Firms compete in a market for tablet computers, where in each round each firm chooses between a Clean and a Dirty technology. The Dirty technology lowers production costs, but increases pollution—increasing healthcare costs for all—and its widespread use leads to more intense price competition.
Individual payoff maximization leads to the excess pollution, as players do not internalize their pollution's negative externalities on others.
Payoffs equal profits minus healthcare costs. With #Clean equaling the number choosing Clean, profits are (1.5#Clean)×10 for choosing Clean and (1.5#Clean)×100 for choosing Dirty. Number choosing Dirty (#Dirty) determines each firm’s healthcare costs=1.5#Dirty. As choosing Dirty increases everyone’s healthcare costs, including its own, a firm only partially internalizes the externality.
Equilibrium: With the default Group Size of 15, one firm chooses clean in equilibrium. The following table identifies the Nash equilibrium (in terms of number of firms choosing clean) as we vary Group Size. (With Group Size of 13 or smaller, no firms choose clean in equilibrium.) Most groups will qualitatively converge to equilibrium play in 3–5 rounds.
|Size||# Clean||Payoffs Clean||Payoffs Dirty|
Efficiency: The efficient outcome depends on group size. With 8 or fewer firms, two firms choosing dirty maximizes total payoffs. With 9 through 17 firms per group, one firm choosing dirty maximizes total payoffs. With 18 or more firms, total payoffs are maximized when all firms choose clean. (For a fixed number of firms choosing dirty, total external costs increase with the total number of firms.)
The first graph, showing the payoffs from each action as a function of the number of other firms choosing Clean, helps establish the Nash equilibrium. Below is the chart for 15 firms. If 0 of the 14 other firms chooses Clean, then choosing Clean gives you a higher payoff, bringing the total to 1. If 1 of the 14 other firms choose Clean, then choosing Dirty gives you a higher payoff, thus keeping the total choosing Clean at 1.
The next table showing for each round the average number choosing each action across all groups, highlights the extent to which your players converged to the Nash equilibrium.
The final table allows you to focus on the distinction between the efficient outcome maximizing total surplus and the Nash equilibrium. The first two rows show these benchmarks, identifying for each the number choosing clean, and the payoff to each choice. The final column is the weighted average payoff measuring total surplus.
Beneath these benchmarks are entries for each round for all the groups. Sorting on round allows you to focus on round 5 and discuss how payoff maximization drives play away from the efficient outcome.