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Alice and Bob participate in a gameshow with the following rules : each participant (Alice and Bob) says an integer between 1 and 4 (i., 1, 2, 3, or...
Alice and Bob participate in a gameshow with the following rules
:a. each participant (Alice and Bob) says an integer between 1 and 4 (i.e., 1, 2, 3, or 4).
b. They both win $x where x is the smallest number stated (e.g., if Alice says 3 and Bob 2, they get$2)
c. The person that reported the higher number has to pay back 10 cents to the host. If there is a tie, no one pays anything back.
Solve the game using backward induction. What is each player’s strategy?Â