The payoff matrix below lists the total revenue earned by Hailey and Bailey as a

Question

The payoff matrix below lists the total revenue earned by Hailey and Bailey as a function of how much they sell. Payoffs are written as

2) The "payoff matrie below lis thc total evenue camed by Haile and Bil s a finction of how much they both sell. Payoffs are written as (7,laley, kiley) Bailey 94 -5 6 q2 (16, 16) (15, 21) (12,24) (10,25) (8, 24) Hailey 3 (21, 14) (8, 18) (5, 20) (12, 20) (9, 18) q4 (24, 12 (20, 15) (16, 16) (12, 15) (8, 12) q-5 (25, 10) (20, 12) (15, 12) (10, 10) (5, 6) q-6 (24, 8) (18, 9) (12, 8) (6, 5) (0, 0) a) Find and circle the strategy that maximizes the TOTAL PROFIT, i.e. the sum of Hailey and Bailey's profits. We'll refer to this as the "coperative" solution. b) Using the "underline" method, determine if either Hailey or Bailey can make a higher profit if the other player plays the "cooperative" solution c) Will Hailey and Bailey cooperate? Why or why not? (Assume they are rational and answer in 4 sentences or fewer). d) Find the Nash equilibrium of this game. How much cider will each player bring, and what will their individual payoffs be?

Explanation / Answer

A) Total Profit herr means combined profit of A and B. From the above payoff matrix it can be observed that there are more than one bundles in which profit is maximised which are mentioned below:-

1) When Hailey is at q4 and Bailey is at q2.

2)When Hailey is at q3 and Bailey is at q3.

3)When Hailey is at q2 and Bailey is at q4.

B) If we consider the situation of co-operative solution then each bundle of Hailey and Bailey will have the same values ie, (16,16), (18,18) etc. But in these cases the profit will not be maximised. Thus, if Hailey and Bailey play cooperative solution the will not make higher profit.

C) Being Rational means to make optimum choices irrespective of other choice. Thus if each player is rational it will not lead to maximisation of total profit. Therefore they will not cooperate.

D) Equilibrium refers to a situtaion where each player gives best response to the other players stragety. Thus, from Haileys side equilibrium will be:-

16 at q2, 18 at q3, 24 at q4, 25 at q5, 24 at q6

And from Bailey's side it will be:-

16 at q2, 21 at q3, 24 at q4, 25 at q5, 24 at q6

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