4/15 In a gambeling game player A and player B both have a $1 and $5 bill. Each

Question

4/15

In a gambeling game player A and player B both have a $1 and $5 bill. Each player selects one of the bills. Each player selects one of the bills without the other player knowing the bill selected. If the bills do not match, player A wins player B's bill. If the bills match player B wins player A's bill.

a. Develop the game theory for this game. The values should be expressed as the gains or losses of player A.

b. Is there a pure strategy? Why or why not?

c. Determine the optimal stratagies and the value of this game. Does the game favor one player over the other?

d. suppose player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should player A do to improve player A's winnings? Comment on why it is important to follow an optimal game theory strategy?

Please show all work

Explanation / Answer

A)Player B

Player A Match Do not Match

Match - $1, $6 $1,$5

Try not to Match $1, $5 6$, - $5

B)Yes there is an immaculate methodology since we can get an unadulterated system balance here.

C)Optimal Strategy can be called nash harmony where do no match and match is a choice. This diversion supports An over B as he loses just $1 and increases $5.

D)Then there is a danger as player A can lose his $1 the greater part of the times. In such a case player A can likewise play his bill half of the times. It is vital to take after an ideal system since then no player needs to go amiss from that technique and that methodology boosts the welfare of both players.

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