DOCSLIB.ORG

Political Game Theory Nolan Mccarty Adam Meirowitz

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Political Game Theory Nolan Mccarty Adam Meirowitz Political Game Theory Nolan McCarty Adam Meirowitz To Liz, Janis, Lachlan, and Delaney. Contents Acknowledgements vii Chapter 1. Introduction 1 1. Organization of the Book 2 Chapter 2. The Theory of Choice 5 1. Finite Sets of Actions and Outcomes 6 2. Continuous Outcome Spaces* 10 3. Utility Theory 17 4. Utility representations on Continuous Outcome Spaces* 18 5. Spatial Preferences 19 6. Exercises 21 Chapter 3. Choice Under Uncertainty 23 1. TheFiniteCase 23 2. Risk Preferences 32 3. Learning 37 4. Critiques of Expected Utility Theory 41 5. Time Preferences 46 6. Exercises 50 Chapter 4. Social Choice Theory 53 1. The Open Search 53 2. Preference Aggregation Rules 55 3. Collective Choice 61 4. Manipulation of Choice Functions 66 5. Exercises 69 Chapter 5. Games in the Normal Form 71 1. The Normal Form 73 2. Solutions to Normal Form Games 76 3. Application: The Hotelling Model of Political Competition 83 4. Existence of Nash Equilibria 86 5. Pure Strategy Nash Equilibria in Non-Finite Games* 93 6. Application: Interest Group Contributions 95 7. Application: International Externalities 96 iii iv CONTENTS 8. Computing Equilibria with Constrained Optimization* 97 9. Proving the Existence of Nash Equilibria** 98 10. Strategic Complementarity 102 11. Supermodularity and Monotone Comparative Statics* 103 12. Refining Nash Equilibria 108 13. Application: Private Provision of Public Goods 109 14. Exercises 113 Chapter 6. Bayesian Games in the Normal Form 115 1. Formal Definitions 117 2. Application: Trade restrictions 119 3. Application: Jury Voting 121 4. Application: Jury Voting with a Continuum of Signals* 123 5. Application: Public Goods and Incomplete Information 126 6. Application: Electoral Competition under Uncertainty 127 7. Application: Campaigns, Contests and Auctions* 131 8. Existence of Bayesian Nash equilibria* 133 9. Exercises 134 Chapter 7. Extensive Form Games 135 1. Backward Induction 138 2. Dynamic Games of Complete but Imperfect Information 140 3. Subgame Perfection and Perfect Equilibria 144 4. Applications 145 5. Exercises 158 Chapter 8. Dynamic Games of Incomplete Information 161 1. Perfect Bayesian Equilibria 163 2. Application: Entry Deterrence in Elections 172 3. Application: Information and Legislative Organization 178 4. Application: Informational Lobbying 183 5. Refinements of Perfect Bayesian Equilibrium* 186 6. Exercises 195 Chapter 9. Repeated Games 199 1. The Repeated Prisoner’s Dilemma 200 2. The Grim Trigger Equilibrium 202 3. Tit-for-Tat Strategies 203 4. Intermediate Punishment Strategies 204 5. The Folk Theorem* 206 6. Application: Interethnic Cooperation 208 7. Application: Trade Wars 213 8. Exercises 215 CONTENTS v Chapter 10. Bargaining Theory 217 1. The Nash Bargaining Solution 217 2. Non-cooperative Bargaining 222 3. Majority Rule Bargaining Under Closed Rule 226 4. Bargaining with Incomplete Information 234 5. Application: Veto Bargaining 235 6. Application: Crisis Bargaining 244 7. Exercises 254 Chapter 11. Mechanism Design and Agency Theory 257 1. The Mechanism Design Problem 260 2. Applications 263 3. Incentive Compatibility and Individual Rationality 274 4. Constrained Mechanism Design 276 5. Mechanism Design and Signaling Games 291 6. Exercises 295 Chapter 12. Mathematical Appendix 299 1. Sets and Functions 301 2. The Real Number System 304 3. Points and sets 306 4. Continuity of Functions 308 5. Correspondences* 310 6. Calculus 311 7. Probability Theory 324 Bibliography 335 Acknowledgements The origin of this book lies in the utter inability of either of its authors to write legibly on a black board (or any other surface, for that matter). To save our students from what would have been the most severe form of pedagogical torture, we were forced to commit our lecture notes to the electronic form. This also compensated for our inability to spell without the aid of a spell checker.1 We ultimately decided that all of the late nights spent typesetting game theory notes should not go in vain. So we undertook to turn them into this book, which of course, led to more late nights spent typing. We hope these weren’t wasted either. We are most grateful to the students at Columbia and Princeton on whom early versions of our notes and manuscript were inflicted. Puzzled looks and panicked office hours helped us to figure out how convey game theory to students of politics. We also benefited from early conversations with Chris Achen, Scott Ashworth, Larry Bartels, Keith Krehbiel, David Lewis and Thomas Romer on what a book on political game theory ought to look like. Along the way Stuart Jordan and Natasha Zharinova have provided valuable assistance and feed- back. Finally, our greatest debts are to those who taught us political game theory: David Austen-Smith, Jeffrey Banks, David Baron, Bruce Bueno de Mesquito, Thomas Romer, and Howard Rosenthal. Nolan McCarty Adam Meirowitz Princeton NJ 1Our mispelling styles are quite distinctive, however. For