Explain and graphically represent the equilibria of the Cournot and Bertrand duopoly models. Indicate if they are Nash equilibria and why. Reason your answer.
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Exercise A.4
Explain and graphically represent the equilibria of the Cournot and Bertrand duopoly models. Indicate if they are Nash equilibria and why. Reason your answer.
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- . OPEC, the Organization of Petroleum Exporting Countries, was founded in 1969. Their original objective was to form a cartel to increase the price that they receive for their oil exports. Create a prisoner’s dilemma type game for two large members of OPEC (e.g. Saudi Arabia and Indonesia). Create numbers, where payoffs are total annual oil export revenues for each of these two countries. Verbally explain how you got your numbers. Find the Nash equilibrium. Based on this model, what strategy is in the oil exporters’ best interest (Nash or otherwise)? How do they make it happen? Create another prisoner’s dilemmamodel for all of OPEC on one side, and all non OPEC oil exporting nations on the other side. Create numbers, where payoffs are total annual oil export revenues for each of the two sides. Verbally explain how you created your numbers. Also create your numbers applying the fact that OPEC’s total production capacity is greater than total non OPEC exports…Please look at the payoff matrix below which shows the benefits that would accrue to each player in a 2-player.non-sequential, non-repeated game. a) Identify the collusive (cooperative) equilibrium. b) Identify the secure strategy (maximin) equilibrium c) Identify the maximax equilibrium d) Identify the Nash equilibrium Apple Inc. Strategy 1 Strategy 2 Strategy 3 20 40 60 60 1000 200 Strategy A 70 50 90 Banana Inc. 400 70 300 Strategy B 40 80 100 90 150 80 Strategy CAnswer all the questions, show all the working. Consider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.
- し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?"Set up the oligopoly method and explain the strategies and you reach the nash equilibrium? "1. Draw a normal form for this tree. 2. Find all the subgames in the tree. 3. Find SPNE (Subgame Perfect Nash Equilibrium) of the tree and explain how it works.
- • (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)Exercise A.5 Discuss the main similarities and differences between Cournot's and Bertrand's oligopoly models. Explain why different balances are reached. Represent graphicallyConsider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.
- Class Exercise Chapter 13: Game Theory Two firms are in the chocolate market. Each can choose to go for the high end of the market (high quality) or the low end (low quality). Resulting profits are given by the following payoff matrix: Firm 2 Low -20, -30 High 100, 800 Firm Low 1 High 900, 600 50, 50 a. What outcomes, if any, are Nash equilibria? b. If the managers of both firms are conservative and each follows a maximin strategy, what will be the outcome? 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 persuade it to collude?Please 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.Micro Nash game theory Show that if in a game G, the sets of actions (A i) i in N are compact, and the payment functions (u i) i in N are continuous, then for all i in N, the application of Best response has a closed graph. Conclude that the application of best response has a closed graph.