AutoSave off) H ~ ~ Game theory questions-1 - Protected. . Saved to this PC Search File Home Insert Page Layout Formulas Data Review View Automate Help PROTECTED VIEW Be careful-files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. Enable Editing 31 vi XVfx A B C D E G M N 0 P Q Two firms, Small and Large, compete by price. Each can choose either a low price or a high price. The following payoff table shows the profit (in thousands of dollars) each firm would earn in each of the four possible decision situations: Large Low price High price Low price $200, $500 $600, $600 Small High price $0, $1,500 $400, $1,000 11 12 Part A: 13 Treating this as a one-shot simultaneous game, 14 1. Find dominant strategy for each player. 15 2. Find a secure strategy for each player. 16 3. Find Nash equilibrium 17 4. What is the payoff for each player at Nash equilibrium? 5 points 18 19 Part B: 20 Do you think cooperation works in this case? If "No", explain why. If "Yes," answer the rest of the questions in Parts B and C. 21 a. What is the cooperation strategy? 22 b. If the interest rate is 7.25%, what strategy would be better for each firm? Should they choose to cooperate or cheat? How much will each player earn for both cheating and cooperation? 23 c. For what range of interest rates could these firms use trigger strategies to support the collusive level of pricing? 24 d. Assuming the probability of ending this price game is 2%, what is the optimal strategy for the firms: cheating or cooperation? What if the probability of ending the game is 90%? 25 26 27 Part C: 28 Consider a two-player, sequential-move game where each player can choose to charge a high or low price. Large firm moves first 29 a. Draw the sequential-move game payoff diagram. You can draw this in a Word file and use the screenshot here. 30 b. Is there any credible threat from Small firm? If yes, what's that threat? 31 C. Find the subgame-perfect equilibrium and the payoff. Final Project Bonus Question Ready 51'F Sunny Q Search O 8 O W R 5 G B N MPart A 1. Find dominant strategy for each player: + A dominant strategy is one that yields a higher payoff regardless of the opponent's choice. Look at the payoff table and determine which strategy (low price or high price) each player should always choose. 2. Find a secure strategy for each player: A secure strategy ensures a minimum payoff regardless of the opponent's choice. Analyze the payoff table to identify such strategies. 3. Find Nash equilibriums: * A Nash equilibrium is a set of strategies where no player has an incentive to unilaterally change their strategy. Identify combinations of strategies where neither player wants to deviate. 4. What are the payoffs for each player at Nash equilibrium? + Once you've identified the Nash equilibrium(s), determine the payoffs for each player in those situations. PartB 5. Do you think cooperation works in this case? Explain whether cooperation between the firms would be beneficial or not. Justify your answer. 6. What is the cooperation strategy? |f cooperation is deemed beneficial, outline what the firms should do to cooperate effectively. 7. Given the interest rate of 2.25%, what strategy would be better for each firm? * Analyze whether cooperation or cheating would be more profitable for each firm given the interest rate. Calculate the payoffs for both strategies. 8. For what range of interest rates could the firms use collusive strategies? Determine the range of interest rates where it would be advantageous for the firms to collude on pricing. 9. Assuming a probability of ending the price game is 25%, what is the optimal strategy? * Consider whether it's better to cheat or cooperate given the probability of the game ending. Repeat for a 50% probability. PartC 10. Consider a two-player, sequential-move game where each player can choose high or low price: + Draw the extensive form game tree to visualize the possible outcomes and decisions. 11.Isthere any credible threat from Small firm? |dentify if Small firm has any credible threat against Large firm and describe it. 12. Find the subgame perfect equilibrium and payoffs: * Analyze the game tree to identify the subgame perfect equilibrium and calculate the payoffs for each player. Final Bonus Question 13. Analyzing Sunny's decision: + Understand Sunny's possible choices and their implications in the given context