Suppose two entities are considering collusion - to make things 'legal', consider a situation similar to OPEC, except with only two countries: Saudi Arabia and Indonesia. The two countries have negotiated an agreement to restrict their production of petroleum. If both countries follow the agreement, the market price of petroleum will be high and both countries will make $100 million per year. If one country reneges and produces more petroleum than dictated in the agreement, then the market price will decrease. However, the increased production will offset the lower price for the country that reneges so that country will make $120 million per year, while the country who adhered to the agreement will make $75 million. If both countries renege on the agreement then the market price will drop further and both countries will make $80 million per year. The game is illustrated in the table below, with Indonesia's payoff listed first and Saudi Arabia's payoff listed second in every pair:
|
|
Saudi Arabia
|
|
Adhere
|
Renege
|
|
Indonesia
|
A
|
100, 100
|
75, 120
|
|
R
|
120, 75
|
80, 80
|
Find the Nash Equilibria of this game.
Suppose the game was repeated indefinitely. Explain how if both countries follow a trigger strategy in which they adhere in the first period and continue to adhere to the agreement as long as the other country has always adhered but will renege otherwise leads to a long-term collusive arrangement. consider one country following the trigger strategy and determine what happens to the other country's payoff if it decides to deviate from the strategy - to play renege. What are the payoffs in that period and in all future periods?