when opponent cooperates

p: fraction (0..1) of defectors in the first round

Applet FAQ

Applet source code
Get Java if the applet does not start:

suggested experiments

Try different b values between 1.00 and 3.00. Find out how the behavior changes. When do defectors tend to be isolated and when do they form interconnected structures around moving colonies of cooperators?
To see the gradual defector invasion pattern choose a low value for p (like 0.001) and a b value about 1.85... and if you're lucky enough to start with just one defector you'll get the kaleidoscope.
Chen figures. Rowland Chen discovered that if you use b = 1.9 and p = 0.6 a "walking man" will appear in about 1 out of 20 runs. Also a "crawling bug" can emerge. A stable figure that looks like a rotating F appears more often. Rory Plaire noted that some interesting patterns emerge when b = 1.800000015 and p = 0.5, e.g. the "crawling bug" (or "walking man" seen from above) making the kaleidoscope explode. The FAQ may be helpful in explaining these phenomena.
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