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 necessary. Then identify and eliminate any dominated strategies.