- Email: [email protected]
Introduction to the special issue in memory of Robert W. Rosenthal
Games and Economic Behavior 45 (2003) 271–277 www.elsevier.com/locate/geb
Introduction to the special issue in memory of Robert W. Rosenthal The sudden death of Bob Rosenthal on February 27, 2002, at the age of 57, brought a deep sense of loss to Bob’s family and friends. His steadfast friendship, engaging conversation, and mordant wit were gone forever. This issue testifies to our vivid memory of Bob as a valued colleague and important contributor to the continuing task of building a foundation for economics with the tools of game theory. Scholars will look back on recent decades as a golden age of economic theory, a time when infusion of game-theoretic perspectives gave everyone a chance to contribute to the emerging analysis of strategic behavior. Bob had the good fortune to begin his research career as the realization was taking hold that game theory held answers to many perplexing problems in economics. His talent for probing criticism of received ideas and creative development of new approaches enabled Bob to contribute to a wide range of topics. Variants of his “Centipede Game” will remain classroom staples as long as game theory is taught, as well as key tests for theories of rational behavior. A piece that captures his quirky and creative temperament is the analysis by Bob with his student Balazs Szentes of the “Chopstick Auction” that continues posthumously in this issue. Bob worked as a consultant on several auctions of telecommunications spectrum licenses, including one in the Netherlands. The rules said that the government reserved the right to interrupt the auction and sell small packages of spectrum in a large number of simultaneous auctions. He was asked what strategy would be optimal. Should one spread bids over a large number of packages, or concentrate on just a few? Bob promised an answer in the morning, but years passed until he and Balazs came up with a solution to the toy version that is the Chopstick Auction. In the Chopstick Auction, three chopsticks are offered to two bidders. Each bidder regards one chopstick as worthless, and a bundle of two or three chopsticks as worth one dollar. The three chopsticks are auctioned in three simultaneous, first-price, sealed-bid auctions. Equilibrium play is a mathematical delight. A pure strategy is a triple in which each coordinate is the amount bid in each auction, but there are no equilibria in pure strategies. However, there is a symmetric equilibrium in which each player mixes uniformly over the surface of the tetrahedron with vertices (0, 0, 0), (0, 1/2, 1/2), (1/2, 0, 1/2), and (1/2, 1/2, 0). Thus each player contrives to spread his dollar over all the chopsticks, and to concentrate it on pairs at the same time! This pastiche will perhaps go some way toward explaining why the two editors of this special issue felt such loss at the death of a respected teacher and an admired student. 0899-8256/$ – see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0899-8256(03)00174-X
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A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
We wanted to commemorate his life, and to recognize his unique insights that shaped the modern theory of strategic behavior. Among those scholars sharing Bob’s research interests, many shared our desire to publish an issue of current research that illustrates the impact of Bob’s work on game theory and its economic applications. The articles in this special issue of Games and Economic Behavior testify to the influence of Bob’s creativity and his critical acumen. The authors include some of Bob’s mentors, colleagues, and former students writing on topics to which Bob made important contributions, including auctions, bargaining, equilibrium selection, purification, learning, pricing, reputations, and voting. As editors we feel fortunate to receive submissions whose excellence provides a lasting tribute to Bob Rosenthal’s life and work, and engraves permanently our collective memory in the pages of a journal he served since its founding.
Curriculum Vitae Robert W. Rosenthal Education: PhD, Operations Research, Stanford University, 1971 MS, Operations Research, Stanford University, 1968 BA, Political Economy, John Hopkins University, 1966 Professional Positions: Professor of Economics, Boston University, 1987–2002 Professor of Economics, State University of New York at Stony Brook, 1984–1987 Professor of Economics, Virginia Polytechnic Institute and State University, 1983–1984 Member of Technical Staff, Bell Laboratories, 1976–1983 Assistant and Associate Professor of Industrial Engineering and Management Sciences, Northwestern University, 1970–1976 Fulbright Chair in Economics, University of Siena, Spring 2001 Visiting Professor, Department of Economics, Massachusetts Institute of Technology, 2000–2001 Visiting Professor, Department of Economics, Harvard University, Fall 1993 Charge de Cours Invité, CORE, Catholic University of Louvain, Fall 1973 Fellow of the Econometric Society, Phi Beta Kappa Associate Editor: Games and Economic Behavior, 1988–2002; Journal of Economic Theory, 1999–2002; Mathematics of Operations Research, 1981–1988; Operations Research, 1978–1982 Academic Papers and Articles, in chronological order: “Computation of Equilibria of Extensive Games” (with K. Boudwin and R. Wilson), Tech. Report #69-12, Operations Research Department, Stanford University,1969. “Computing Equilibrium Behavioral Strategies for N -Person Extensive Games” (with K. Boudwin, R. Wilson), Working Paper #175, Graduate School of Business, Stanford University, 1970.