a given word, Mc- Carty uses completely random spellings while Meirowitz consistently mispells the word in the exact same way. vii CHAPTER 1 Introduction In a rather short period of time, game theory has become one of the most powerful analytical tools in the study of politics. From its ear- liest applications in electoral and legislative behavior, game theoretic models have proliferated in such diverse areas as international secu- rity, ethnic cooperation, to democratization. Indeed all of the major fields in political science have been the recipients of important contri- butions from political game theoretic models. Rarely does an issue of the American Political Science Review, the American Journal of Po- litical Science,orInternational Organization appear without at least one article formulating a new game theoretic application to politics or providing an empirical test of an existing one. Nevertheless, applications of game theory have not developed as fast as they have in economics. One of the consequences of this un- even development is that most political scientists who wish to learn game theory are forced to rely on textbooks written by and for econo- mists. While there are many excellent economic game theory texts, their treatments of the subject are often not well-suited to the needs of many political scientists. First and perhaps most importantly, the applications and topics are generally those of interest to economists. For example, it is not always obvious to novice political scientists what duopoly or auction theory tells us about political phenomena. Alter- natively, there are topics such as voting theory that are indispensable to political game theorists which receive scant coverage in economics texts. Finally, many economics treatments presume some level of ex- posure to ideas in classical price theory. Thus, the entry barriers to political scientists are not only the math, but also a knowledge of demand curves, marginal rates of substitution, and the like. Certainly, there have been a few texts by and for political scientists such as those by Ordeshook and Morrow. However, we feel that each is dated both in terms of the applications but also in terms of the needs of modern political science. Ordeshook remains an outstanding treat- ment of social choice and spatial theory, yet it was written well before the emergence of non-cooperative theory as the dominant paradigm in 1 2 1. INTRODUCTION political game theory. Morrow does provide an accessible introduction tothetoolsofnon-cooperativegametheory.However,theanalytical level of his presentation falls somewhat below the contemporary needs of students of political game theory. It has also been a decade since its publication — a decade in which there have been hundreds of important articles and books deploying the tools of game theory. We feel that there is a need to introduce today’s students to today’s literature. So we kept several goals in mind while writing this book. First, we wanted to write a textbook on political game theory instead of a book on abstract or economic game theory. We wanted to focus on appli- cations of interest to political scientists. We wanted to present topics that are unique to political analysis. Secondly, in writing a book for political scientists, we wanted to be cognizant of the diversity of back- grounds and interests in political science. We recognize that most doctoral students in the field enter graduate school with limited math- ematical and modelling backgrounds. However, we felt that it would not serve even those students to ignore the role of mathematical rigor and the importance of theoretical concepts in contemporary political models. Thus, for those students we have included a detailed mathe- matical appendix covering necessary tools ranging from set theory to basic optimization. At the other end of the spectrum are students who come to graduate study in political science with strong backgrounds in mathematics and economics. We wanted to write a book that would be useful to that audience as well and have chosen to provide in depth coverage of some more difficult and subtle concepts that are of the first importance to political game theory. As a result, we have included a number of “starred” advanced sections which provide a bit more detail about the analytical and mathematical structure of the models that we encounter. All of these can be safely skipped upon first readings for those not quite ready for the more technical material. 1. Organization of the Book In terms of the organization, our book departs from standard treat- ments by including a number of topics that are either specifically rel- evant for political science or designed for remediation in areas which students of political science often have limited background. Chapter 2 is reasonably self contained exposition of classical choice theory under certainty. In this chapter, we lay out the basic ideas of preferences and their relation to utility theory. We prove a few key results, but oth- erwise focus on providing the intuition and language of rational choice theory.
