Isotone equilibrium in games of incomplete information
Date
2003-01-01
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Abstract
An isotone pure strategy equilibrium exists in any game of incomplete information in which each player's action set is infinite sublattice of multidimensional Euclidean space, types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "nonprimitive conditions" whenever others adopt isotone pure strategies: (i) single-crossing in own action and type and (ii) quasi-supermodularity in own action. Conditions (i), (ii) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies supermodularity in own action and nondecreasing differences in own action and type. This result is applied to provide the first proof of pure strategy equilibrium existence in the uniform price auction when bidders have multi-unit demand, nonprivate values, and independent types.
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Scholars@Duke
David McAdams
David McAdams is Professor of Business Administration at the Fuqua School of Business, Duke University. He is also Professor of Economics in the Economics Department at Duke. He earned a B.S. in Applied Mathematics at Harvard University, an M.S. in Statistics from Stanford University, and a Ph.D. in Business from the Stanford Graduate School of Business. Before joining the faculty at Duke, he was Associate Professor of Applied Economics at the MIT Sloan School of Management. He has also worked as Special Assistant to the Director, Bureau of Economics, Federal Trade Commission.
Professor McAdams' primary research interests are microeconomic theory and game theory, with a special focus on strategic interactions between buyers and sellers, including auctions, pricing, negotiations, and relationships. His work has been published in the leading journals of economics, including Econometrica, American Economic Review, Review of Economic Studies, Journal of Political Economy, Journal of Economic Theory, and Journal of Econometrics. Currently, he is an associate editor of Journal of Economic Literature, International Journal of Industrial Organization, and International Journal of Game Theory.
Professor McAdams is author of "Game-Changer: Game Theory and the Art of Transforming Strategic Situations" (W.W. Norton, 2014).
Professor McAdams teaches the economics elective "Game Theory for Strategic Advantage" in the Daytime MBA program at Fuqua, as well as the PhD elective "Market Design I: Auctions" in the Economics Department.
Professor McAdams' consulting work focuses on two areas: (i) “market design / bidding strategy consulting” for those designing or participating in an auction market (e.g. FCC spectrum auctions, electricity procurement auctions, B2B exchanges); and (ii) “game-theory consulting” for firms (from startup to Fortune 50) facing mission-critical strategic challenges or opportunities.
Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.