The Prisoner’s Dilemma

Co-opetition - The Value Net

Company

Suppliers

Customers

ComplementorsCompetitors

The Prisoner’s DilemmaSource: Strategy and Conflict: An Introductory Sketch of Game Theory, Roger A. McCain. McCain attributes the original formulation of the game to Albert W. Tucker

Click Here for a Modern Version of the Game

Two suspected burglars,Ellie and Shea, are captured near the scene of a recent break-in and are given the "third degree" separately by the police. Each has to choose whether or not to confess and implicate the other. If neither woman confesses, then both will serve one year on a charge of carrying a concealed weapon. If each confesses and implicates the other, both will go to prison for 10 years. However, if one burglar confesses and implicates the other, and the other burglar does not confess, the one who has collaborated with the police will go free, while the other burglar will go to prison for 20 years on the maximum charge.

PD Payoff Matrix

#s = Yrs. in Prison

Shea

Ellie

Confess Don’t

Confess

Confess 10, 10 0, 20

Don’t

Confess

20, 0 1, 1

Why Study the Prisoner’s Dilemma?

The Tragedy of the Commons

Why Study the Prisoner’s Dilemma?

PD is the E. coli bacteria of Social Science

Click here for more on the PD

"When should a person cooperate, and when should a person be selfish, in an on going interaction with anotherperson?"

The Evolution of Cooperation, Robert Axelrod, 1984.

The PD Tournament

Player 2

Player 1

Cooperate Defect

Cooperate 3, 3 0, 5

Defect 5, 0 1, 1

Tournament Conditions

Round 1– Round Robin– 200 Rounds– 14 Entrants + Random

Round 2– Same except 5 Games of varying lengths averaging

151 moves each– 62 Entrants + Random

Round 1 Tournament Results

Rank Name Program Length

Score

1 Anatol Rapoport 4 504.5

6 William Stein and Amnon Rapoport

50 477.8

13 Gordon Tullock 18 300.5

15 RANDOM 5 276.3

Winning Strategy: Tit-for-Tat

Tit-for-Tat1. Begin the game by choosing Cooperate.

2. Choose whatever your opponent chose in the prior round.

Tit-for-Tat

Round TFT Opponent Choice

Payoffs

1 C D 0/5

2 D D 1/1

3 D C 5/0

4 C C 3/3

Average 2.25/2.25

Tit-for-Tat

Round TFT Opponent Choice

Payoffs

1 C D 0/5

2 D D 1/1

3 D D 1/1

4 D D 1/1

Average 0.75/2.0

Tit-for-Tat

Round TFT Opponent Choice

Payoffs

1 C C 3/3

2 C C 3/3

3 C C 3/3

4 C C 3/3

Average 3.0/3.0

Tit-for-Tat

In a round robin format how do you beat TFT? Is this a wise strategy? What is likely to happen?

Tit-for-Tat

What does TFT do so well?– Nice– Forgiving– Retaliatory– Clear

WWI – Trench Warfare

WWI – Trench Warfare

Tit-for-Tat

The Power of Reciprocity– "(I was) astonished to observe German soldiers

walking about within rifle range behind their own line. Our men appeared to take no notice. I privately made to do away with that sort of thing when we took over; such things should not be allowed. These people evidently did not know there was a war on. Both sides apparently believed in the policy of "live and let live." (EoC, pg. 73-74; Dugdale, 1932, pg. 94)

Tit-for-Tat

The Power of Reciprocity – “In one section the hour of 8 to 9 a.m. was

regarded as consecrated to “private business,” and certain places indicated by a flag were regarded as out of bounds by the snipers on both sides” (EoC pg. 78; Morgan, 1916, pp. 270-71).

Reciprocity

Evolutionary Dynamics

– Friends and Family– In Business

Social Dilemmas

Social Dilemmas

"Imagine that you and a group of friends are dining at a fine restaurant with an unspoken agreement to divide the check evenly. What do you order? Do you choose the modest chicken entrée or the pricey lamb chops? The house wine or the 1978 French Bordeaux? If you are extravagant, you could enjoy a superlative dinner at a bargain price. But if everyone in the party reasons as you do, the group will end up with a hefty bill to pay. And why should others settle for past primavera when someone is having grilled pheasant at their expense." (Scientific American, March 1994)

Give Some – Take Some GameExtra-Credit Points

Your Choice:

If more than 80% of the class

chooses give:

Is less than 80% of the class

chooses give:

Give 6 0

Take 10 2

Social Dilemmas

A. Defining characteristics:– 1. Each player has a dominant strategy. In the

language of social dilemmas an individual receives a higher payoff for a socially defecting choice than for a socially cooperative choice no matter what the other individuals in society do.

– 2. All individuals are better off if all cooperate than if all defect (Dawes, 1980).

Social Dilemmas

Contrary to dominant theory logic, experiments often find substantial deviation from this standard. Specifically, in "one shot" experiments, subjects typically contribute between 40-60% of the maximum. But, in "repeated play" experiments, contributions rates typically fall off quite rapidly as multiple rounds of the game are played. These results beg the questions of when and why people are willing to cooperate and voluntarily contribute to a public good. The following answers have been proposed for why people contribute:

Social Dilemmas

Explanations for why people contribute to a public good:– 1. Reciprocal Altruism: Tit-For-Tat, people tend

to reciprocate kindness with kindness, cooperation with cooperation, hostility with hostility, and defection with defection.

– 2. Pure Altruism: People are motivated because the take pleasure in others' pleasure.

– 3. Impure Altruism: People are motivated to "do the right thing."

Social Dilemmas

Factors that affect the level of contribution rates to a public good in the laboratory:

– 1. Communication - allowing people to communicate with each other face-to-face increases contribution rates.

– 2. Anonymity vs. Public Disclosure - a subject is more likely to contribute if her choice is public.

– 3. Expectation about others' behavior - a subject is more likely to contribute if he thinks others will contribute

– 4. Group size - the larger the group the lower contribution rates