Browsing by Author "McLennan, Andrew"
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Item Approximation of Contractible Valued Correspondences by Functions(Center for Economic Research, Department of Economics, University of Minnesota, 1989-12) McLennan, AndrewItem Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents(Center for Economic Research, Department of Economics, University of Minnesota, 1996-10) McLennan, AndrewThe Condorcet Jury Theorem pertains to elections in which the agents have common preferences but diverse information. We show that, whenever "sincere" voting leads to the conclusions of the Theorem-decisions superior to those that would be made by any individual based on private information, and asymptotically correct decisions as the population becomes large--there are also Nash equilibria with these properties, and in symmetric environments the equilibria may be taken to be symmetric. These conclusions follow from a simple property of common interest games: a mixed strategy profile of a (symmetric) common interest game that is optimal in the set of (symmetric) mixed strategy profiles is a Nash equilibrium.Item The Expected Number of Nash Equilibria of a Normal Form Game(Center for Economic Research, Department of Economics, University of Minnesota, 2002-05) McLennan, AndrewItem The Expected Number of Nash Equilibria of a Normal Form Game(Center for Economic Research, Department of Economics, University of Minnesota, 1999-03) McLennan, AndrewItem The Expected Number of Real Roots of a Multihomogeneous System of Polynomial Equations(Center for Economic Research, Department of Economics, University of Minnesota, 1999-03) McLennan, AndrewThe methods of Shub and Smale [SS93] are extended to the class of multihomogeneous systems of polynomial equations, yielding Theorem 1, which is a formula expressing the mean (with respect to a particular distribution on the space of coefficient vectors) number of real roots as a multiple of the mean absolute value of the determinant of a random matrix. Theorem 2 derives closed form expressions for the mean in special cases that include: (a) Shub and Smale's result that the expected number of real roots of the general homogeneous system is the square root of the generic number of complex roots given by Bezout's theorem; (b) Rojas' [Roj96] characterization of the mean number of real roots of an "unmixed" multihomogeneous system. Theorem 3 gives upper and lower bounds for the mean number of roots, where the lower bound is the square root of the generic number of complex roots, as determined by Bernstein's [Ber75] theorem. These bounds are derived by induction from recursive inequalities given in Theorem 4.Item Games with Communication(Center for Economic Research, Department of Economics, University of Minnesota, 1982-04) McLennan, AndrewItem Generic 4 x 4 Two Person Games Have At Most 15 Nash Equilibria(Center for Economic Research, Department of Economics, University of Minnesota, 1997-04) McLennan, Andrew; Park, In-UckThe maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1995), who arrives at this result by computer enumeration, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any common number d of pure strategies for the two agents.Item The Market for Liars: Reputation and Auditor Honesty(Center for Economic Research, Department of Economics, University of Minnesota, 2003-06) McLennan, Andrew; Park, In-UckIn the model there are two types of financial auditors with identical technology, one of which is endowed with a prior reputation for honesty. We characterize conditions under which there exists a "two-tier equilibrium" in which "reputable" auditors refuse bribes offered by clients for fear of losing reputation, while "disreputable" auditors accept bribes because even persistent refusal does not create a good reputation. The main findings are: (a) honest auditors charge higher fees, and have economic profits accruing to reputation; (b) as the fraction of auditors who are honest increases, the premium charged by reputable auditors eventually decreases, which diminishes the incentive to refuse bribes; (c) if the fraction of honest auditors exceeds an upper bound, there does not exist a two-tier equilibrium; (d) thus the reputation mechanism may be undermined by entry into the honest segment of the industry, if it is possible; (e) increasing auditor independence increases the upper bound.Item The Maximal Generic Number of Pure Nash Equilibria(Center for Economic Research, Department of Economics, University of Minnesota, 1994-07) McLennan, AndrewItem The Maximal Number of Regular Totally Mixed Nash Equilibria(Center for Economic Research, Department of Economics, University of Minnesota, 1994-07) McKelvey, Richard D.; McLennan, AndrewItem On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms(Center for Economic Research, Department of Economics, University of Minnesota, 1997-04) Govindan, Srihari; McLennan, AndrewItem Selected Topics in the Theory of Fixed Points(Center for Economic Research, Department of Economics, University of Minnesota, 1989-12) McLennan, AndrewWe present a treatment for mathematical economists of three topics in the theory of fixed points: (a) the Lefschetz fixed point index; (b) the Lefschetz fixed point theorem; (c) the theory of essential sets of fixed points. Our treatment is geometric, based on elementary techniques, and largely self-contained. In particular there is no essential reference to algebraic topology. Within the chosen scope of the paper the results are at the level of generality of the mathematical literature. The development of these theories for correspondences is emphasized. It emerges that the solution concepts of Kohlberg and Mertens (1986) have a definite, though obscure, place in this theory.