Load more

Recommended publications
  • Reactionary Postmodernism? Neoliberalism, Multiculturalism, the Internet, and the Ideology of the New Far Right in Germany
    University of Vermont ScholarWorks @ UVM UVM Honors College Senior Theses Undergraduate Theses 2018 Reactionary Postmodernism? Neoliberalism, Multiculturalism, the Internet, and the Ideology of the New Far Right in Germany William Peter Fitz University of Vermont Follow this and additional works at: https://scholarworks.uvm.edu/hcoltheses Recommended Citation Fitz, William Peter, "Reactionary Postmodernism? Neoliberalism, Multiculturalism, the Internet, and the Ideology of the New Far Right in Germany" (2018). UVM Honors College Senior Theses. 275. https://scholarworks.uvm.edu/hcoltheses/275 This Honors College Thesis is brought to you for free and open access by the Undergraduate Theses at ScholarWorks @ UVM. It has been accepted for inclusion in UVM Honors College Senior Theses by an authorized administrator of ScholarWorks @ UVM. For more information, please contact [email protected]. REACTIONARY POSTMODERNISM? NEOLIBERALISM, MULTICULTURALISM, THE INTERNET, AND THE IDEOLOGY OF THE NEW FAR RIGHT IN GERMANY A Thesis Presented by William Peter Fitz to The Faculty of the College of Arts and Sciences of The University of Vermont In Partial Fulfilment of the Requirements For the Degree of Bachelor of Arts In European Studies with Honors December 2018 Defense Date: December 4th, 2018 Thesis Committee: Alan E. Steinweis, Ph.D., Advisor Susanna Schrafstetter, Ph.D., Chairperson Adriana Borra, M.A. Table of Contents Introduction 1 Chapter One: Neoliberalism and Xenophobia 17 Chapter Two: Multiculturalism and Cultural Identity 52 Chapter Three: The Philosophy of the New Right 84 Chapter Four: The Internet and Meme Warfare 116 Conclusion 149 Bibliography 166 1 “Perhaps one will view the rise of the Alternative for Germany in the foreseeable future as inevitable, as a portent for major changes, one that is as necessary as it was predictable.
    [Show full text]
  • Lecture 1 Mathematical Preliminaries
    Lecture 1 Mathematical Preliminaries A. Banerji July 26, 2016 (Delhi School of Economics) Introductory Math Econ July 26, 2016 1 / 27 Outline 1 Preliminaries Sets Logic Sets and Functions Linear Spaces (Delhi School of Economics) Introductory Math Econ July 26, 2016 2 / 27 Preliminaries Sets Basic Concepts Take as understood the notion of a set. Usually use upper case letters for sets and lower case ones for their elements. Notation. a 2 A, b 2= A. A ⊆ B if every element of A also belongs to B. A = B if A ⊆ B and B ⊆ A are both true. A [ B = fxjx 2 A or x 2 Bg. The ‘or’ is inclusive of ‘both’. A \ B = fxjx 2 A and x 2 Bg. What if A and B have no common elements? To retain meaning, we invent the concept of an empty set, ;. A [; = A, A \; = ;. For the latter, note that there’s no element in common between the sets A and ; because the latter does not have any elements. ; ⊆ A, for all A. Every element of ; belongs to A is vacuously true since ; has no elements. This brings us to some logic. (Delhi School of Economics) Introductory Math Econ July 26, 2016 3 / 27 Preliminaries Logic Logic Statements or propositions must be either true or false. P ) Q. If the statement P is true, then the statement Q is true. But if P is false, Q may be true or false. For example, on real numbers, let P = x > 0 and Q = x2 > 0. If P is true, so is Q, but Q may be true even if P is not, e.g.
