H1game - 4 Consider a f rst-price auction with two players...

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Department of Economics The Ohio State University Econ 817—Game Theory Homework #1—Due Monday October 8 Directions: Answer all questions, and be neat. If you discuss the questions in study groups, list the members of your study group, and make sure that the writeup is your own work. Do not look at answer sheets from previous years’ homeworks or the Osborne-Rubinstein solutions manual. Here is a hint for showing that there is no Nash equilibrium or that a given strategy pro f le is the unique Nash equilibrium: Show that for any "candidate" strategy pro f le, some player must have a pro f table deviation. This approach is usually easier than constructing the best reply correspondence and showing there is no f xed point. 1. O-R, exercise 19.1. 2. O-R, exercise 28.1. 3. O-R, exercise 35.2.
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Unformatted text preview: 4. Consider a f rst-price auction with two players and certain (non-random) values. The player with the highest bid wins the object and pays his/her bid. Letting v i denote the object’s value to player i and letting b i denote player i ’s bid, the payo f s are u i = v i − b i if b i > b − i u i = v i − b i 2 if b i = b − i u i = 0 if b i < b − i . (a) If we have v 1 = 1 and v 2 = 2 , show that there are no pure strategy Nash equilibria. (b) If we have v 1 = 1 and v 2 = 2 , construct a Nash equilibrium in which at least one player uses a mixed strategy. 5. For the “chicken” game of Figure 47.1, f nd the correlated equilibrium for which the sum of the payo f s of the two players is the highest. 1...
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