prisoner’s dilemma game with an external selecting agent: a metacontingency experiment 1

Prisoner’s Dilemma Game with an External Selecting Agent: A Metacontingency Experiment1

• 4 participants, can’t see each other, each facing a computer• Each player presses either X or Y on each trial• Amount of money a press earns depends on whether X or Y is chosen

and on what the other players press• Value of pressing X and Y depends on all players’ responses on that

trial• The more players press X - by giving up immediate advantage of Y -,

the higher the global gain • Each choice is immediately seen by every player. When each player

has made a choice everyone receives feedback on how much he’s gained and on how much everybody else has gained Each choice can be seen as an SD for the next one

Daniele Ortu, Tomas Woelz & Sigrid Glenn

Points Earned Aggregate Product

7 7 7 7 = YYYY (28)

4 11 11 11 = XYYY (35)

8 8 15 15 = XXYY (46)

12 12 12 19 = XXXY (55)

16 16 16 16 = XXXX (64)

Results of Previous Research

• Usually, with 2 players, they learn the advantages of pressing X and get into a stable pattern of X presses

• But as the number of players increases, pressing X generally decreases and stable patterns are unlikely2

Experimental Design• We added an external selecting agent to function as the

independent variable in an A-B-A-B design

• We call the action of the external agent “feedback from the market”

• The players receive on a VR2 schedule feedback showing how the market is reacting to the product

• The experimenter decides a maximum gain/loss possible per trial

per player, e.g. 10cents (market feedback magnitude)

• In each condition all four players have to pick the required key to have any gains from market

Condition A : Press X

The market feedback is contingent on how many players press X

The greater the number of players who press X in the period since last feedback, the more the market pays

The more the market pays, the more money the company and the players gain (company money is equally shared)

Condition is changed when criterion is reached - 8 consecutive trials of XXXX - or after 15 minutesif criterion is not reached

Points Earned Aggregate Product Cultural Consequence

7 7 7 7 = YYYY (28) -10

4 11 11 11 = XYYY (35) -6.6

8 8 15 15 = XXYY (46) -3.3

12 12 12 19 = XXXY (55) 0

16 16 16 16 = XXXX (64) 10

Condition A: Press X

Condition B : Press Y

The market feedback is contingent on how many players press Y

The greater the number of players who press Y in the period since last feedback, the more the market pays

The more the market pays, the more money the company and the players gain (company money is equally shared)

Condition is changed when criterion is reached - 8

consecutive trials of YYYY - or after 15 minutesif criterion is not reached

Points Earned Aggregate Product Cultural Consequence

7 7 7 7 = YYYY (28) 10

4 11 11 11 = XYYY (35) 0

8 8 15 15 = XXYY (46) -3.3

12 12 12 19 = XXXY (55) -6.6

16 16 16 16 = XXXX (64) -10

Condition B: Press Y

Independent Variables

Number of X presses in X condition

Number of Y presses in Y condition

Coordination across time among players, in pressing X or Y (can’t be measured by looking at individual data)

Dependent Variables

Market delivering positive consequences for all players pressing X or pressing Y

Magnitude of Market’s Feedback

Player 1

0

5

10

15

20

Trials

Tr ials

Player 1

Player 2

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20

Trials

Trials

Player 2

Player 3

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Trials

Trials

Player 3

Player 4

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Trials

Trials

Player4

Mar ket

-100

-50

0

50

100

T r ials

T r i al s

Mar ket

EARNINGS

P1

P2

P3

P4

$ MARKET

M A R K E T F E E D B A C K M A G N I T U D E

10 10 25 25 INCREASE 70 10 10 25 25 FADE OUT NO MARKET

X Y X Y X Y X Y Y FADE OUT NOConditions

Player 1

0

5

10

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20

Trials

Tr ials

Player 1

Player 2

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Trials

Trials

Player 2

Player 3

0

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20

Trials

Trials

Player 3

Player 4

0

5

10

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20

Trials

Trials

Player4

Mar ket

-100

-50

0

50

100

T r ials

T r i al s

Mar ket

EARNINGS

P1

P2

P3

P4

$ MARKET

M A R K E T F E E D B A C K M A G N I T U D E

10 10 25 25 INCREASE 70 10 10 25 25 FADE OUT NO MARKET

X Y X Y X Y X Y Y FADE OUT NO

Operant Culturant

Conditions

References1 Ortu, D., Woelz, T., & Glenn, S. S. Prisoner’s Dilemma Game with an

External Selecting Agent: A Metacontingency Experiment (2008) Paper presented at Association for Behavior Analysis Convention, Chicago, IL

2 Yi & Rachlin, 2004