    [Show full text]
  • A Class of N-Player Colonel Blotto Games with Multidimensional Private Information
    University of Zurich Department of Economics Working Paper Series ISSN 1664-7041 (print) ISSN 1664-705X (online) Working Paper No. 336 A Class of N-Player Colonel Blotto Games with Multidimensional Private Information Christian Ewerhart and Dan Kovenock Revised version, February 2021 A Class of N-Player Colonel Blotto Games With Multidimensional Private Information Christian Ewerhart Dan Kovenocky Department of Economics Economic Science Institute University of Zurich Chapman University Revised version: February 1, 2021 Abstract. In this paper, we study N-player Colonel Blotto games with incomplete information about battlefield valuations. Such games arise in job markets, research and development, electoral competition, security analysis, and conflict resolution. For M N + 1 battlefields, we identify a Bayes-Nash equilibrium in which the resource ≥ allocation to a given battlefield is strictly monotone in the valuation of that battlefield. We also explore extensions such as heterogeneous budgets, the case M N, full-support ≤ type distributions, and network games. Keywords. Colonel Blotto games Private information Bayes-Nash equilibrium · · · Generalized Dirichlet distributions Networks · *) Corresponding author. Postal address: Schönberggasse 1, 8001 Zurich, Switzerland. E-mail address: [email protected]. ) E-mail address: [email protected]. y 1 Introduction In a Colonel Blotto game, players simultaneously and independently allocate their en- dowments of a resource across a set of battlefields. The player that deploys the largest amount of the resource to a given battlefield scores a win and enjoys a gain in utility equivalent to her valuation of that battlefield. Thus, a player’s utility corresponds to the sum of the valuations of all battlefields won by the player.
    [Show full text]
  • Equilibrium Refinements
    Equilibrium Refinements Mihai Manea MIT Sequential Equilibrium I In many games information is imperfect and the only subgame is the original game. subgame perfect equilibrium = Nash equilibrium I Play starting at an information set can be analyzed as a separate subgame if we specify players’ beliefs about at which node they are. I Based on the beliefs, we can test whether continuation strategies form a Nash equilibrium. I Sequential equilibrium (Kreps and Wilson 1982): way to derive plausible beliefs at every information set. Mihai Manea (MIT) Equilibrium Refinements April 13, 2016 2 / 38 An Example with Incomplete Information Spence’s (1973) job market signaling game I The worker knows her ability (productivity) and chooses a level of education. I Education is more costly for low ability types. I Firm observes the worker’s education, but not her ability. I The firm decides what wage to offer her. In the spirit of subgame perfection, the optimal wage should depend on the firm’s beliefs about the worker’s ability given the observed education. An equilibrium needs to specify contingent actions and beliefs. Beliefs should follow Bayes’ rule on the equilibrium path. What about off-path beliefs? Mihai Manea (MIT) Equilibrium Refinements April 13, 2016 3 / 38 An Example with Imperfect Information Courtesy of The MIT Press. Used with permission. Figure: (L; A) is a subgame perfect equilibrium. Is it plausible that 2 plays A? Mihai Manea (MIT) Equilibrium Refinements April 13, 2016 4 / 38 Assessments and Sequential Rationality Focus on extensive-form games of perfect recall with finitely many nodes. An assessment is a pair (σ; µ) I σ: (behavior) strategy profile I µ = (µ(h) 2 ∆(h))h2H: system of beliefs ui(σjh; µ(h)): i’s payoff when play begins at a node in h randomly selected according to µ(h), and subsequent play specified by σ.
