integer), to spend on cleaning their apartment. The payoff (per unit) to roommate i = 1,2 is given by the following function: if ji a) Set-up this problem as a two-person zero-sum game. b) Using the appropriate game theory techniques, determine the optimal mixed strategies to each player. c) Determine and interpret the value of the above game.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. Suppose two roommates i = 1,2 must decide how much time, 5< tį < 10 (and
integer), to spend on cleaning their apartment. The payoff (per unit) to roommate
i = 1,2 is given by the following function:
(20i
Pij
(50j – 30i if j 2i
if j<i
a) Set-up this problem as a two-person zero-sum game.
b) Using the appropriate game theory techniques, determine the optimal mixed
strategies to each player.
c) Determine and interpret the value of the above game.
Transcribed Image Text:1. Suppose two roommates i = 1,2 must decide how much time, 5< tį < 10 (and integer), to spend on cleaning their apartment. The payoff (per unit) to roommate i = 1,2 is given by the following function: (20i Pij (50j – 30i if j 2i if j<i a) Set-up this problem as a two-person zero-sum game. b) Using the appropriate game theory techniques, determine the optimal mixed strategies to each player. c) Determine and interpret the value of the above game.
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