(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?
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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.
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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