Math Home Work Help

(1) Consider the 3 *3 two-person non-zero-sum game with payoff matrix: (3; 2) (3; 0) (2; 2) (1; 0) (3; 3) (0; 3) (0; 2) (0; 0) (3; 2) Find all the Nash equilibria (pure and mixed) of the game. Hint: There is no strict domination here, but what can you say about a Nash equilibrium which gives nonzero weight to the second strategy of the first player? (2) A war of [login to view URL] players are involved in a dispute over an [login to view URL] value of the object to player1 is V1>[login to view URL] is modeled as a continuous variable that starts at 0 and runs indefinitely .Each player chooses when to concede the object to the other player; if the first player to concede does so at time t ,the other player obtains the object at that time. If both players concede simultaneously, the object is split equally between them, player1 receiving a payoff of V1/[login to view URL] is valuable: until the first concession each player loses one unit of payoff per unit of time. Formulate this situation as a strategic game and show that in all Nash equilibria one of the players concedes immediately. Also Considering this game again as an NTU cooperative game , describe the feasible payoff set. Describe all Pareto optimal payoff vectors. (3) Let us consider a general sum game m×n game. a)Prove that for a fixed p∈∆m the set of points {q∈∆n:(p,q)is a Nash equilibrium.} is convex. b)Show that the set {(p,q)∈∆m×∆n:(p,q)is a Nash equilibrium.} does not have to be convex. My budget for this job is 12USD. Do not if you are not agreed.