Previous example incorporated a feature that is present in many oligopolies: Conflict between collective and individual interests. Duopolists’ collective interest: Form a cartel; restrict output to 30 each; share monopoly profit. (“Cooperate”) Each duopolist’s individual interest: “Whether or not my rival produces 30, I can increase my profit by producing 40.” (“Compete”)

So the duopolists are unlikely to sustain cooperation. Nash equilibrium (each produces 40) is a more likely outcome. Nash equilibrium: From duopolists’ point of view:... less favorable than cooperation (“monopoly”) -- because profit is lower. From “our” point of view (as widget consumers):... more favorable than cooperation -- more widgets at a lower price.

Conflict between collective and individual interests is a very common theme in economics. (Remember common resources (e.g. Ogallala aquifer) and the “tragedy of the commons.” Also OPEC and the world oil market.) Essential nature of these situations is described by a “game” economists call the “Prisoners’ Dilemma”... ( illustrating why cooperation is difficult to maintain even when mutually beneficial.

Prisoners’ Dilemma Detectives Andy Sipowicz and John Clark. My version -- based on “NYPD Blue” (my favorite show)

A murder has been committed in the 15th precinct. Clark and Sipowicz pick up two suspects (Bill and Jack) for questioning. Evidence on murder is thin, but suspects are found in possession of illegal drugs. Conviction on murder charge requires one (or both) suspects confess and testify against accomplice. Suspects are taken to different interrogation rooms and questioned separately.

Bill and Jack each have two strategies: “Confess”: confess own (minor) role in murder and testify against accomplice (the “trigger-man”). “Lawyer-up”: refuse to answer questions -- demand right to lawyer. Describe “game” situation using “payoff matrix” showing “payoffs” (prison sentences) for each player for any combination of strategies.

20 yrs., 20 yrs.1 year, life life, 1 year 5 yrs., 5 yrs. “Confess” “Lawyer-up” Jack “Confess” “Lawyer-up” Bill How is this “game” likely to be played? (Remember: Players have to choose strategies independently, with no communication between them.) (Note: In each cell of the table: 1st: Jack’s sentence. 2nd: Bill’s sentence.)

“Confess” “Lawyer-up” 20 yrs., 20 yrs.1 year, life life, 1 year 5 yrs., 5 yrs. “Confess” “Lawyer-up” Jack Bill (Note: In each cell of the table: 1st: Jack’s sentence. 2nd: Bill’s sentence.) Dominant strategy: A strategy that is best for a player, regardless of the strategies chosen by other players. Regardless of whether Bill “confesses” or “lawyers-up” Jack is better off “confessing.”

“Confess” “Lawyer-up” 20 yrs., 20 yrs.1 year, life life, 1 year 5 yrs., 5 yrs. “Confess” “Lawyer-up” Jack Bill (Note: In each cell of the table: 1st: Jack’s sentence. 2nd: Bill’s sentence.) “Confess” is a dominant strategy for Jack. “Confess” is a dominant strategy for Bill. Also notice: (“Confess,” “Confess”) is a Nash equilibrium.

“Confess” “Lawyer-up” 20 yrs., 20 yrs.1 year, life life, 1 year 5 yrs., 5 yrs. “Confess” “Lawyer-up” Jack Bill (Note: In each cell of the table: 1st: Jack’s sentence. 2nd: Bill’s sentence.) Bill and Jack both go to prison for 20 years even though there is another possible outcome (each “lawyers-up”) that both prefer. Conflict between collective and individual interests.

Our duopoly example has the features of Prisoners’ Dilemma. Players are firms 1 and 2. Instead of “Confess”: “Compete” -- produce 40 widgets/day Instead of “Lawyer-up”: “Cooperate” -- produce 30 widgets/day; that is, adhere to quota. Payoffs are profit levels.

“Compete” “Cooperate” Firm 1 “Compete” “Cooperate” Firm 2 “Compete” = produce 40; “Cooperate” = produce 30, adhere to quota. (Note: In each cell of the table: 1st: Firm 1’s profit. 2nd: Firm 2’s profit.) (180, 180) (160, 160)(200, 150) (150, 200) “Compete” is a dominant strategy for each firm. (“Compete,” “Compete”) is a Nash equilibrium. Cooperation ever possible?Repeated games.