3. (20 points) Consider the following simple version of a two-player poker game.

Question

3. (20 points) Consider the following simple version of a two-player poker game. Each player may be one of two types, strong (S) or weak (W). Each player knows his type, but not the type of his opponent. The probability that the opponent is strong is 3. The pot begins with two dollars. The players then simultaneously decide whether to call or fold. If a player calls, he adds 1 dollar to the pot. If a player folds, the plaver quits the game with pavoff zero. If one plaver calls and the other folds, the plaver that called wins all of the money in the pot, taking back his dollar and winning an additional two. If both plavers call, then the payoffs depend on the types of each plaver. If both players are of the same type, then they are equally likely to win the pot, giving each player a one half probability of winning the pot, worth 4; thus the player's payoff in this case is (4)-1-1. If one player is strong and the other is weak, then the strong player wins the entire pot, for a net payoff of 3. The weak plaver loses the dollar that she added to the pot, for a payoff of -1. The payoffs are summarized below If both players fold, payoffs are (0,0) If one folds and the other calls the folding player receives 0 and the calling player receives 2. If both call, then the pavoff is determined by the player tvpes. If b the payoffs are (1,1). If the types are different then the payoff of the strong player is 3 and the weak player is-1. oth types are the same, then We will look for an equilibrium in which a strong player always calls and a weak player calls with probability c. a) Explain why a strong player always calls, no matter what he or she expects the other player to do. You do not need to do anv math (b) Suppose Player 1 expects Player 2 to always call when strong and to call with probability c when weak. If Player 1 is weak, what is his expected payoff of calling? What is his expected payoff folding? What is the equilibrium value of c? (Hint: in order for a weak Player 1 to be willing to call with probability c. Plaver 1 must expect the same pavoff from calling and foldirn

Explanation / Answer

The picture is not visible. In case of a sequential game, the players move in order and so the correct option for the number of strategies will be give by D. But this will depend on the diagram which is not clear. The strategies are one after the other.

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