    [Show full text]
  • Campaigning Is Hard but Approximately Manageable
    Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable Sina Dehghani,1 Hamed Saleh,2 Saeed Seddighin,3 Shang-Hua Teng4 1 Institute for Research in Fundamental Sciences 2 University of Maryland 3 TTIC 4 University of Southern California [email protected], [email protected], [email protected], [email protected] Abstract Electoral College, Political Campaigns, and In the classical discrete Colonel Blotto game—introduced Multi-Battleground Resource Allocation by Borel in 1921—two colonels simultaneously distribute their troops across multiple battlefields. The winner of each The president of the United States is elected by the Electoral battlefield is determined by a winner-take-all rule, indepen- College, which consists of electors selected based on 51 con- dently of other battlefields. In the original formulation, each current elections. The number of electors each of the 50 colonel’s goal is to win as many battlefields as possible. The states and D. C. can select is determined every 10 years by Blotto game and its extensions have been used in a wide the United States Census. All but two states1 use a winner- range of applications from political campaign—exemplified take-all system, and in typical election without any third- by the U.S presidential election—to marketing campaign, party candidate, the ticket that wins the majority votes in the from (innovative) technology competition to sports compe- state earns the right to have their slate of electors from that tition. Despite persistent efforts, efficient methods for find- state chosen to vote in the Electoral College. Thus, in prin- ing the optimal strategies in Blotto games have been elu- sive for almost a century—due to exponential explosion in ciple, the team that receives the majority of electoral votes the organic solution space—until Ahmadinejad, Dehghani, wins the race and its main candidate is elected as president.
    [Show full text]
  • Recent Advances in Understanding Competitive Markets
    Recent Advances in Understanding Competitive Markets Chris Shannon Department of Economics University of California, Berkeley March 4, 2002 1 Introduction The Arrow-Debreu model of competitive markets has proven to be a remark- ably rich and °exible foundation for studying an array of important economic problems, ranging from social security reform to the determinants of long-run growth. Central to the study of such questions are many of the extensions and modi¯cations of the classic Arrow-Debreu framework that have been ad- vanced over the last 40 years. These include dynamic models of exchange over time, as in overlapping generations or continuous time, and under un- certainty, as in incomplete ¯nancial markets. Many of the most interesting and important recent advances have been spurred by questions about the role of markets in allocating resources and providing opportunities for risk- sharing arising in ¯nance and macroeconomics. This article is intended to give an overview of some of these more recent developments in theoretical work involving competitive markets, and highlight some promising areas for future work. I focus on three broad topics. The ¯rst is the role of asymmetric informa- tion in competitive markets. Classic work in information economics suggests that competitive markets break down in the face of informational asymme- 0 tries. Recently these issues have been reinvestigated from the vantage point of more general models of the market structure, resulting in some surpris- ing results overturning these conclusions and clarifying the conditions under which perfectly competitive markets can incorporate informational asymme- tries. The second concentrates on the testable implications of competitive markets.
    [Show full text]
  • Czech Elections: How a Billionaire Populist Upstaged Established Parties Written by Sean Hanley
    Czech Elections: How a Billionaire Populist Upstaged Established Parties Written by Sean Hanley This PDF is auto-generated for reference only. As such, it may contain some conversion errors and/or missing information. For all formal use please refer to the official version on the website, as linked below. Czech Elections: How a Billionaire Populist Upstaged Established Parties https://www.e-ir.info/2013/11/09/czech-elections-how-a-billionaire-populist-upstaged-established-parties/ SEAN HANLEY, NOV 9 2013 Voters in the Czech Republic went to the polls in early legislative elections on 25-26 October. The elections followed the collapse in June, amid personal and political scandal, of the minority centre-right government of Petr Nečas and the subsequent failure of a technocrat administration imposed by President Miloš Zeman to win a parliamentary vote of confidence. As in the previous May 2010 elections, the result saw losses for established parties and breakthroughs by new anti- establishment groupings campaigning on platforms of fighting corruption, renewing politics and making government work better. However, the 2013 results represent a decisive breach in the Czech Republic’s previously stable pattern of party politics party whose four main pillars – pro-market conservatives, Social Democrats, Christian Democrats and Communists – made it arguably Central and Eastern Europe’s best approximation to a West European style party system. The new political landscape that has emerged is both fluid and highly fragmented, with no fewer than seven parties now represented in the Chamber of Deputies. Seats held by parties following Czech parliamentary elections of 25-26 October.
