Answered: Nash equilibria

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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you and a friend decide to run a three mile race. If you agree to run together, you keep up with him
for the first mile, but you overexert yourself and run the last two miles at slower paces on your own. To
make up for lost time, your friend runs the last two miles at a faster pace. Your mile times are 6:30, 7:00,
and 7:30. Your friend’s times are 6:30, 6:00, and 6:00. If you both agree to run on your own, you run a
constant pace of 7:05 while your friend runs at a constant pace of 6:05. If you want to run together but
your friend wants to run solo, he runs his constant pace of 6:05. You, on the other hand, want to show
him that you can run faster, but you end up overexerting yourself after the first mile. You run times of
6:20, 7:05, and 7:30. If he wants to run together but you do not, you both run at your pace of 7:05. This
situation can be turned into an economic game, with the payoffs the overall race times. You each want
to run the fastest time you possibly can.
(a) Who are the players in the game?
(b) What are the possible strategies for each player?
(c) Create a payoff matrix for this game, with the payoffs for each player being total time.
(d) Does either player have a dominant strategy? If yes, list who has a dominant strategy and what the
strategy is.
(e) Are there any Nash equilibria in this game? If so, what are they?

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