Institutional Change in the Infinitely Repeated Prisoners’ Dilemma

The aim of the experiment is to test the cooperative behavior of individuals in the infinitely repeated prisoners’ dilemma (IRPD) with reinforcement, i.e., cooperation has neutral feedback, positive feedback or negative feedback. In case of positive (negative) feedback, mutual cooperation in round t of the IRPD leads to an increase (decrease) of payoffs in the payoff matrix in round t + 1, compared to neutral feedback where payoffs in the payoff matrix stay constant during the entire game.

We differentiate between two cases: In the first round of the infinitely repeated prisoners’ dilemma, mutual cooperation is either a sub-game perfect equilibrium (SPE) or not.

We plan to run 5 main treatments:

• Neutral Feedback – Cooperation is a SPE and remains so
• Positive Feedback – Cooperation is a SPE and remains so
• Negative Feedback – Cooperation is a SPE but can stop being a SPE in the mid-term
• Neutral Feedback – Cooperation is not a SPE and can never become a SPE
• Positive Feedback – Cooperation is not a SPE but can become a SPE in the mid-term

We furthermore plan to run 4 sub-treatments, where mutual cooperation has short-term or long-term consequences (compared to mid-term consequences in the main treatments):

• Negative Feedback – Cooperation is a SPE but can stop being a SPE in the short-term
• Negative Feedback – Cooperation is a SPE but can stop being a SPE in the long-term
• Positive Feedback – Cooperation is not a SPE but can become a SPE in the short-term
• Positive Feedback – Cooperation is not a SPE but can become a SPE in the long-term

We finally plan to run 3 control treatments, where individuals play a finitely repeated prisoner’s dilemma (FRPD) instead of an IRPD (in the FRPD, players know the exact number of rounds of the prisoner’s dilemma):

• Negative Feedback (FRPD) – Cooperation is a SPE but can stop being a SPE in the mid-term
• Neutral Feedback (FRPD) – Cooperation is not a SPE and can never become a SPE
• Positive Feedback(FRPD) – Cooperation is not a SPE but can become a SPE in the mid-term

2022-05-30

2023-06-30

We are interested in the strategy choice of players (cooperation or no cooperation).

We are interested in:
i) beliefs of players about the opponents’ strategy choice in each round (belief dynamic).
ii) the correlation between the strategy choice and personal attitudes towards optimism and pessimism.
iii) the personal discount factor (belief about average rounds in a match).

The experiment will be programmed in oTree (Chen et al. 2016) and conducted as a laboratory experiment with participants of the Vienna University of Economics and Business and University of Magdeburg.

The experiment:

• The experiment will consist of 2 parts and a post-experimental questionnaire.
• Each of the 2 parts is accompanied by control questions.

Part 1:

• One-shot (=one round) prisoner’s dilemma without feedback.
• Groups of 2 players.
• Incentivized.
• Belief query about the strategy choice of the other player (incentivized).

Part 2:

• Infinitely repeated prisoners’ dilemma with neutral, positive or negative feedback (control treatments: Finitely repeated prisoner’s dilemma).
• Positive and negative feedback ends after 10 cooperations. That means after 10 cooperations, mutual cooperation has neutral feedback instead of positive/negative feedback.
• Groups of 2 players playing the prisoner’s dilemma (=game). One group of 2 players = Match.
• Continuation probability (= probability that the game will have another round/ match will continue for another round) is common knowledge.
• If the game/match ends, another game/match starts with another group player.
• Part 2 is played over 20 minutes (common knowledge). The game/match that ends after this 20 minutes marks the end of part 2.
• Belief query about the strategy choice of the other player before every round (incentivized).
• Belief query about the number of rounds in a game before the game/match starts (incentivized).

In the post-experimental questionnaire, we ask participants for:

• gender, age, field of study, self-reported risk attitude
• Life-Orientation-Tests (LOT-R) to measure attitudes towards optimism and pessimism
• items from the Locus of Control Scale
• Temporal Focus Scale

Further design details:

• Part 2: Feedback after each round: Own strategy choice, strategy choice of the other player, own payoff for the respective round.
• Feedback at the end of the experiment: Own accumulated payoff.

Common parameters for all treatments:

• Discount Factor δ = 0,90
• Increase of payoffs under positive feedback: 1 experimental point
• Decrease of payoffs under negative feedback: 1 experimental point
• Sucker’s Payoff: 0 experimental points

Number of rounds in the FRPD: 11 rounds

Parametrization of the payoff matrix (in experimental points, C = Cooperation, D = Defection):

Case 1: Main treatments and control treatment – Cooperation is a SPE:

• (C, C): 66
• (D, C): 121
• (C, D): 0
• (D, D): 55

Case 2: Main treatments and control treatments – Cooperation is not a SPE:

• (C, C): 57
• (D, C): 112
• (C, D): 0
• (D, D): 55

Case 3: Sub-treatment – Cooperation is a SPE – Negative short-term:

• (C, C): 107
• (D, C): 202
• (C, D): 0
• (D, D): 96

Case 4: Sub-treatment – Cooperation is not a SPE – Positive long-term:

• (C, C): 98
• (D, C): 193
• (C, D): 0
• (D, D): 96

Case 5: Sub-treatments– Cooperation is a SPE – Negative long-term:

• (C, C): 71
• (D, C): 130
• (C, D): 0
• (D, D): 56

Case 6: Sub-treatment – Cooperation is not a SPE – Positive short-term:

• (C, C): 62
• (D, C): 121
• (C, D): 0
• (D, D): 56

Randomization and Matching is done by a computer program.

Experimental session level.

Yes

2 sessions à 20 participants per treatment:

One session with students from the University of Magdeburg and one session with students from the Vienna University of Economics and Business.

2 sessions * 20 participants * x rounds = x individual observations per treatment. As the number of rounds and matches is unknown in the IRPD (in the FRPD, just the number of matches is unknown), no specification is possible.

2 sessions à 20 participants per treatment = 40 participants per treatment.

40 participants à 12 treatments = 480 participants in total (= 240 participants from Magdeburg and 240 participants from Vienna).