15. Which of the following statements about the 'Stag Hunt' game is true? (a) The pure strategy Nash equilibria can be Pareto ranked. (b) All players have a dominant strategy. (c) There cannot be a mixed strategy Nash equilibrium. (d) The surplus maximising outcome is not a Nash equilibrium. (e) None of the above.
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- Solve Both Questions!2. Do we depict the equilibrium of a game in pay-offs or strategies in Game theory? 3- 3. What is meant by the phrase, "Best Response of a player"? in Game Theory?QUESTION 1: Game theory a) What is the pure strategy Nash equilibrium outcome if there is one? b) Is this a socially optimal outcome? If not, which outcome is preferred? c) Do all three solution approaches for simultaneous games work independently (not together)? If not, which do not? d) Draw the game as a game tree (extensive form). e) Switch the payoffs in cells (A, A) and (D, D). What is the pure strategy Nash equilibrium outcome if there is one?1. Suppose Company A is about to play a game with Company B. The following facts are known about the two players. The first Company (Company A) is a row player and uses three different strategies i.e. (Strategy X, Strategy Y and Strategy Z). Whereas the column player (Company B) has two different strategies i.e. (M and N) that can be used accordingly. The payoff matrix is given in the table below. Player B Player A M N X -5 3 Y 3 -7 Z -6 5 Answer the following questions based on the information given above a. Determine the strategies of each firm using graphical technique b. Compute the value of the game.
- 1. With nash equilibrium, do you always choose the optimal strategy? 2. Can a game have more than one nash equilibrium?33. When neither player has a dominant strategy, A) game theory will not provide information.B) no Nash-Equilibrium exists.C) at least one Nash-Equilibrium exists.D) the game cannot be analyzed.8 Please use the game theory matrix to answer the following question We have 110,000 Homes • The low price is $79.95 and the high price is 10% more • Set up fees of $49.50 + $6.50 per subscriber The company's profit is based on its price and its competitor’s price: What is the contribution margin per house in each scenario? *Contribution margin = Price – total costs
- 10. Game theory terminology Select the term that best describes each definition listed in the following table. Definition Nash Equilibrium Dominant Strategy Collusion Tit-for-tat Strategy Payoff Matrix/Table Prisoners' Dilemma Game A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again A case in which individually rational behaviour leads to a jointly inefficient outcome A player's best choice, if it exists, regardless of his or her opponent's strategy4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.Which of the following gambles is “unfair”? a. A game that promises to pay you $1 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. b. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. c. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with an entry fee of $4.50 for the right to play. d. All of the above.
- 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 strategiesQuestion 4: (Answer in 200-400 words in total PLEASE ANSWER THIS HOMEWORK QUESTION The purpose of the Paris agreement was to set a coordination mechanism between countries and limit carbon emissions at a global level. In this period of climate emergency, high carbon emissions and the non respect of Paris agreement by numerous countries, have been criticized in the newspapers and described as dangerous for future generations. From a game theory perspective, respecting or not the Paris agreement can be modeled as a strategic game. Let’s assume that we have two countries who can choose between option 1: not respecting and exiting the Paris agreement (increase their carbon emission); and option 2: respecting the Paris agreement (limit their carbon emission). The following matrix gives the payoffs of each choice, where in each cell, the first number is the payoff of country A and the second number is the payoff of country B. Country B Repect the agreement Exiting the…6)Game Theory: The Prisoners’ Dilemma: Assume that the Wilson and Spalding athletic equipment companies are in a one-shot game for market share and profits, but that they have the option of choosing only one of two possible price strategies for basketballs: $20 or $80. Obviously if they choose different strategies, the firm with the lower price will win the entire market. The firms face the following payoff matrix (See Chap. 10). Wilson\ \Spalding Wilson $ 20 Price Wilson $ 80 Price Spalding $ 20 Price $ 400, $ 400 $ 1500, $ 0 Spalding $ 80 Price $ 0, $ 1500 $ 1000, $ 1000 What strategy will each firm choose? Why? Which strategy is dominant? Which strategy is preferred by each firm? What will be the outcome of the one-shot game? Where is the Nash equilibrium? Which outcome would be best for the two firms? What will happen if the game is repeated an infinite number of times?