In the following table, the profits from a duopoly model of competition are shown. Firms 1...

In the following table, the profits from a duopoly model of competition are shown. Firms 1 and 2 simultaneously choose the quantity of outputs to produce. Each firm is restricted to producing 25, 35, 50 or 100 units of output. Is there a Nash equilibrium? What is it? Briefly explain.

Firm 2

		Q2 = 25	35	50	100
	Q1 = 25	125, 125	100, 140	63, 125	-63, -250
Firm 1	35	140, 100	105, 105	53, 75	-123, -350
	50	125, 63	75, 53	0, 0	-250, -500
	100	-250, -63	-350, -130	-500,-250	-900, -900

Solutions

Expert Solution

First look at the strategy of firm 1. When firm 2 selects 25 units, firm 1 selects 35 units as its profit are 140 at highest. When firm 2 selects 35 units, firm 1 selects 35 units as its profit are 105 at highest. When firm 2 selects 50 units, firm 1 selects 25 units as its profit are 63 at highest. When firm 2 selects 100 units, firm 1 selects 100 units as its losses are lowest at 63.

Now look at the strategy of firm 2. When firm 1 selects 25 units, firm 2 selects 35 units as its profit are 140 at highest. When firm 1 selects 35 units, firm 2 selects 35 units as its profit are 105 at highest. When firm 1 selects 50 units, firm 2 selects 25 units as its profit are 63 at highest. When firm 1 selects 100 units, firm 2 selects 100 units as its losses are lowest at 63.

There is a single Nash equilibrium where both firms produce 35 units.

Rahul Sunny answered 2 years ago

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