Please provide working-out/ explanation for the correct answer. 9. Two players,

Question

Please provide working-out/ explanation for the correct answer.

9. Two players, A and B, play a simultaneous move game, each of which has two strategies, R or L. If both play R, each will get a payoff of 10. In contrast, if both play L, each will get 5. If both of them play differently, the one who plays R will get 15, while the one who plays L will get 0. Now suppose the game changes. Suppose A has the right to choose his strategy first, then after observing A's choice, B chooses his strategy. In the equilibrium, how much does A gain from the right to choose his strategy first? (b) 5 (c) 10 (d) 15 (e) None of the above

Explanation / Answer

Strategies and the outcomes:-

(i). If both play 'R'- A and B get 10 payoff each

(ii). If both play 'L'- A and B get 5 payoff each

(iii).If both play differently, the one who plays 'R' gets 15 while the one who plays 'L' will get 0

Now in the new game where A chooses his strategy first and B chooses his strategy after observing A's choice.

The second option (i.e) choosing strategy ii or R for both will be the best option for A as he does not lose out any and equalizes both players' gain. Otherwise he stands to lose as B's choice will be based on A's move.

Hence, A gains 0 from the right to choose first.

Answer: option (a) = 0

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