Payoffs, Beliefs, and Cooperation in Infinitely Repeated Games

In our model (see Andres et al., 2023), we show that a player's belief about the probability of cooperation by their opponent moderates the effect of changes in the payoff parameters on cooperation in a prisoner's dilemma. If beliefs are optimistic, increasing the gain from unilateral defection has a large negative effect on cooperation, while increasing the loss from unilateral cooperation has a negligible effect. However, if beliefs are pessimistic, increasing the gain has only a negligible effect, while increasing the loss has a large negative effect on cooperation.

Participants in the experiment face different versions of the infinitely repeated prisoner's dilemma game. We induce beliefs by informing participants truthfully that we will match them to a partner only after they have chosen their strategy in the infinitely repeated game and by telling them ex ante the probability that we will match them to a partner who plays Grim or AlwaysDefect, respectively.

For more details, see the accompanying document.

2024-01-14

2024-02-13

Differences in the critical discount factors between the Base game and the HighGain game, and between the Base game and the HighLoss game. (-1,1)

For more details, including the formal definition of the outcome variables, hypotheses, planned statistical analyses and power, see the accompanying document.

All participants choose strategies in three different prisoner's dilemma games that vary the stage-game payoff-parameters. Participants play infinitely repeated versions of all three games. For each of the stage-games, participants choose among the two strategies Grim and AlwaysDefect. They make this choice for nine possible discount factors {0.1,...,0.9}. We compare three treatments in which beliefs vary exogenously between participants.

For more details, including details of the experimental setup, parametrization, treatment variations, filtering rule and instructions, see the accompanying document.

Randomization by computer for each individual in each session.

Individual.

No

250 individuals.

250 individuals. These refer to individuals for which critical discount factors, and, thus, our outcome variables, can be computed. See the Section "Filtering Rule" in the accompanying document for more details.

About 83 individuals per treatment. Exact numbers depend on the realized random draws by the computer.

We have powered the study for an approximate Cohen's d of 0.5. Power analysis was conducted using a Monte Carlo simulation of the underlying data generating process. For more details, see the accompanying document.