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Consider two identical firms (A and B), each with a constant marginal cost of 10 and zero fixed costs. The inverse market demand function is: .
- Derive the Cournot reaction functions for both firms and solve to find the output produced by each
- Explain what would happen if the two firms now have different
- Return to the case where each firm has a constant marginal cost of 10 and zero fixed costs. Assuming that firm A is now the Stackelberg leader and firm B is the follower, find the level of output that both firms will now
- Why there is a difference between the Cournot and Stackelberg equilibrium output levels and prices and what the implications are for the profits made by each firm?
- If the two firms form a cartel and act as a profit maximizing monopolist, what level of profits would each make?
Does firm 1 have an incentive to deviate from the cartel? If firm 1 deviated from the cartel, state how much the deviation quantities and profits for each firm would be and the market price?
Consider a simultaneous game in which both players choose once between the actions of ‘Cooperate’ denoted by C and ‘Defect’ denoted by D. Suppose the following payoffs in the game: If both players play C, each gets a payoff of 1; if both play D, both players get 0; and if one player plays C and the other plays D, the cooperating player gets while the defecting player gets .
- Illustrate the payoff matrix for this
- What restrictions on would you have to impose in order for this game to be a Prisoner’s Dilemma?
Now consider a repeated version of this game in which players 1 and 2 meet twice. Suppose you are player 1 in this game and you knew that player 2 would co-operate in round 1 and then copy what you do – known as a ‘Tit-for-Tat’ player.
- Assuming you do not discount the future, would you ever cooperate with this player?
- In the repeated game with three encounters, what is the intuitive reason why you might play D in the first stage?
- Suppose that each time the two players meet, they know they will meet again with probability . Explain intuitively why ‘tit-for-tat’ can be an equilibrium strategy for both players if is relatively large (i.e. close to 1) but not if it is relatively small (i.e. close to 0).
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