Question

Suppose two oil-producing countries are interested in forming a cartel with the goal of colluding -– an agreement to raise oil prices (and profits) by limiting supply. Suppose, in each period, simultaneously choose between their individual options: to collude (Co) or to cheat (Ch) and over-produce, impacting the other nation's revenues (shown in the following matrix)

country A   Co 3,3    1,6,

                Ch 6,1    2,2

a. What famous game format does this game follow (or what game that we have played does it remind you of)? b. What is Country A’s best response to Country B’s choice to collude (limit supply)? c. Is there a strictly dominant strategy for either player? d. What is the Nash equilibrium of this game if it will be played only one period and that is common knowledge (be specific as to why)? e. Is there a Pareto efficient outcome of the game, if played only once? f. If this game were played for exactly 5 periods and that is common knowledge, would the two firms be able to sustain collusion? Why or why not? g. What is the Sub-game perfect Nash equilibrium if the stage game above is played exactly 5 times? h. Suppose the game will be repeated infinitely (as a stage game) and that both countries intend to use grim trigger strategies (such that a country will continue to collude, as long as the other country does, but if the other country ever cheats, the country will resort to cheating in every following period). If each country discounts future earnings according to discount rate=δt what is the payoff from colluding for each? What is the payoff of cheating from each, given that the other country plans to collude (by using the trigger strategy discussed above)? I. What range of discount rate=δt allows the two countries to sustain collusion? k. Suppose that there were only a 70% chance that the game would be repeated/continued in the following period. Would collusion be more or less likely than in the previous part (no calculation required)? Explain

Answer 1

a. The normal form game is similar to the prisoner's dilemma where each player's dominant strategy is to cheat than to collude. However, both player would get a higher payoff in case both collude which is Pareto efficient allocation.

b. If country B collude then player 1 that is country A would be better off choosing to cheat compared to collude as 6>3.

c. Each player's strictly dominant strategy is to cheat as given whatever other player does, each player is better off choosing to cheat compared to choosing to collude.

d. If it is a one period game and players playing a simultaneous game then each player would play its strictly dominant strategy .i.e.to cheat. Nash equilibrium is (to cheat, to cheat)