Suppose that there are two firms in a market, firm 1 and firm 2. The market is declining in size. The game starts in period 0, and the firms can compete in periods 0, 1, 2, 3, ... (i.e., indefinitely) if they so choose. Duopoly profits in period t for firm 1 are equal to 105 −10t, and they are 10.5 −t for firm 2. Monopoly profits (those if a firm is the only one left in the market) are 510 −25t for firm 1 and 51 −2t for firm 2. At the start of each period, each firm must decide either to “stay in” or “exit” if it is still active (they do so simultaneously if both are still active). Once a firm exits, it is out of the market forever and earns zero in each period thereafter. Firms maximize their (undiscounted) sum of profits. What is this game’s subgame perfect Nash equilibrium?
Suppose that there are two firms in a market, firm 1 and firm 2. The market
is declining in size. The game starts in period 0, and the firms can compete in periods 0, 1,
2, 3, ... (i.e., indefinitely) if they so choose. Duopoly profits in period t for firm 1 are equal
to 105 −10t, and they are 10.5 −t for firm 2.
one left in the market) are 510 −25t for firm 1 and 51 −2t for firm 2. At the start of each
period, each firm must decide either to “stay in” or “exit” if it is still active (they do so
simultaneously if both are still active). Once a firm exits, it is out of the market forever and
earns zero in each period thereafter. Firms maximize their (undiscounted) sum of profits.
What is this game’s subgame perfect Nash equilibrium?
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