Answer the attached question (30%) Suppose there is a joint project that generates an amount 10 for each of theindividuals A and B, provided the sum total of A's and B's investments in the project isat least 7. Suppose A's investment is denoted by x and B's by y, where x and y can takeany values in {0,1,2,3,4,..,8,9,10}. A player always has to incur the cost of the investment(equal to a or y respectively) and gets the benefit if and only if the project goes ahead.Suppose each player is interested in his own net benefit (benefit-cost) and players choosetheir investment levels simultaneously. The following relate to pure strategies.(a) Is there a Nash equilibrium in which both players invest 0?(b) Is there a Nash equilibrium in which one player invests 0 and the other does not?(c) What is the lowest payoff a player can get in any Nash equilibrium?

Answered: (30%) Suppose there is a joint project…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Answer the attached question

(30%) Suppose there is a joint project that generates an amount 10 for each of the
individuals A and B, provided the sum total of A's and B's investments in the project is
at least 7. Suppose A's investment is denoted by x and B's by y, where x and y can take
any values in {0,1,2,3,4,..,8,9,10}. A player always has to incur the cost of the investment
(equal to a or y respectively) and gets the benefit if and only if the project goes ahead.
Suppose each player is interested in his own net benefit (benefit-cost) and players choose
their investment levels simultaneously. The following relate to pure strategies.
(a) Is there a Nash equilibrium in which both players invest 0?
(b) Is there a Nash equilibrium in which one player invests 0 and the other does not?
(c) What is the lowest payoff a player can get in any Nash equilibrium?

Expert Solution

Step 1

Nash Equilibrium Means an optimal solution in a non - cooperative games in which every player is lacking any incentives to change their initial strategy. In a Nash Equilibrium, a player does not gain anything from deviating from their chosen strategy.

Step 2

Answer a)

When the player invest 0 there is no Nash Equilibrium

There is no Nash Equilibrium when the players invest Zero

Net Benefit is equal to 0

Now, consider the following deviation:

Individual A invests Rs 3 and Individual B invests Rs 4 in the project.

Net Benefit of A = 10-3
= 7 > 0 ( when player invests 0)

Net Benefit of B= 10-4
=6 >0

Thus, both individuals have an incentive in the unilateral deviation.

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