Question: Problem 8. Consider the following parlor game between two players. It begins when a referee flips a coin, notes whether it comes up heads or

Problem 8. Consider the following parlor game between two players. It begins when a referee flips a coin, notes whether it comes up heads or tails, and then shows this result to player 1 only. Player 1 may then (i) pass and thereby pay $5 to player 2 or (ii) bet. If player 1 passes, the game is terminated. However, if he bets, the game continues, in which case player 2 may then either (i) pass and thereby pay $5 to player 1 or (ii) call. If player 2 calls, the referee then shows him the coin; if it came up heads, player 2 pays $10 to player 1; if it came up tails, player 2 receives $10 from player 1. (a) Give the pure strategies for each player. (Hint: Player 1 will have four pure strategies, each one specifying how he would respond to each of the two results the referee can show him; player 2 will have two pure strategies, each one specifying how he will respond if player 1 bets.) (b) Develop the payoff table for this game, using expected values for the entries when neces- sary. Then identify and eliminate any dominated strategies. (c) Do there exist optimal pure strategies? If yes, find them. If no, find the optimal mixed strategies. What is the value of the game

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