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The ability to understand and predict behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others, has been the domain of game theory since the 1950s. Developing the theories at the heart of game theory has resulted in 8 Nobel Prizes and insights that researchers in many fields continue to develop. In Volume 4, top scholars synthesize and analyze mainstream scholarship on games and economic behavior, providing an updated account of developments in game theory since the 2002 publication of Volume 3, which only covers work through the mid 1990s. Focuses on innovation in games and economic behavior Presents coherent summaries of subjects in game theory Makes details about game theory accessible to scholars in fields outside economics
Who is William Baumol Economist William Jack Baumol was a native of the United States. In addition to his position as Professor Emeritus at Princeton University, he held the position of Academic Director of the Berkley Center for Entrepreneurship and Innovation. He was also a professor of economics at New York University. More than eighty books and several hundred journal papers were included in his body of work. He was a prolific author. Baumol is the name of the phenomenon that bears his name. How you will benefit (I) Insights about the following: Chapter 1: William Baumol Chapter 2: Kenneth Arrow Chapter 3: Oskar R. Lange Chapter 4: James Mirrlees Chapter 5: Harold Hotelling Chapter 6: Fernando Alvarez (economist) Chapter 7: Michio Morishima Chapter 8: Fritz Machlup Chapter 9: Jan Mossin Chapter 10: Entrepreneurial economics Chapter 11: Lars Peter Hansen Chapter 12: Evsey Domar Chapter 13: Susan Athey Chapter 14: Roger Myerson Chapter 15: Paul Klemperer Chapter 16: Jacques Drèze Chapter 17: Don Patinkin Chapter 18: Parag Pathak Chapter 19: Fuhito Kojima Chapter 20: Dave Donaldson (economist) Chapter 21: Stefanie Stantcheva Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information about William Baumol.
An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two non-primitive conditions whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action. Similarly, given that (134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists. Conditions (34) 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 (a) supermodularity in own action and (b) non-decreasing differences in own action and type. These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.
The approach presented in this book combines two aspects of generalizations of the noncooperative game as developed by Nash. First, players choose their acts dependent on certain information variables, and second there are constraints on the sets of decisions for players. After the derivation of a general (Nash)equilibrium existence theorem, some results from purification theory are used to prove the existence of an approximate equilibrium in pure strategies, that is in nonrandomized decision functions. For some types of payoff-functions and constraints, these games prove to have an (exact) equilibrium in pure strategies. The reason for considering constrained games with incomplete information is that, apart from their game-theoretic importance, they have rather widespread application. Market games with a continuum of traders as well as some statistical decision problems are covered with this approach.