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15. In a gambling game, Player A and Player B both have a $1 and $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills 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 table for this game. The values should be expressed as the gains (or Losses) for Player A.
Player A Match Do not Match
Match -$1, $6 $1,$5
Do not Match $1, $5 6$, -$5
b. Is there a pure strategy? Why or why not?
Yes there is a pure strategy because we can get a pure strategy equilibrium here.
c. Determine the optimal strategies and he value of this game. Does the game favor one player over the other?
Optimal Strategy can be called nash equilibrium where do no match and match is an option. This game favours A over B as he loses just $1 and gains $5.
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.
Then there is a risk as player A can lose his $1 most of the times. In such a case player A can also play his bill 50% of the times. It is important to follow an optimal strategy because then no player wants to deviate from that strategy and that strategy maximizes the welfare of both players.
18. Dante Development Corporation is considering bidding on a contract for a new office
building complex. Figure 21.9 shows the decision tree prepared by one of Dante's analysts.
At node 1, the company must decide whether to bid on the contract. The cost of preparing
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