Problem 1. Each of the three players chooses a real number between 1 and 10. Let s, denote the choice of the i-th player (i = 1,2,3). The payoffs of this game are determined as follows: • If S1 S283 ≤ 100 then i-th player receives s;. If $1$283 > 100 then all three players receive 0. Each player cares for only her/his payoff. (a) State the definition of a best response strategy for each of the three players, and that of a Nash equilibrium. (b) Calculate all Nash equilibria of this game.

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Chapter1: Combinatorial Analysis
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Problem 1. Each of the three players chooses a real number between 1 and 10. Let s, denote the
choice of the i-th player (i = 1,2,3). The payoffs of this game are determined as follows:
If $18283 ≤ 100 then i-th player receives s;.
If S1 S283 > 100 then all three players receive 0.
Each player cares for only her/his payoff.
(a) State the definition of a best response strategy for each of the three players, and that of a
Nash equilibrium.
(b) Calculate all Nash equilibria of this game.
Transcribed Image Text:Problem 1. Each of the three players chooses a real number between 1 and 10. Let s, denote the choice of the i-th player (i = 1,2,3). The payoffs of this game are determined as follows: If $18283 ≤ 100 then i-th player receives s;. If S1 S283 > 100 then all three players receive 0. Each player cares for only her/his payoff. (a) State the definition of a best response strategy for each of the three players, and that of a Nash equilibrium. (b) Calculate all Nash equilibria of this game.
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