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- (a) What are the sets of pure strategies of players A and B?(b) Find the subgame perfect equilibrium(c) Provide a brief argument why the SPE is unique (i.e., why there are no more SPE, whether in pure or mixed strategies).Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?Two identical firms each have a cost function TC = 2y2 and the market demand for their output is P = -4Q+192a) Write the “best response†function for each firm.b) Find the Nash equilibrium in this model c) Show that if each firm produces 1 fewer units than the result in (b), both firms make more profit. Use this information to construct a normal form game. Explain why this game is a prisoner’s dilemma.
- Consider this extensive form game. The top number is player 1’s payoff, themiddle number is player 2’s payoff, and the bottom number is player 3’spayoff.a. Describe the general form of a strategy for each player.b. Find the SPNE.Whas is the dominant strategy and identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.Anashequilibriumisastrategyprofilesuchthat: a)Both players are playing a best response strategy b)Both players must be playing a dominant strategyc)Both players achieve their highest possible payoff d)a) and c) e)b) and c)
- The soft drink industry is dominated by TCCC and PSC. The market is worth $6 billion. Each firm can decide whether to advertise, but advertising costs $1 billion to any firm undertaking it. Moreover, advertising will create only negligible new demand as the market is already saturated. So, for the purpose of this question, assume that the market remains at $6 billion regardless of advertising. If one firm advertises and the other does not, then the former captures the whole market. If both firms advertise, then TCCC captures 60% of the market and PSC captures 40% of the market, but the advertising must be paid for. If neither firm advertises, then the market is again split 60:40, with 60% going to TCCC and 40% to PSC. 1. Draw the payoff matrix for this game where each player’s payoff is equal to the value of market it captures less the cost of advertisement. 2. Do any of the firms have dominant strategies? If so, what are they? Is there a dominant strategy equilibrium? If so,…Find the optimal strategy for the column player. 2 -1 -3 4 1 3Explain 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 equilibrium
- What is the secure strategy for player B in the game presented in TablePlease answer all parts. Two construction companies EdilA and EdilB take part in a race contract to build a school. Both can bid 1000, 2000 or 3000. The winner (the lowest offer) builds the school and pays 900 of costs. 1. When both bid the same amount, EdilA wins the contract. Find the Nash equilibrium. 2. Assume instead that when both bid the same, neither gets the contract, and furthermore suffer a penalty of 10. Find the Nash equilibrium. 3. Assume instead that when both bid the same, each builds half the school (but sustains 600 of costs, thus more than half). Find the Nash equilibrium. 4. Under the hypothesis of point 2 assume that EdilB can observe the offer made by EdilA before it makes its offer, and that EdilA anticipates that. Find the Nash equilibrium by backward induction of this sequential game.A) Focus on the strategic game at the lower-right side of the gametree. Find all the Nash equilibria for this subgame, including the mixed-strategyones. (b) Find all the subgame perfect equilibria for the entire game, allowingfor both pure and mixed strategies