    [Show full text]
  • Collusion Constrained Equilibrium
    Theoretical Economics 13 (2018), 307–340 1555-7561/20180307 Collusion constrained equilibrium Rohan Dutta Department of Economics, McGill University David K. Levine Department of Economics, European University Institute and Department of Economics, Washington University in Saint Louis Salvatore Modica Department of Economics, Università di Palermo We study collusion within groups in noncooperative games. The primitives are the preferences of the players, their assignment to nonoverlapping groups, and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This al- lows groups to put positive probability on alternatives that are suboptimal for the group in certain razor’s edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained equilibria exist and are a subset of the correlated equilibria of the underlying game. We examine four per- turbations of the underlying game. In each case,we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. We also show that for a sufficiently broad class of perturbations, every collusion constrained equilibrium arises as such a limit. We give an application to a voter participation game that shows how collusion constraints may be socially costly. Keywords. Collusion, organization, group. JEL classification. C72, D70. 1. Introduction As the literature on collective action (for example, Olson 1965) emphasizes, groups often behave collusively while the preferences of individual group members limit the possi- Rohan Dutta: [email protected] David K.
    [Show full text]
  • Optimal Power Allocation Strategy Against Jamming Attacks Using the Colonel Blotto Game
    Optimal Power Allocation Strategy Against Jamming Attacks Using the Colonel Blotto Game Yongle Wu, Beibei Wang, and K. J. Ray Liu Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA. {wuyl, bebewang, kjrliu}@umd.edu Abstract—Cognitive radio technologies have become a promis- adversaries. So far, there have been only a few papers regard- ing approach to increase the efficiency of spectrum utilization. ing security issues. For instance, the primary user emulation Although cognitive radio has been intensively studied in recent attack was described and a transmitter verification scheme was years, only a few works have discussed security aspects. In this paper, we focus on the jamming attack, one of major threats to proposed to test whether the given signal came from a primary cognitive radio networks, where a malicious user wants to jam user in [8]; [9] employed a Hammer model to identify, analyze the communications of secondary users by injecting interference. and assess denial of service attacks; in [10], security issues Aware of the absence of several primary users and the presence of the IEEE 802.22 standard were addressed; [11] discussed of a malicious user, a secondary user can allocate power to those an attack that malicious users attempted to affect an artificial- fallow bands with a randomized strategy, in hope of alleviating the damage caused by the malicious user. We model this scenario intelligence-based secondary user’s behavior by misleading the into a two-player zero-sum game, and derive its unique Nash learning process. Equilibrium under certain conditions using the Colonel Blotto In this paper, we mainly focus on one kind of malicious at- game approach, which provides a minimax strategy that the tacks in cognitive radio networks, namely, the jamming attack secondary user should adopt in order to minimize the worst- [12], where a malicious user, or the “jammer”, wants to prevent case damage caused by the malicious user.
