Provide an example of a 2-player extensive form game when one of the players has 3 strategies, and for which the set of Nash equilibrium coincide with the set of Subgame Perfect Nash Equilibrium.

Consider the following game: PLAYER 2 Left Middle Right Up 0,0 2,5 5.4 PLAYER 1 Middle 1,2 7,3 4,3 Down 5,5 3, 1 2, 1 Which of the following statements is true? There are two Nash equilibria, and they are both Pareto efficient. There is a unique Nash equilibrium. There are two Nash equilibria, and they are both Pareto inefficient. There are two Nash equilibria, but only one is Pareto efficient. None of these.

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Let G be the following static game. Rose Colin A A (3,4) B (4,2) B (1,5) (0, 1) (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium of H. (You do not have to verify this.) Determine the expected payoffs of both players given that they choose their strategies according to this Nash equilibrium. (c) Draw the payoff polygon of H. Indicate on your diagram the points corresponding to the Nash equilibria of H, and the points corresponding to Pareto optimal solu- tions of H.

Assume a simultaneous-move game. ​     Firm B       Low Price High Price Firm A Low Price 10,10 100,2   High Price 2,100 90, 90   ​What is the Nash equilibrium of the game?

Consider the following two player game: Player 1 ABCD X 1,2 4,1 5,2 2,3 Player 2 Y 2,2 3.5 1 4,4 0.4 Z 5.1 3,3 7,0 7,5 a. Find the strategies that survive iterated elimination of weakly and strictly dominated strategies. b. Find the best responses to each strategy and find all (pure strategy) Nash equilibria.

What is the subgame perfect Nash equilibrium in the extensive form game below? Make sure your answer is formally correct. Player 2 255,255 Player I Player 2 Player I 15,256 16,3 2,4 3,1

Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.

Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land.                                                   Farmer 2   Farmer1                                                1 cow                  2+ cows                       1 cow                             8,8                    2,10                        2+cows                           10,2                     4,4   What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off)   The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…

In the following two-user game, the payoffs of users Alice and Bob are exactly negative of each other in all the combinations of strategies (a,a), (a,b), (b,a), (b,b). This models an extreme case of competition, and is called a zero-sum game. Please point out every pure-strategy Nash equilibrium of this game, and explain why it is. a b a (1, -1) (3, -3) (2, -2) (5, -5)