In: Economics
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 |
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.