    [Show full text]
  • 0<GFGEB<J &&%, 5GDBKB<:D 0<GFGEO 11
    Economics 221: Political Economy II Winter 2006-2007 Professor Matthew Jackson Oce: 241; Phone: 723-3544 Email: [email protected] Web site: http://www.stanford.edu/ jacksonm Overview: This course examines political processes and the studies how the design of political in- stitutions a ect societal welfare and economic outcomes. The course starts by examining the motivations for and challenges of forming political states and institutions, and how the structure and workings of political institutions a ect economic outcomes and societal welfare. Topics include: the origins of states, anarchy and the social contract, liberalism, wars and arms races, constitutional design, federalism, models of strategic voting behavior, asymme- tries of information and voting behavior, agenda formation and control, logrolling, lobbying, vote-buying and political in uence, nomination processes, and the politics of federations of states. Prerequisite: Economics 220. Requirements: You will be continuing the work on the projects that you began in Economics 220. This will involve re ning a model and producing some results if the problem you proposed in 220 was theoretical in nature, and if the work is empirical, then you should begin or continue your analysis of data. There will be several di erent due dates of updates on the project. The projects will be judged based on the progress made past what was completed in 220. In the latter part of the course, there will also be student presentations and discussions of some of the papers. A note on the readings and class discussions: Reading the papers before class is critical to the course, as much of the emphasis of the course will not only be on \what" the papers tell us, but also on \why" these are interesting issues and \how" the research was conducted.
    [Show full text]
  • Informational Size and Incentive Compatibility
    Econometrica, Vol. 70, No. 6 (November, 2002), 2421–2453 INFORMATIONAL SIZE AND INCENTIVE COMPATIBILITY By Richard McLean and Andrew Postlewaite1 We examine a general equilibrium model with asymmetrically informed agents. The presence of asymmetric information generally presents a conflict between incentive com- patibility and Pareto efficiency. We present a notion of informational size and show that the conflict between incentive compatibility and efficiency can be made arbitrarily small if agents are of sufficiently small informational size. Keywords: Incentive compatibility, mechanism design, incomplete information. 1 introduction The incompatibility of Pareto efficiency and incentive compatibility is a central theme in economics and game theory. The issues associated with this incompatibility are particularly important in the design of resource allocation mechanisms in the presence of asymmetrically informed agents where the need to acquire information from agents in order to compute efficient outcomes and the incentives agents have to misrepresent that information for personal gain come into conflict. Despite a large literature that focuses on these issues, there has been little work aimed at understanding those situations in which informational asymmetries are quantitatively important. Virtually every transaction is characterized by some asymmetry of information: any investor who buys or sells a share of stock generally knows something rel- evant to the value of the share that is not known to the person on the other side of the transaction. In order to focus on more salient aspects of the problem, many models (rightly) ignore the incentive problems associated with informa- tional asymmetries in the belief that, for the problem at hand, agents are “infor- mationally small.” However, few researchers have investigated the circumstances under which an analysis that ignores these incentive problems will yield results similar to those obtained when these problems are fully accounted for.
    [Show full text]
  • Generalizations on the Colonel Blotto Game
    Generalizations on the Colonel Blotto Game Dan Kovenock∗and Brian Robersony Abstract In this paper we characterize the equilibrium in a relaxed version of the Colonel Blotto game in which battlefield valuations maybe heterogeneous across battlefields and asymmetric across players and the, possibly asymmetric, budget constraints hold only on average, and then show how this characterization partially extends to the full Colonel Blotto game, in which the budget constraints must be satisfied with probability one. For the non-constant-sum generalization of the Colonel Blotto game examined, we find that there exist non-pathological parameter configurations with multiple, payoff inequivalent, equilibria. ∗Dan Kovenock, Economic Science Institute, Argyros School of Business and Economics, Chapman Uni- versity, One University Drive, Orange, CA 92866 USA t:714-628-7226 E-mail: [email protected] yBrian Roberson, Purdue University, Department of Economics, Krannert School of Management, 403 W. State Street, West Lafayette, IN 47907 USA t: 765-494-4531 E-mail: [email protected] (Correspondent) 1 1 Introduction The Colonel Blotto game is a two-player resource allocation game in which each player is endowed with a level of resources to allocate across a set of battlefields, within each battlefield the player that allocates the higher level of resources wins the battlefield, and each player's payoff is the sum of the valuations of the battlefields won. This simple game, that originates with Borel (1921), illustrates the fundamental strategic considerations that arise in multi- dimensional resource allocation competition such as: political campaign resource allocation, research and development competition where innovation involves obtaining a collection of interrelated patents, attack and defense of a collection of targets, etc.
    [Show full text]