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2008SpringHomework2Answers - SABANCI UNIVERSITY ECON 201 A...

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SABANCI UNIVERSITY ECON 201 – A GAMES AND STRATEGY ASSIGNMENT 2 ANSWERS 1 ( 25 points ). A pedestrian and a motorist play the following game: Each player has three strategies: exercise NO CARE, SOME CARE, and DUE CARE. An accident happens with probability %2 (0.02) if both players choose “due care.” In all other cases, an accident happens for sure (with probability 1). When an accident happens, pedestrian’s cost is 100 , whereas motorist has no cost. For each player, exercising no care is costless , to exercise “ some care” costs 1 , and to exercise due care costs 3 . The payoffs are (0,0) if no accident occurs (any care cost must be subtracted). Consider the following legal liability rule: Liability rule: If the motorist exerts more care than the pedestrian, the motorist has no liability. If the players exert the same level of care, when an accident happens, the motorist compensates the pedestrian for half of the damage. In all other cases, the motorist is liable for any harm that the pedestrian may incur. (i) [10p] Construct the strategic form game under the liability rule given above. (ii) [5p] What are each player’s rationalizable strategies? (iii) [5p] What is (or are) the Nash equilibrium? (iv) [5p] Does the liability rule generate a desirable outcome? In what sense is it or is not desirable? Answer : Motorist Pedestrian No Care Some Care Due Care No Care -50 , -50 -100 , -1 -100, -3 Some Care -1 , -100 -51 , -51 -101, -3 Due Care -3, -100 -3, -101 -4, -4 All three strategies of the pedestrian are rationalizable (one can find a strategy fort he motorist to which each strategy of the pedestrian becomes a best response). Fort he motorist, No Care is not rationalizable (in fact, it is strictly dominated by Due Care), while “some care” and “due care” are rationalizable. The Nash equilibrium is “due care, due care”. The liability rule changes the game you had to solve in the first midterm. It generates a Pareto Efficient Nash equilibrium in the game (it is impossible to improve one player’s payoff without harming the other) Moreover total payoffs are maximal: we also have a Pareto Efficient outcome with ex-post transfers. These are desirable features in game-like social interactions.

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2. ( 40 points ) Some of you may be familiar with the children’s game “rock-scissors- paper”: two players simultaneously choose between either “rock” or “scissors” or “paper” by putting their hands in the shape of one of the three choices. Rules are: scissors beats paper, paper beats rock, and rock beats scissors. If the players choose the same object, there is a tie: no one wins, no one looses.
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