eco204_HW_22 - University of Toronto Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain ECO 204 20082009 Ajaz Hussain HW 22 Question 1 (20072008 Test 4 Question) Two hospitals compete on the basis of service to patients. The following table gives the profits (in millions of $): Basic Hospital A's Services All Purpose Specialty Basic 5, 7 4, 5 6, 10 Hospital B's Services All Purpose 5, 4 8, 7 3, 12 Specialty 12, 6 7, 4 3, 3 (a) Does either hospital have a dominant strategy? If so, solve the game by dominant/dominated strategies. Show all steps below. 1 University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain (b) Solve for the pure strategy Nash equilibrium. Show your reasoning in the matrix below: Basic Hospital A's Services All Purpose Specialty Basic 5, 7 4, 5 6, 10 Hospital B's Services All Purpose 5, 4 8, 7 3, 12 Specialty 12, 6 7, 4 3, 3 (c) If these hospitals merge and coordinate their hospital services, what actions should they take? Explain briefly. If necessary, show your reasoning below: Basic Hospital A's Services All Purpose Specialty Basic 5, 7 4, 5 6, 10 Hospital B's Services All Purpose 5, 4 8, 7 3, 12 Specialty 12, 6 7, 4 3, 3 Question 2 (20072008 Final Exam question) In a business deal, Gussy has been identified as sometimes being straightforward and at other times bluffing, while Jen has been identified as being sometimes trusting and at other times skeptical. The payoffs from a oneshot simultaneous game between Gussy and Jen are: Gussy 2 Straightforward Bluffing Jen Trusting 20, 20 50, 10 Skeptical 10, 10 0, 0 University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain (a) What is the pure strategy Nash equilibrium? (b) What is the mixed strategy Nash equilibrium? Show your calculations, clearly stating any assumptions you've made. Question 3 (20072008 Final Exam Question) Courtney and Alma play a game: Courtney Left Right Alma Up 1, 1 0, 5 Down 5, 0 4, 4 (a) What is the pure strategy Nash equilibrium in a oneshot game? Show your work in the matrix below: Courtney Left Right Alma Up 1, 1 0, 5 Down 5, 0 4, 4 (b) Suppose Courtney and Alma play the game for three rounds. Predict the outcome of the game in each round. Show all calculations and steps. (c) Suppose Courtney and Alma play the game repeatedly forever. Predict the possible outcomes of the game. State any assumptions and show all calculations clearly. 3 ...
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