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
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“Stability Analysis of Cooperative Games in Effectiveness Form,” PhD thesis, Tech. Report #70-11, Operations Research Department, Stanford University, 1970. “External Economies and Cores,” Journal of Economic Theory 3 (1971), 182–188. Review of Parthasarathy and Raghavan, “Some Topics in Two-Person Games,” SIAM Review 14 (1972), 356–357. “Cooperative Games in Effectiveness Form,” Journal of Economic Theory 5 (1972), 88– 101. “Voting and Economic Externalities: A Game-Theoretic Approach,” Tech. Report, presented at Econometric Society Meetings, Budapest, 1972. “The Network Equilibrium Problem in Integers,” Networks 3 (1973), 53–59. “A Class of Games Possessing Pure-Strategy Nash Equilibria,” International Journal of Game Theory 2 (1973), 65–67. “Taxation vs. Prohibition of an External Diseconomy by Direct Vote: A Game-Theoretic Approach,” International Economic Review 14 (1973), 414–420. “Bayesian Equilibria of Finite Two-Person Games with Incomplete Information” (with J.T. Howson, Jr.), Management Science 21 (1974), 313–315. “Disadvantageous Syndicates” (with A. Postlewaite), Journal of Economic Theory 9 (1974), 324–326. “Correlated Equilibria in Some Classes of Two-Person Games,” International Journal of Game Theory 3 (1974), 119–128. “On Lindahl Equilibria in Economies with Public Goods” (with P. Champsaur), CORE Discussion Paper No. 7413, 1974. “Voting Majority Sizes,” Econometrica 43 (1975), 293–299. “Induced Outcomes in Cooperative Normal-Form Games,” Discussion Paper No. 178, Center for Math. Studies, Northwestern University, 1975. “On Cores in Economies with Public Goods” (with P. Champsaur and D.J. Roberts), International Economic Review 16 (1975), 751–764. “Market Games with Production and Public Commodities,” Discussion Paper No. 156, Center for Math. Studies, Northwestern University, revised 1976. “An Arbitration Model for Normal-Form Games,” Mathematics of Operations Research 1 (1976), 82–88. “Lindahl’s Solution and Values for a Public-Goods Example,” Journal of Mathematical Economics 3 (1976), 37–42. “Discussion of Lloyd S. Shapley’s ‘Noncooperative General Exchange’,” in Theory and Measurement of Economic Externalities (S. Lin, ed.), Academic Press, 1976, 177–178.
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A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
“Sufficient Conditions for Insensitivity in Linear Models,” Operations Research 24 (1976), 183–188. “Core and Value for a Public-Goods Economy: An Example” (with R. Aumann and R. Gardner), Journal of Economic Theory 15 (1977), 363–365. “Arbitration of Two-Party Disputes under Ignorance” (with E. Kalai), International Journal of Game Theory 7 (1978), 65–72. “Arbitration of Two-Party Disputes under Uncertainty,” Review of Economic Studies 45 (1978), 595–604. “A Model of Cooperative Games with Binding Commitments,” in Game Theory and Political Science (P. Ordeshook, ed.), NYU Press, 1978, 97–111. “Sequences of Games with Varying Opponents,” Econometrica 47 (1979), 1353–1366. “A Game-Theoretic Analysis of Bargaining with Reputations” (with H. Landau), Journal of Mathematical Psychology 20 (1979), 233–255. “Congestion Tolls: Equilibrium and Optimality,” Naval Research Logistics Quarterly 27 (1980), 231–232. “New Equilibria for Noncooperative Two-Person Games,” Journal of Mathematical Sociology 7 (1980), 15–26. “A Model in Which an Increase in the Number of Sellers Leads to a Higher Price,” Econometrica 48 (1980), 1575–1579. “Repeated Bargaining with Opportunities for Learning” (with H. Landau), Journal of Mathematical Sociology 8 (1981), 61–74. “Games of Perfect Information, Predatory Pricing and the Chain-Store Paradox,” Journal of Economic Theory 25(1981), 92–100. Reprinted in Game Theory in Economics (A. Rubinstein, ed.), Elgar, 1990, 298–306. “A Note on Exact Purification” (with R. Radner), Working Paper, 1981. “A Dynamic Model of Duopoly with Customer Loyalties,” Journal of Economic Theory 27 (1982), 69–76. “Private Information and Pure-Strategy Equilibria” (with R. Radner), Mathematics of Operations Research 7 (1982), 401–409. “A Model of Far-Sighted Electoral Competition,” Mathematical Social Sciences 2 (1982), 289–297. “A Dynamic Oligopoly Game with Lags in Demand: More on the Monotonicity of Price in the Number of Sellers,” International Economic Review 23 (1982), 353–360. “Mixed-Strategy Equilibria in Markets with Asymmetric Information” (with A. Weiss), Working Paper, 1982. “Approximate Purification of Mixed Strategies” (with R. Aumann et al.), Mathematics of Operations Research 8 (1983), 327–341.
