Assume that both Apple and Samsung have a marginal cost of 20. Apple’s payoff function is VA(PA, PS) = (PA - 20)(100 - 2PA + PS), whereas Samsung’s payoff function is VS(PA, PS) = (PS - 20)(100 - 2PS + PA). Find all Nash equilibria.

Assume that both Apple and Samsung have a marginal cost of 20. Apple’s payoff function is VA(PA, PS) = (PA - 20)(100 - 2PA + PS), whereas Samsung’s payoff function is VS(PA, PS) = (PS - 20)(100 - 2PS + PA). Find all Nash equilibria.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

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Question

Assume that both Apple and Samsung have a marginal cost of 20. Apple’s
payoff function is
V^A(P^A, P^S) = (P^A - 20)(100 - 2P^A+ P^S),
whereas Samsung’s payoff function is
V^S(P^A, P^S) = (P^S - 20)(100 - 2P^S+ P^A).
Find all Nash equilibria.

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