Consider a three-player game where the strategy of player i is ri ∈ [1,2]. Player 1’s payoff function is V1(r1, r2, r3) = 1 - r1 + 2r2 - 3r3, player 2’s payoff function is V2(r1, r2, r3) = 1 + r1 + 4r2 + 2r3, and player 3’s payoff function is V3(r1, r2, r3) = (3 - r1 - r2)r3. Find all Nash equilibria.

1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1

8.8

Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 6 units of utility, while the small rival suffers a loss of utility of 2. If the two companies select the same technology, Microsoft suffers a loss of utility of 2 while the rival gains 2 units of utility. Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously.   Microsoft Technology A Technology B Rival Technology A Rival:   , Microsoft   Rival:   , Microsoft   Technology B Rival:   , Microsoft   Rival:   , Microsoft   True or False: There is no equilibrium in pure strategies. True False Note:- Do not provide handwritten…