Advance Microeconomics and Game Theory

Consider a market for a homogeneous good with demand function :

with , in which there are firms. In Bertrand competition each firm announce a price at which it is willing to sell. The firms that announce the lowest price share the demand equally and receive the profit on sales minus production costs. The other firms do not sell at all and therefore receive payment 0 "zero".

1. Suppose now that the cost function is . Describe the associated game.

2. Calculate the Walrasian equilibrium price . For a given price, firms maximize their profit and generate a supply as a function of price. is the price that equals total supply and demand.

3. Show that can be sustained as a symmetric Nash Equilibrium of the game.

Note: it is the continuation of the Bertrand exercise chapter 3 Osborne "an introduction to Game Theory"

It is the continuation of the "3.2.2 Example: duopoly with constant unit cost and linear demand function", page 62, MArtin j, Osborne "an introduction to Game Theory"

D: R+ + R. + a - bp if po a b D(P) = p = 0 if py b a, b> 0 C;(q) = =C C 2 D: R+ + R. + a - bp if po a b D(P) = p = 0 if py b a, b> 0 C;(q) = =C C 2