a) Clearly indicate the eliminated dominated strategies. Apply the EIE algorithm, and determine the solution set of the game in normal form. b) Assuming that each player would not choose strategies that are strictly dominated, determine the Nash equilibria of the reduced game
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- Explain all will rate what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibriumPlayers 1, 2, and 3 are playing a game in which the strategy of player i isdenoted yi and can be any nonnegative real number. The payoff function for player 1 is V1(y1,y2,y3) = y1 + y1y2 - (y1)2,for player 2 is V2(y1,y2,y3) = y2 + y1y2 - (y2)2,and for player 3 is V3(y1,y2,y3) = (10 - y1 - y2 - y3)y3.These payoff functions are hill shaped. Find a Nash equilibrium. (Hint: Thepayoff functions are symmetric for players 1 and 2.)Consider the two-person Stag Hunt game. First, find each player’s best response functions; then plot the best response functions and find all Nash equilibria, including both pure-strategy and mixed-strategy equilibria.
- Is the set of SPE of any extensive form game with perfect information is identical to the set of Nash Equilibria of the induced normal form game? If yes, provide a proof. If no, provide an explanation by illustrating a game. [Maximum word limit for this question is 80 words.]Consider a simultaneous move game between a union and a company. If both the parties bargain hard, each would gain nothing. If only one party bargains hard the accommodating party gets a profit of $1 million while the bargaining party gets a $5 million, while if they both accommodate, they each get $3 million. If the union leader has already sent strikers to the picket line before entering negotiations, the union has a. Eliminated half of the strategies of the game b. Forced the firm to choose the best response in the union’s best interest c. Made it in the firm’s best interest to accommodate their requests d. All of the aboveConsider a simultaneous move game between a union and a company. If both the parties bargain hard, each would gain nothing. If only one party bargains hard the accommodating party gets a profit of $1 million while the bargaining party gets a $5 million, while if they both accommodate, they each get $3 million. If the union leader has already sent strikers to the picket line before entering negotiations, the union has a. Eliminated half of the strategies of the game b. Forced the firm to choose the best response in the union’s best interest c. Made it in the firm’s best interest to accommodate their requests
- Consider the two-player game illustrated here. a. For each player, derive those strategies which survive the iterativedeletion of strictly dominated strategies.b. Derive all strategy pairs that are Nash equilibria.Suppose that there are only two firms in a market in which demand is given by p = 64 - Q, where Q is the total production of the two firms. Each firm can choose either a low level of output, qL = 15, or a high level of output, qH = 20. The unit cost of production for both firms is $4. Write down the normal-form representation of the game in which the strategic variable for each firm is the quantity of output and the firms make their choices simultaneously. Find the pure strategy Nash equilibrium of this game (quantities produced and market price).For the game in FIGURE 7.6, derive players’ best-reply functions, plot them as shown in Figure 7.5, and find the Nash equilibrium.
- Find mixed-strategy Nash equilibria for the following two games.1 \ 2 a b c A 2,2 2,1 0,0 B 3,1 3,0 1,3 C 1,3 3,2 3,1 a) Eliminate iteratively all strictly dominated strategies. b) Find all Nash equilibria. c) What is the player 1’s best response to the strategy σ2 = (z , ½ , ½ - z) of player 2, where z is a parameter that lies in the closed interval [0, ½]. d) Compute the payoffs to player 1 and to player 2 for their respective strategy profiles σ1 = (0,½,½) and σ2 = (½,0,½).Firm A Firm B Low Price High Price Low Price (2, 2) (10, −8) High Price (−8, 10) (15, 15) Suppose the game is infinitely repeated, and the interest rate is 10 percent. The firms are allowed to collude and make joint decisions. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats (by charging a low price), then the agreement is no longer valid and each firm may make their own independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.