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
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“Repeated Two-Player Games with Ruin” (with A. Rubinstein), International Journal of Game Theory 13 (1984), 155–177. “Strategic Analysis of the Competitive Exercise of Certain Financial Options” (with G.M. Constantinides), Journal of Economic Theory 34 (1984), 128–138. “Discussion of: Anderson and Sundaresan, ‘Futures Markets and Monopoly’,” in The Industrial Organization of Futures Markets (R. Anderson, ed.), Heath, 1984, 107–108. “Mixed-Strategy Equilibrium in a Market with Asymmetric Information” (with A. Weiss), Review of Economic Studies 51(1984), 333–342. “An Approach to Some Noncooperative Game Situations with Special Attention to Bargaining,” in Game-Theoretic Models of Bargaining (A. Roth, ed.), Cambridge University Press, 1985, 63–72. “A Dynamic Screening Example,” Working Paper, 1985. “Dynamic Duopoly with Incomplete Customer Loyalties,” International Economic Review 27 (1986), 399–406. “Noncooperative Games and Nontransitive Preferences” (with P. Fishburn), Mathematical Social Sciences 12 (1986), 1–7. “A Positive Approach to Noncooperative Games” (with J. Friedman), Journal of Economic Behavior and Organization 7 (1986), 235–251. “Anonymous Sequential Games” (with B. Jovanovic), Journal of Mathematical Economics 17 (1988), 77–87. “More on the ‘Anti-Folk Theorem’ ” (with J. Masso), Journaj of Mathematical Economics 18 (1989), 281–290. “A Bounded-Rationality Approach to the Study of Noncooperative Games,” International Journal of Game Theory 18 (1989), 273–292. “Duopoly with Both Ruin and Entry” (with R. Spady), Canadian Journal of Economics 22 (1989), 834–851. “Testing the Minimax Hypothesis: A Re-examination of O’Neill’s Game Experiment” (with J. Brown), Econometrica 58 (1990), 1065–1081. “A Strategic Altruism Model in which Ricardian Equivalence Does Not Hold” (with L. Kotlikoff and A. Razin), Economic Journal 100 (1990), 1261–1268. “Strategic Models of Sovereign-Debt Renegotiations” (with R. Fernandez), Review of Economic Studies 57 (1990), 331–349. “On the Incentives Associated with Sovereign Debt,” Journal of International Economics 30 (1991), 167–176. “A Note on Robustness of Equilibria with Respect to Commitment Opportunities,“ Games and Economic Behavior 3 (1991), 237–243.
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A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
“The Contractors’ Game” (with K. Lang), RAND Journal of Economics 22 (1991), 329– 338. “A Note on Abreu–Matsushima Mechanisms” (with J. Glazer), Econometrica 60 (1992), 1435–1438. “Some Inefficiency Implications of Generational Politics and Exchange” (with L. Kotlikoff), Economics and Politics 5 (1993), 27–42. “Suicide Attempts and Signalling Games,” Mathematical Social Sciences 26 (1993), 25– 33. “An Explanation of Inefficiency in Markets and a Justification for Buy-and-Hold Strategies” (with R. Wang), Canadian Journal of Economics 26 (1993), 609–624. “Rules of Thumb in Games,” Journal of Economic Behavior and Organization 22 (1993), 1–13. “Bargaining Rules of Thumb,” Journal of Economic Behavior and Organization 22 (1993), 15–24. “Price and Quality Cycles for Experience Goods” (with D. Gale), RAND Journal of Economics 25 (1994), 590–607. “Dynamic Duopoly with Slowly Changing Customer Loyalties” (with Y. Chen), International Journal of Industrial Organization 14 (1996), 269–296. “Asking Prices as Commitment Devices” (with Y. Chen), International Economic Review 37 (1996), 129–155. “On the Use of Ceiling-Price Commitments by Monopolists” (with Y. Chen), RAND Journal of Economics 27 (1996), 207–220. “Simultaneous Auctions with Synergies” (with V. Krishna), Games and Economic Behavior 17 (1996), 1–31. “Simultaneous Auctions with Synergies and Common Values” (with R. Wang), Games and Economic Behavior 17 (1996), 32–55. “On Some Myths about Sequenced Common-value Auctions” (with M.A. de Frutos), Games and Economic Behavior 23 (1998), 201–221. “Experimentation, Imitation, and Stochastic Stability” (with D. Gale), Journal of Economic Theory 84 (1999), 1–40. “Experimentation, Imitation, and Stochastic Stability: Addendum” (with D. Gale), Journal of Economic Theory 97 (2001), 164–174. “Trust and Social Efficiencies,” Review of Economic Design 6 (2001), 413–428. “Coordination Through Reputations: A Laboratory Experiment” (with D. Dale and J. Morgan), Games and Economic Behavior 38 (2002), 52–88. “Bargaining Piecemeal or All at Once?” (with K. Lang), Economic Journal 3, No. 473, 526–540.
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
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“Three-Object, Two-Bidder Simultaneous Auctions: Chopsticks and Tetrahedra” (with B. Szentes), Games and Economic Behavior, to appear. “Hide and Seek in Arizona” (with J. Shachat and M. Walker), International Journal of Game Theory, to appear. “Beyond Chopstick: Symmetric Equilibria in Majority Auction Games” (with B. Szentes), Games and Economic Behavior, this issue. Andrew Postlewaite Robert Wilson E-mail address: [email protected] (A. Postlewaite) 7 May 2003
Introduction to the special issue in memory of Robert W. Rosenthal The sudden death of Bob Rosenthal on February 27, 2002, at the age of 57, brought a deep sense of loss to Bob’s family and friends. His steadfast friendship, engaging conversation, and mordant wit were gone forever. This issue testifies to our vivid memory of Bob as a valued colleague and important contributor to the continuing task of building a foundation for economics with the tools of game theory. Scholars will look back on recent decades as a golden age of economic theory, a time when infusion of game-theoretic perspectives gave everyone a chance to contribute to the emerging analysis of strategic behavior. Bob had the good fortune to begin his research career as the realization was taking hold that game theory held answers to many perplexing problems in economics. His talent for probing criticism of received ideas and creative development of new approaches enabled Bob to contribute to a wide range of topics. Variants of his “Centipede Game” will remain classroom staples as long as game theory is taught, as well as key tests for theories of rational behavior. A piece that captures his quirky and creative temperament is the analysis by Bob with his student Balazs Szentes of the “Chopstick Auction” that continues posthumously in this issue. Bob worked as a consultant on several auctions of telecommunications spectrum licenses, including one in the Netherlands. The rules said that the government reserved the right to interrupt the auction and sell small packages of spectrum in a large number of simultaneous auctions. He was asked what strategy would be optimal. Should one spread bids over a large number of packages, or concentrate on just a few? Bob promised an answer in the morning, but years passed until he and Balazs came up with a solution to the toy version that is the Chopstick Auction. In the Chopstick Auction, three chopsticks are offered to two bidders. Each bidder regards one chopstick as worthless, and a bundle of two or three chopsticks as worth one dollar. The three chopsticks are auctioned in three simultaneous, first-price, sealed-bid auctions. Equilibrium play is a mathematical delight. A pure strategy is a triple in which each coordinate is the amount bid in each auction, but there are no equilibria in pure strategies. However, there is a symmetric equilibrium in which each player mixes uniformly over the surface of the tetrahedron with vertices (0, 0, 0), (0, 1/2, 1/2), (1/2, 0, 1/2), and (1/2, 1/2, 0). Thus each player contrives to spread his dollar over all the chopsticks, and to concentrate it on pairs at the same time! This pastiche will perhaps go some way toward explaining why the two editors of this special issue felt such loss at the death of a respected teacher and an admired student. 0899-8256/$ – see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0899-8256(03)00174-X
272
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
We wanted to commemorate his life, and to recognize his unique insights that shaped the modern theory of strategic behavior. Among those scholars sharing Bob’s research interests, many shared our desire to publish an issue of current research that illustrates the impact of Bob’s work on game theory and its economic applications. The articles in this special issue of Games and Economic Behavior testify to the influence of Bob’s creativity and his critical acumen. The authors include some of Bob’s mentors, colleagues, and former students writing on topics to which Bob made important contributions, including auctions, bargaining, equilibrium selection, purification, learning, pricing, reputations, and voting. As editors we feel fortunate to receive submissions whose excellence provides a lasting tribute to Bob Rosenthal’s life and work, and engraves permanently our collective memory in the pages of a journal he served since its founding.
Curriculum Vitae Robert W. Rosenthal Education: PhD, Operations Research, Stanford University, 1971 MS, Operations Research, Stanford University, 1968 BA, Political Economy, John Hopkins University, 1966 Professional Positions: Professor of Economics, Boston University, 1987–2002 Professor of Economics, State University of New York at Stony Brook, 1984–1987 Professor of Economics, Virginia Polytechnic Institute and State University, 1983–1984 Member of Technical Staff, Bell Laboratories, 1976–1983 Assistant and Associate Professor of Industrial Engineering and Management Sciences, Northwestern University, 1970–1976 Fulbright Chair in Economics, University of Siena, Spring 2001 Visiting Professor, Department of Economics, Massachusetts Institute of Technology, 2000–2001 Visiting Professor, Department of Economics, Harvard University, Fall 1993 Charge de Cours Invité, CORE, Catholic University of Louvain, Fall 1973 Fellow of the Econometric Society, Phi Beta Kappa Associate Editor: Games and Economic Behavior, 1988–2002; Journal of Economic Theory, 1999–2002; Mathematics of Operations Research, 1981–1988; Operations Research, 1978–1982 Academic Papers and Articles, in chronological order: “Computation of Equilibria of Extensive Games” (with K. Boudwin and R. Wilson), Tech. Report #69-12, Operations Research Department, Stanford University,1969. “Computing Equilibrium Behavioral Strategies for N -Person Extensive Games” (with K. Boudwin, R. Wilson), Working Paper #175, Graduate School of Business, Stanford University, 1970.
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
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“Stability Analysis of Cooperative Games in Effectiveness Form,” PhD thesis, Tech. Report #70-11, Operations Research Department, Stanford University, 1970. “External Economies and Cores,” Journal of Economic Theory 3 (1971), 182–188. Review of Parthasarathy and Raghavan, “Some Topics in Two-Person Games,” SIAM Review 14 (1972), 356–357. “Cooperative Games in Effectiveness Form,” Journal of Economic Theory 5 (1972), 88– 101. “Voting and Economic Externalities: A Game-Theoretic Approach,” Tech. Report, presented at Econometric Society Meetings, Budapest, 1972. “The Network Equilibrium Problem in Integers,” Networks 3 (1973), 53–59. “A Class of Games Possessing Pure-Strategy Nash Equilibria,” International Journal of Game Theory 2 (1973), 65–67. “Taxation vs. Prohibition of an External Diseconomy by Direct Vote: A Game-Theoretic Approach,” International Economic Review 14 (1973), 414–420. “Bayesian Equilibria of Finite Two-Person Games with Incomplete Information” (with J.T. Howson, Jr.), Management Science 21 (1974), 313–315. “Disadvantageous Syndicates” (with A. Postlewaite), Journal of Economic Theory 9 (1974), 324–326. “Correlated Equilibria in Some Classes of Two-Person Games,” International Journal of Game Theory 3 (1974), 119–128. “On Lindahl Equilibria in Economies with Public Goods” (with P. Champsaur), CORE Discussion Paper No. 7413, 1974. “Voting Majority Sizes,” Econometrica 43 (1975), 293–299. “Induced Outcomes in Cooperative Normal-Form Games,” Discussion Paper No. 178, Center for Math. Studies, Northwestern University, 1975. “On Cores in Economies with Public Goods” (with P. Champsaur and D.J. Roberts), International Economic Review 16 (1975), 751–764. “Market Games with Production and Public Commodities,” Discussion Paper No. 156, Center for Math. Studies, Northwestern University, revised 1976. “An Arbitration Model for Normal-Form Games,” Mathematics of Operations Research 1 (1976), 82–88. “Lindahl’s Solution and Values for a Public-Goods Example,” Journal of Mathematical Economics 3 (1976), 37–42. “Discussion of Lloyd S. Shapley’s ‘Noncooperative General Exchange’,” in Theory and Measurement of Economic Externalities (S. Lin, ed.), Academic Press, 1976, 177–178.
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A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
“Sufficient Conditions for Insensitivity in Linear Models,” Operations Research 24 (1976), 183–188. “Core and Value for a Public-Goods Economy: An Example” (with R. Aumann and R. Gardner), Journal of Economic Theory 15 (1977), 363–365. “Arbitration of Two-Party Disputes under Ignorance” (with E. Kalai), International Journal of Game Theory 7 (1978), 65–72. “Arbitration of Two-Party Disputes under Uncertainty,” Review of Economic Studies 45 (1978), 595–604. “A Model of Cooperative Games with Binding Commitments,” in Game Theory and Political Science (P. Ordeshook, ed.), NYU Press, 1978, 97–111. “Sequences of Games with Varying Opponents,” Econometrica 47 (1979), 1353–1366. “A Game-Theoretic Analysis of Bargaining with Reputations” (with H. Landau), Journal of Mathematical Psychology 20 (1979), 233–255. “Congestion Tolls: Equilibrium and Optimality,” Naval Research Logistics Quarterly 27 (1980), 231–232. “New Equilibria for Noncooperative Two-Person Games,” Journal of Mathematical Sociology 7 (1980), 15–26. “A Model in Which an Increase in the Number of Sellers Leads to a Higher Price,” Econometrica 48 (1980), 1575–1579. “Repeated Bargaining with Opportunities for Learning” (with H. Landau), Journal of Mathematical Sociology 8 (1981), 61–74. “Games of Perfect Information, Predatory Pricing and the Chain-Store Paradox,” Journal of Economic Theory 25(1981), 92–100. Reprinted in Game Theory in Economics (A. Rubinstein, ed.), Elgar, 1990, 298–306. “A Note on Exact Purification” (with R. Radner), Working Paper, 1981. “A Dynamic Model of Duopoly with Customer Loyalties,” Journal of Economic Theory 27 (1982), 69–76. “Private Information and Pure-Strategy Equilibria” (with R. Radner), Mathematics of Operations Research 7 (1982), 401–409. “A Model of Far-Sighted Electoral Competition,” Mathematical Social Sciences 2 (1982), 289–297. “A Dynamic Oligopoly Game with Lags in Demand: More on the Monotonicity of Price in the Number of Sellers,” International Economic Review 23 (1982), 353–360. “Mixed-Strategy Equilibria in Markets with Asymmetric Information” (with A. Weiss), Working Paper, 1982. “Approximate Purification of Mixed Strategies” (with R. Aumann et al.), Mathematics of Operations Research 8 (1983), 327–341.
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
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“Repeated Two-Player Games with Ruin” (with A. Rubinstein), International Journal of Game Theory 13 (1984), 155–177. “Strategic Analysis of the Competitive Exercise of Certain Financial Options” (with G.M. Constantinides), Journal of Economic Theory 34 (1984), 128–138. “Discussion of: Anderson and Sundaresan, ‘Futures Markets and Monopoly’,” in The Industrial Organization of Futures Markets (R. Anderson, ed.), Heath, 1984, 107–108. “Mixed-Strategy Equilibrium in a Market with Asymmetric Information” (with A. Weiss), Review of Economic Studies 51(1984), 333–342. “An Approach to Some Noncooperative Game Situations with Special Attention to Bargaining,” in Game-Theoretic Models of Bargaining (A. Roth, ed.), Cambridge University Press, 1985, 63–72. “A Dynamic Screening Example,” Working Paper, 1985. “Dynamic Duopoly with Incomplete Customer Loyalties,” International Economic Review 27 (1986), 399–406. “Noncooperative Games and Nontransitive Preferences” (with P. Fishburn), Mathematical Social Sciences 12 (1986), 1–7. “A Positive Approach to Noncooperative Games” (with J. Friedman), Journal of Economic Behavior and Organization 7 (1986), 235–251. “Anonymous Sequential Games” (with B. Jovanovic), Journal of Mathematical Economics 17 (1988), 77–87. “More on the ‘Anti-Folk Theorem’ ” (with J. Masso), Journaj of Mathematical Economics 18 (1989), 281–290. “A Bounded-Rationality Approach to the Study of Noncooperative Games,” International Journal of Game Theory 18 (1989), 273–292. “Duopoly with Both Ruin and Entry” (with R. Spady), Canadian Journal of Economics 22 (1989), 834–851. “Testing the Minimax Hypothesis: A Re-examination of O’Neill’s Game Experiment” (with J. Brown), Econometrica 58 (1990), 1065–1081. “A Strategic Altruism Model in which Ricardian Equivalence Does Not Hold” (with L. Kotlikoff and A. Razin), Economic Journal 100 (1990), 1261–1268. “Strategic Models of Sovereign-Debt Renegotiations” (with R. Fernandez), Review of Economic Studies 57 (1990), 331–349. “On the Incentives Associated with Sovereign Debt,” Journal of International Economics 30 (1991), 167–176. “A Note on Robustness of Equilibria with Respect to Commitment Opportunities,“ Games and Economic Behavior 3 (1991), 237–243.
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A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
“The Contractors’ Game” (with K. Lang), RAND Journal of Economics 22 (1991), 329– 338. “A Note on Abreu–Matsushima Mechanisms” (with J. Glazer), Econometrica 60 (1992), 1435–1438. “Some Inefficiency Implications of Generational Politics and Exchange” (with L. Kotlikoff), Economics and Politics 5 (1993), 27–42. “Suicide Attempts and Signalling Games,” Mathematical Social Sciences 26 (1993), 25– 33. “An Explanation of Inefficiency in Markets and a Justification for Buy-and-Hold Strategies” (with R. Wang), Canadian Journal of Economics 26 (1993), 609–624. “Rules of Thumb in Games,” Journal of Economic Behavior and Organization 22 (1993), 1–13. “Bargaining Rules of Thumb,” Journal of Economic Behavior and Organization 22 (1993), 15–24. “Price and Quality Cycles for Experience Goods” (with D. Gale), RAND Journal of Economics 25 (1994), 590–607. “Dynamic Duopoly with Slowly Changing Customer Loyalties” (with Y. Chen), International Journal of Industrial Organization 14 (1996), 269–296. “Asking Prices as Commitment Devices” (with Y. Chen), International Economic Review 37 (1996), 129–155. “On the Use of Ceiling-Price Commitments by Monopolists” (with Y. Chen), RAND Journal of Economics 27 (1996), 207–220. “Simultaneous Auctions with Synergies” (with V. Krishna), Games and Economic Behavior 17 (1996), 1–31. “Simultaneous Auctions with Synergies and Common Values” (with R. Wang), Games and Economic Behavior 17 (1996), 32–55. “On Some Myths about Sequenced Common-value Auctions” (with M.A. de Frutos), Games and Economic Behavior 23 (1998), 201–221. “Experimentation, Imitation, and Stochastic Stability” (with D. Gale), Journal of Economic Theory 84 (1999), 1–40. “Experimentation, Imitation, and Stochastic Stability: Addendum” (with D. Gale), Journal of Economic Theory 97 (2001), 164–174. “Trust and Social Efficiencies,” Review of Economic Design 6 (2001), 413–428. “Coordination Through Reputations: A Laboratory Experiment” (with D. Dale and J. Morgan), Games and Economic Behavior 38 (2002), 52–88. “Bargaining Piecemeal or All at Once?” (with K. Lang), Economic Journal 3, No. 473, 526–540.
A. Postlewaite, R. Wilson / Games and Economic Behavior 45 (2003) 271–277
277
“Three-Object, Two-Bidder Simultaneous Auctions: Chopsticks and Tetrahedra” (with B. Szentes), Games and Economic Behavior, to appear. “Hide and Seek in Arizona” (with J. Shachat and M. Walker), International Journal of Game Theory, to appear. “Beyond Chopstick: Symmetric Equilibria in Majority Auction Games” (with B. Szentes), Games and Economic Behavior, this issue. Andrew Postlewaite Robert Wilson E-mail address: [email protected] (A. Postlewaite) 7 May 2003