The prisoner's dilemma is the classic game depicting the tension between the common good and individual payoff maximization. Each student is matched with another over a number of rounds. In each round, each student sees the two-by-two matrix and each chooses between cooperate ("C") or defect ("D"). Actions and payoffs are revealed after each round.
Note that MobLab's Push and Pull game is a non-matrix version of a prisoner's dilemma.
In a one-shot prisoner's dilemma, defect is the dominant strategy. The Nash equilibrium is therefore for each player to defect despite the fact that cooperation is efficient (maximizes overall payoffs).
Indefinite repetition, especially when combined with communication, facilitates cooperative outcomes.
Our game uses the following parameters. One feature is switching from cooperate to defect increases a players own payoffs by less than in decreases the other player's payoffs (4 versus 8).
By default, each pair plays 5 rounds, which should lead to Nash-equilibrium play for most pairs by the final round, particularly if the number of rounds is announced in advance.
By reducing strategic uncertainty, allowing Chat will generally lead to more cooperative behavior. This will be especially true when the number of rounds is uncertain.
To implement an indefinitely repeated game, choose the Minimum Rounds, then set an Ending Probability less than 100%. For example, with Minimum Rounds equal to 3 and Ending Probability equal to 40, there is a 60% chance that the game proceeds to round 4. If so, there is then a 60% chance that the game proceeds to round 5, etc.
In the default game, cooperation can be a Nash equilibrium of the indefinitely repeated game—supported by a grim trigger strategy—as long as the ending probability is less than or equal to 50%.
The results screen presents a table and a chart.
The table indicates for each round the percentage of students choosing each action. However, this information may miss important heterogeneity between groups. For example, half playing cooperate and half playing defect could range from every group having one C and one D to half of the groups having two cooperators (and the other half having two defectors).
The chart presents this information in a slightly different way. It shows for each round the incidence of the three outcomes: both played Defect; both played Cooperate; and one played Defect while the other played Cooperate. It is likely that groups playing Cooperate/Defect in early rounds will convert to Defect/Defect in later rounds.
Note that the chart has dynamic elements. Click the checkboxes in the legend to hide a particular category. Also, hovering the cursor over a label in the legend highlights the corresponding bars in the chart.
By default, robots (i.e. automated players) choose randomly between cooperate and defect (i.e. Always Random). With the Robot Strategies drop-down menu, you can choose alternative strategies, including: