# Question

Consider the odds and evens game introduced in Sec. 15.1 and whose payoff table is shown in Table 15.1.

(a) Show that this game does not have a saddle point.

(b) Write an expression for the expected payoff for player 1 (the evens player) in terms of the probabilities of the two players using their respective pure strategies. Then show what this expression reduces to for the following three cases: (i) Player 2 definitely uses his first strategy, (ii) player 2 definitely uses his second strategy, (iii) player 2 assigns equal probabilities to using his two strategies.

(c) Repeat part (b) when player 1 becomes the odds player instead.

(a) Show that this game does not have a saddle point.

(b) Write an expression for the expected payoff for player 1 (the evens player) in terms of the probabilities of the two players using their respective pure strategies. Then show what this expression reduces to for the following three cases: (i) Player 2 definitely uses his first strategy, (ii) player 2 definitely uses his second strategy, (iii) player 2 assigns equal probabilities to using his two strategies.

(c) Repeat part (b) when player 1 becomes the odds player instead.

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