The Variability of Conditional Cooperation in Sequential Prisoner’s Dilemmas

Last registered on June 06, 2022

Pre-Trial

Trial Information

General Information

Title
The Variability of Conditional Cooperation in Sequential Prisoner’s Dilemmas
RCT ID
AEARCTR-0009536
Initial registration date
June 02, 2022

Initial registration date is when the trial was registered.

It corresponds to when the registration was submitted to the Registry to be reviewed for publication.

First published
June 06, 2022, 5:51 AM EDT

First published corresponds to when the trial was first made public on the Registry after being reviewed.

Locations

Primary Investigator

Affiliation

Other Primary Investigator(s)

PI Affiliation
University of Nottingham
PI Affiliation
Bank of Korea
PI Affiliation
University of Nottingham

Additional Trial Information

Status
In development
Start date
2022-06-08
End date
2022-06-29
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Abstract
In a previous study, we examined how conditional cooperation is related to the material payoffs in a Sequential Prisoner’s Dilemma (SPD) experiment. We asked subjects to play eight SPDs with varying payoffs, systematically varying the material gain to the second-mover and the material loss to the first-mover in case the second-mover defects in response to cooperation. We find that few second-movers are conditionally cooperative in all eight games, and most second-movers change their strategies between games. Second-movers are less likely to conditionally cooperate when the gain is higher and when the loss is lower. This pattern is consistent with models of noisy decisions as well as distributional preferences. To further disentangle these potential explanations, we now plan to collect rich decision data in similar environments as above that allow us to independently estimate social preference parameters and decision noise.
External Link(s)

Registration Citation

Citation
Baader, Malte et al. 2022. "The Variability of Conditional Cooperation in Sequential Prisoner’s Dilemmas." AEA RCT Registry. June 06. https://doi.org/10.1257/rct.9536
Experimental Details

Interventions

Intervention(s)
Intervention Start Date
2022-06-08
Intervention End Date
2022-06-29

Primary Outcomes

Primary Outcomes (end points)
Measurement of conditional cooperation in simple 2-strategy sequential games. We are interested in second-mover decisions to ‘cooperate’ or ‘defect’ after the first-mover has ‘cooperated’.
Primary Outcomes (explanation)

Secondary Outcomes

Secondary Outcomes (end points)
Secondary Outcomes (explanation)

Experimental Design

Experimental Design
Methodology

We rely on simple sequential games with two strategies and two movers. As most of the employed games have prisoner dilemma structures, we label the two strategies as ‘cooperate’ and ‘defect’. In all games, the first-mover makes a decision to cooperate or defect, followed by the second-mover to make the same choice. For the second-movers we utilise the strategy method to elicit decisions, only focusing on behaviour after the first-mover has ‘cooperated’. Previous research has shown that unconditional cooperation (cooperate after defection) is very rare and it is not relevant for the estimation of our distributional preference parameters. The payoffs that can be achieved vary across games, where ‘cooperate-cooperate’ (CC) yields payoffs of (R,R), ‘cooperate-defect’ (CD) yields (S,T) and ‘defect-cooperate’ (DC) as well as ‘defect-defect’ (DD) yields (P,P). In our design we hold R (500 Tokens) constant, and vary P, T and S along 4 values, resulting in 4x4x4 = 64 games in total. The table below presents details on the specific values for P, T and S.
P T S
100 400 20
200 600 40
300 800 90
400 1000 180

Using the decisions from the second-mover, we then estimate three social preference models following the Charness-Rabin (2002) framework. We consider the second-movers choice to ‘cooperate’ to be a result of their social preferences as well as the ‘level of kindness’ by the first-mover. We measure ‘kindness’ along two dimensions, first we define R-P as the amount the first-mover has given to the second-mover and P-S as the risk of the first-mover that is associate with the decision to ‘cooperate’.
The three models we estimate then account for

1. Social preferences + noise
2. Social preferences + first-mover giving to second mover (R-P) + noise
3. Social preferences + first-mover risk to ‘cooperate’ (P-S) + noise

Using logit regressions, we estimate individual distributional preferences and sensitivity to the kindness of the first-mover in the three models described above. Most importantly, the estimated models also include a rationality parameter that captures noisy decisions, thereby allowing us to separate social preferences from noisy decision making.

Data collection

For the data collection we assign subjects to either the role of the first- or second-mover for the entire experiment. In the beginning of the experiment, we group one first-mover with one second-mover. This match stays the same for the duration of the experiment and each group faces the same 64 game decisions in the identical random order. We always implement ‘defection’ after ‘defection’ for the second-mover and thus use the strategy method to elicit second-mover willingness to ‘cooperate’ after the first-mover’s decision to ‘cooperate’. Thus, both players in our set-up make a binary decision between cooperating and defecting (C, D) in each game. Choices are incentivised by selecting one random game for a group and pay a bonus according to the decisions made.
In addition, we also elicit incentivised beliefs of each player after each game, where the player reports the probability of the other player to choose ‘cooperate’. We incentivise these using a binary scoring mechanism, where honest reporting yields a higher chance to win a fixed bonus than misreporting the probability.

References
Charness, G., & Rabin, M. (2002). Understanding social preferences with simple tests. The Quarterly Journal of Economics, 117(3), 817-869.
Giamattei, M., Yahosseini, K. S., Gächter, S., & Molleman, L. (2020). LIONESS Lab: a free web-based platform for conducting interactive experiments online. Journal of the Economic Science Association, 6(1), 95-111.
Experimental Design Details
Randomization Method
We randomise subjects into the role of first-mover and second-mover as well as randomly match them with another subject using a random number generator built in LIONESS Lab (Giamattei et al, 2020), our experimental software.
Randomization Unit
Individuals
Was the treatment clustered?
No

Experiment Characteristics

Sample size: planned number of clusters
The study will be conducted in the CeDEx laboratory at the University of Nottingham. The subjects are recruited from the CeDEx ORSEE subject pool and will therefore consist of students at the University of Nottingham. The sample sizes are based on previous publications that have estimated social preference parameters (e.g. Fisman et al (2007); Charness & Rabin (2007)).

200 total subjects: 100 first-movers, 100 second-movers
Sample size: planned number of observations
200 subjects
Sample size (or number of clusters) by treatment arms
100 first-movers; 100 second-movers
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Supporting Documents and Materials

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IRB

Institutional Review Boards (IRBs)

IRB Name
Nottingham School of Economics Research Ethics Committee
IRB Approval Date
2022-05-09
IRB Approval Number
N/A

Post-Trial

Post Trial Information

Study Withdrawal

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Intervention

Is the intervention completed?
No
Data Collection Complete
Data Publication

Data Publication

Is public data available?
No

Program Files

Program Files
Reports, Papers & Other Materials

Relevant Paper(s)

Reports & Other Materials