2. Suppose X and S are fighting over the 100 dollar bill they found on the road. S, who holds the bill in her hand offer

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2 Suppose X And S Are Fighting Over The 100 Dollar Bill They Found On The Road S Who Holds The Bill In Her Hand Offer 1 (47.03 KiB) Viewed 36 times

2. Suppose X and S are fighting over the 100 dollar bill they found on the road. S, who holds the bill in her hand offers to give it to S on the condition that S is able to "seek it". S prepares 4 covered boxes labeled A, B, C, D and arranges them in straight line. S tells X that she has hidden the 100 dollar bill in one of the four boxes without him noticing her do so. X must open one (and only one) of the boxes. If X finds the bill, he gets to keep it. If he doesn't S gets to keep it. (a) Write down the strategic representation of this game. Does this game have a pure-strategy Nash equilibrium? (b) Find the mixed-strategy Nash equilibrium. (c) Suppose it is commonly known that S likes the letter 'B' and would get extra satisfaction from putting the money in box B. Let this satisfaction be monetarily equivalent to receiving 50 additional dollars over and above any money received in the game. How does S's preference for the letter 'B' affect the equilibrium mixing probabilities? Calculate the new equilibrium strategy profile. (d) What if S's extra satisfaction from selecting box 'B' is equivalent to receiving 100 dollars? How has the new equilibria changed and why? 18] [03+05+05 + 05 =