ECN 416 Game Theory and Economic Behavior-Assignment Problem

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ECN 416 - Game Theory & Economic Behavior, Arizona State University

Problem Set

1. Consider a sequential version of the Cournot quantity setting game. More precisely, assume that firm 1 picks its quantity q₁ first, then firm 2 observes firm 1's quantity decision, and then picks its own quantity q₂. Suppose the market demand is given by P = a - Q, where Q = q₁ + q₂, and a is a positive number. Each firm has a constant marginal cost, given by c, and has no fixed cost. (This game is called Stackelberg competition in the literature.) Find the equilibrium quantities by backward induction.

2. There are two plates of ice cream. The small plate contains 2 spoons of ice cream and the big plate contains 6 spoons of ice cream. Two friends, Bonnie and Clyde, have to decide who will get which plate. They both love ice cream and a player's payoff is the number of spoons he/she eats.

They play the following game: First, Bonnie offers Clyde one of the plates, keeping the other plate for herself. If Clyde accepts, each takes his/her agreed plate and eats the ice cream in it, and the game ends. If Clyde rejects, half of the ice cream in each plate suddenly melts (it's a hot day!). Then, Clyde offers Bonnie one of the plates, keeping the other plate for himself. If Bonnie accepts, each takes his/her agreed plate and eats the ice cream in it, and the game ends. If Bonnie rejects, the rest of the ice cream melts and they are left with no ice cream, and the game ends.

(a) Draw the extensive form game.

(b) Write the pure strategy sets for both players.

Reference no: EM132402532

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ECN 416 Game Theory and Economic Behavior-Assignment Problem : ECN 416 - Game Theory & Economic Behavior Assignment Help and Solutions, Arizona State University, US-Draw the extensive form game. Write the pure strategy.

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