7) Two competing firms are each planning to introduce a new product. Each will decide whether to produce product A, product B, or product C. They make their choices at the same time. The resulting Payoffs are shown below: Firm 2 A B C A -10.-10 5,30 10, 20 Firm 1 B C 10,0 20, 10 -20, -20 -5,15 15,-5 -30, -30 a) What outcomes, if any, are Pure Strategy Nash equilibria (PSNE)? b) If both firms use maximin strategy, what outcome will result? c) What is the cooperative outcome? ( d) Which firm benefits most from the cooperative outcome? How much would that firm need to offer the other to encourage it to collude? f
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- Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.(2) Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below. Firm 2 A В C -10, -10 10, 0 20, 10 0, 10 -20, -20 15, -5 10, 20 -5, 15 -30, -30 А Firm 1 B C a. Are there any Nash equilibria in pure strategies? If so, what are they? b. If both firms use maxmin strategies, what outcome will result? c. If Firm 1 uses a maxmin strategy and Firm 2 knows this, what will Firm 2 do?rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
- Let G be the following static zero sum game. Rose ABCD А A 4 -2 Colin B C D -4 -3 L с -1 7 5 -2 5236 7123 -2 (a) Draw the movement diagram of G. (b) Using the method of iterated elimination of dominated strategies, find the smallest subgame of G from which the solution of G can be realized. (You do not have to find the solution of the game.)UofC Aggressive Restrained Aggressive 18, 26 29,47 MRU Restrained 45, 59 32, 23 Consider the case of a Sequential-Move game. Uofc moves First Part 1. Is UofC 's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) 1 Part 2. Is MRU's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) Number: Part 3. How much profit does UofC make under the Sub-game perfect Nash-Equilibrium? Number Part 4. How much profit does MRU make under the Sub-game perfect Nash-Equilibrium? Number15. Consider two competing firms, JR and OG. Suppose OG produces an estab- lished product and JR can either produce a clone or a differentiated product. If JR produces a clone, OG can either sue JR or not sue it. If JR produces a differentiated product rather than a clone, OG can either buy JR or not buy it. The two firms are in a non-cooperative game whose extensive form is rep- resented in the tree diagram below, where the payoffs on the right represent profits. -1 for OG 1 for JR sue OG don't -2 for OG clone sue 1 for JR JR don't clone 1 for OG -1 for JR buy OG don't buy 2 for OG 0 for JR If the two firms' managers are rational and recognize each other as rational, then (a) JR clones and OG sues (b) JR does not clone and OG buys (c) JR does not clone and OG does not buy (d) JR clones and OG does not sue (e) JR clones and OG sues with probability .5
- 3 1. Describe the bidding process by which the electricity generation sector provides electricity to pooling and balancing authorities. Additionally, show this process by building an electricity supply curve. a. What antitrust and regulation concerns are present at the wholesale stage of the electricity market? b. Describe a market design that reduces market manipulation in wholesale electricity markets. Show that the Nash equilibrium under this market design will result in generators bidding their true marginal cost of production. c. Describe a vertically integrated industry as it pertains to the electricity sector. d. Describe non-linear (two part) pricing as it pertains to retail electricity sales. What is the purpose of this pricing system?Name: 1. Consider the following simultaneous move game: a. 2.5 4 Row Top Up Down Bottom N 16xe mszbiM Left 5,5 2,6 3,1 3,5 Column Center 8,4 10,1 5,4 9,7 Middle (6,6 2,4 3,3 4,5 Right 5,4 2,4 16 3,4 20hunini 02:hobe Use the method of iterated elimination of dominated strategies to eliminate as many strategies as possible for each player. Briefly explain your steps. (4 marks) 26 5100W sed mexa pm/ ebul b. Using the method of best responses, find the Nash Equilibrium of this game. Mark the best response on the matrix and circle the NE. Briefly explain why this is a NE. (4 marks) anatibunenk c. Consider the outcome (Bottom, Center), briefly explain why this is NOT a Nash Equilibrium. (2 marks)60A- What is the dominant strategy for Firm B? What is the dominant strategy for Firm A? Explain
- 1. Consider the pricing game between firm 1 (row) and firm 2 (column) belowwhere each number represents the profits made by each firm.:Table 1: Pricing gameLow HighLow 288,288 360,216High 216,360 324,324 a) Point out the Nash equilibrium. Is this a unique Nash equilibrium?c) What type of commitment can firm 1 make to improve its pay-off?Can it be classified as a threat or promise? (Assume that the commitmentis credible.)d) How would you represent the game as a game tree with the option tocommit?2. Consider the signalling / production game with the order of play given below.Assuming that the signal is informative (i.e. education is sufficiently costly),how would you change the order of the game to make sure that poolingequilibriums are ruled out? Verbally motivate your answer.• Nature chooses ability of the workers a ∈ (H, L), ability is observed byworkers but not employers.• The worker choose an education level s ∈ (0, 1).• The employer offer contracts w(s).• The worker accepts or…c) Please find below Pricing options for firm A and B, along with individual payoffs (Firm A’s payoff/Firm B’s payoff)Firm BFirm APrice £2 Price £1Price £2 £10,000/£10,000 £5,000/£12,000Price £1 £12,000/£5,000 £6,000/£6,000Assume you are the pricing manager at Firm A;9i) What is your payoff for a ‘maximin’ strategy?ii) What is your payoff for a ‘maximax’ strategy? iii) Does a dominant strategy exist within this prisoners’ dilemma?2. Focus on the following Prisoner's Dilemma which is infinitely repeated. Find for what value of the discount factor the grim trigger strategy is a Subgame Perfect Nash Equilibrium of the game. Player 1 D C Player 2 D 0,0 -2,7 с 7,-2 5,5