Q1.

Give an example of any economic or social or biological phenomenon where the notion of a mixed strategy equilibrium is useful for understanding the phenomenon.

Consider the following 2 player normal form game. Player 1’s strategy set is {T, B} and

Player 2’s strategy set is {L, M, R}. Payoffs are given in the boxes where the first element refers to player 1’s payoff.

Compute a Nash equilibrium for this game. [25]

Q2

Consider an industry with the following demand curve

P = 100 – 2Q, where Q is total output produced.

Two firms serve the market. Firm 1’s constant marginal cost of production is 20 and firm 2’s constant marginal cost of production is 30.

Firms compete by choosing quantities (Cournot competition). Find the equilibrium price and profits.     If the two firms were to collude, what would be the market price and profits? Can such collusion work? [25]

Q3.

Kaushik Basu formulated a simple game called “The Traveller’s Dilemma” in 1994. Consider a version of this game, following Rubinstein (2006).

There are two players. Each of the players chooses an amount between $180 and $300.

Both players are paid the lower of the two chosen amounts.

Five dollars are transferred from the player who chose the larger amount to the player who chose the smaller one.