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- 5,3 4,4 3,6 7,6 Find the pure strategy nash equilibriaFor the game given, find all Nash equilibria.For a two-player game, the payoff function for player 1 is V1(x1, x2) = x1 + 10x1x2and for player 2 is V2(x1, x2) = x2 + 20x1x2.Player 1’s strategy set is the interval [0,100], and player 2’s strategy set is theinterval [0,50]. Find all Nash equilibria.
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.Design the payoffff matrix of a game with no Nash Equilibria. The game should have 2 players, 2 strategies for each player, and the payoffffs for each player should be either 0 or 1.Find mixed-strategy Nash equilibria for the following two games.
- The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?Parameter z = 1 How many pure strategy profiles exist in this game?Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)