Question

Find all symmetric mixed strategy Nash equilibria of the 3-player game: Hint: The quadratic equation in p factors into linear expressions each with constant term -2

Answer 1

To find the symmetric mixed strategy Nash equilibria, set the demand and supply equations equal to each other and solve the resulting quadratic equation.

Step-by-step explanation:

To find the symmetric mixed strategy Nash equilibria of the 3-player game, we need to solve the system of three equations and three unknowns. Since Qd = Qs, we can set the demand and supply equations equal to each other:

16 - 2P = 2 + 5P

By rearranging the equation and combining like terms, we get a quadratic equation:

7P^2 + 3P - 14 = 0

Using the quadratic formula, we can find the values of P that satisfy the equation. In this case, the quadratic equation has two distinct real roots:

P ≈ -2.05, P ≈ 0.45

These values of P represent two possible symmetric mixed strategy Nash equilibria for the game.