Consider a game of rock-scissor-paper. There are two players, player 1 and player 2,and the winner receives $1 from the loser (if they draw, nothing happens). They playthis game simultaneously.1. What kind of game is this? Express this game in normal form.2. What are the set of possible actions and strategies?3. Find all Nash equilibria of this game
Intermediate MicroeconomicsProblem Set 10.Submission options:• in person during lectures or TA sessions;• in Xiaoye Liao’s mail box at 19 West 4th, 6th Floor;• (less recommended) e-mail Xiaoye Liao atxl775@nyu.edu– in that case, be sure to use the subject line: “Submission Problem Set 10â€.Exercise 1Consider a game of rock-scissor-paper. There are two players, player 1 and player 2,and the winner receives $1 from the loser (if they draw, nothing happens). They playthis game simultaneously.1. What kind of game is this? Express this game in normal form.2. What are the set of possible actions and strategies?3. Find all Nash equilibria of this game.Exercise 2Consider a game represented by the following payoff matrix. Find all pure strategyNash equilibria. UMD LCR?10, 0 ?10, ?1 ?10, ?1?8, ?8 0, ?102, ?14, 57, ?101, 1 Exercise 3Consider a game represented by the following payoff matrix. There are two firmscompeting in a duopoly market. Each should decide how much to produce simultaneously and their profits are given in the matrix. Find all pure strategy Nash equilibria.25355010025125, 125100, 14063, 125?63, ?25035140, 100105, 10553, 75?123, ?35050125, 6375, 530, 0?250, ?500100 ?250, ?63 ?350, ?130 ?500, ?250 ?900, ?900 1 Exercise 4Consider two players simultaneously deciding whether to contribute to a public good— the good is said to be public because, if it is made available, a player who free-ridesby paying nothing gets just as much pleasure from its enjoyment as a player who paidfor it. If at least one player contributes to the construction of the public good, bothplayers will enjoy a payoff of four from the public good. To ensure the public goodis constructed, player 1 must pay c1 or player 2 must pay c2. Assume that c1
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