Prisoner’s Dilemma Game with an External Selecting Agent: A Metacontingency Experiment 1

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Prisoner’s Dilemma Game with an External Selecting Agent: A Metacontingency Experiment 1. Daniele Ortu, Tomas Woelz & Sigrid Glenn. 4 participants, can’t see each other, each facing a computer Each player presses either X or Y on each trial

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Presentation Transcript
Daniele Ortu, Tomas Woelz & Sigrid Glenn
• 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
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

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

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)

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

Magnitude of Market’s Feedback

Dependent Variables

10 10 25 X 25 INCREASE 70 X 10 X 10 X 25 X 25X FADE OUT NO

x y X Y x y X Y NO

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 25INCREASE70 10 10 25 25 FADE OUT NO MARKET

\$

MARKET

P1

P2

P3

P4

E

A

R

N

I

N

G

S

X Y X Y X Y X Y YFADE OUT NO

Conditions

x y X Y x y X Y NO

10 10 25 X 25 INCREASE 70 X 10 X 10 X 25 X 25X FADE OUT NO

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 25INCREASE70 10 10 25 25 FADE OUT NO MARKET

\$

MARKET

Culturant

Operant

E

A

R

N

I

N

G

S

P1

P2

P3

P4

X Y X Y X Y X Y YFADE OUT NO

Conditions

References

1 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