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Stag Hunt at the Prison: Risk Dominance and Cooperation in the Indefinitely Repeated Prisoner's Dilemma
Initial registration date
November 24, 2019
November 25, 2019 10:32 AM EST
University of California, Irvine
Other Primary Investigator(s)
Additional Trial Information
Experiments on the repeated prisoner's dilemma (RPD) have recently gained traction making predictions among an "embarrassing" richness of cooperative and non-cooperative equilibria. The most popular experimentally motivated refinement is Blonski and Spagnolo's (2015) riskiness. The idea is to relate the prisoner's other dilemma of selecting among different cooperative and non-cooperative strategies to the equilibrium selection problem in static coordination games. Using systematic variations in RPD payoffs and a novel measure of attitudes towards the risk/efficiency trade-off in coordination games, the present study is the first direct test of the theory.
Jagau, Stephan. 2019. "Stag Hunt at the Prison: Risk Dominance and Cooperation in the Indefinitely Repeated Prisoner's Dilemma." AEA RCT Registry. November 25.
Intervention Start Date
Intervention End Date
Primary Outcomes (end points)
Risk-dominance switching points in Part 1; Initial propensity of cooperation in Part 2
Primary Outcomes (explanation)
Risk-dominance switching point: Game for which individual switches from efficient to inefficient strategy in the choice lists form Part 1
Initial propensity of cooperation: Rate at which subject cooperated in round 1 of the latter 14 RPD's in Part 2.
Secondary Outcomes (end points)
Secondary Outcomes (explanation)
The experiment consists of four parts that are administered in fixed order. Parts 1, 3, and 4 are identical for each subject. The order in which items appear is randomized at the subject level for Parts 1, 3, and 4, and it is fixed for Part 2. Part 2 implements RPD's and includes a between-subject treatment with 4 different levels of the sucker's payoff. Also RPD lengths are matched across treatment groups at the session level, using four independent draws of RPD lengths for a total of 16 sessions. This can be seen as a second between-subject treatment.
(1) 18 one-shot CGs against a fixed partner with no feedback. CG-payoffs are varied according to a choice-list paradigm across two families of CGs.
(2) 17 matches of standard direct-response implementation of a fixed RPD. The payoff matrix is varied between-subject following four treatments. RPD lengths are fixed at session level and matched across treatments. A total of four different length schedules will be run in this fashion.
(3) Auxiliary measures of risk- and ambiguity attitudes using a choice-list paradigm. 4 choice lists with a total of 60 decisions are administered.
(4) An auxiliary measure of social value orientation using the standard slider measure. 6 slider items are administered.
Post Session: Demographic survey
Payment: Randomized incentive scheme, one decision per part is paid. All payment-related feedback is withheld until the end of session.
Experimental Design Details
Motivation and Explanation of Design:
The theoretical backbone of the study is Blonski and Spagnolo's (2015) ''riskiness" which implies a delta-parametrized mapping between CGs and RPDs, and thereby allows us to connect individual heterogeneity regarding the risk/efficiency trade-off in CGs to individual heterogeneity regarding the initial cooperation decision in RPDs. CGs and RPDs in my design are on matched scales according to this mapping. The CG scale relates off-diagonal payoffs to switching probabilities according to Harsanyi and Selten's risk dominance criterion (symmetric 2x2 version). The RPD scale relates variation in the sucker's payoff to the analogous switching probabilities according to Blonski and Spagnolo's ''riskiness".
The CG scales are implemented in Part 1 using a choice-list paradigm. That is, subjects make decisions with no feedback for CGs with varying off-diagonal payoffs that induce a monotonous schedule of switching probabilities. Similar to a risk or ambiguity MPL, there should be a unique game per scale at which an individual switches away from the efficient to the inefficient equilibrium strategy. This gives a composite measure of risk attitude and belief heterogeneity as they drive individual heterogeneity in CG play.
The RPD scale is implemented direct-response using between-subject treatments varying the sucker's payoff, each subject facing 17 round-robin RPD matches with a fixed payoff matrix. This is done in order to minimize complexity and to allow subjects to familiarize with the game structure. Naturally, repeated matches and between subject observations put restrictions on the strength of the experimental test. To alleviate confounding spillovers between matches, all subjects in a session face the same schedule of RPD lengths. Those lengths are balanced across treatments. Sucker's payoffs in the different treatments are chosen to investigate environments in which equilibrium cooperation is high-risk and low-risk, as well as settings where the riskiness of cooperation is just below and just above the critical switching point of 1/2, which, as Blonski et al. (2011) have demonstrated, marks a break-point for empirical cooperation rates at population level.
This setup allows to test the "riskiness" mechanism using in a more or less strict reading of the theory. At population level, Parts 1 and 2 examined in isolation allow to replicate the common findings from the experimental literature on CGs and RPDs, respectively. Matching of results between Part 1 and Part 2 allows for a direct test of "riskiness theory": The minimum bar is a monotonous relationship between Part-1 switching points and propensity for initial cooperation in the RPD. A stronger test comes from the search for individual-level breakpoints: That is, Part-1 switching points should allow us to predict what individual is going to cooperate at the outset of a fixed RPD based on that RPD's "riskiness of cooperation".
A common finding in the previous experimental RPD literature is the insignificance of risk attitudes and social value orientation as predictors of individual differences in cooperation rates. Nevertheless, Parts 3 and 4 are included to control for these potential confounds while investigating the main hypotheses. To get closer to the type of uncertainty that players face in their strategic decisions in Part 1 and Part 2, I add an MPL using ambiguous gambles. Risk and ambiguity measures are implemented according to the ORIV paradigm introduced by Gillen et al. (2019). SVO is measured using the primary items of Murphy et al.'s (2011) slider measure.
Probabilities for ambiguous gambles are randomly drawn by a UCI administrative official with no information regarding the experimental protocol. All other randomization is computerized using native Python procedures or procedures from the Python library NumPy.
All game lengths for Part 2 were randomly drawn on 11/23/2019 using a numpy implementation of a negative Bernoulli process. Lengths and treatments were randomly assigned to session dates, subject to the balancing constraints mentioned in the design description.
All other computerized randomization is carried out in real time during sessions.
Game lengths and treatments for Part 2 are clustered at the session level and lengths schedules are balanced across treatments.
Was the treatment clustered?
Sample size: planned number of clusters
16 experimental sessions
Sample size: planned number of observations
Sample size (or number of clusters) by treatment arms
24 subjects per session
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
INSTITUTIONAL REVIEW BOARDS (IRBs)
UCI Office of Research Institutional Review Board
IRB Approval Date
Post Trial Information
Is the intervention completed?
Is data collection complete?