# Cowles Foundation for Research in Economics, Yale University

# Cowles Foundation Discussion Papers

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### 1982

**648 The Structure of Social Risk***by*William D. Nordhaus & Steven N. Durlauf**645 ERA's: A New Approach to Small Sample Theory***by*Peter C.B. Phillips**644 Core and Competitive Equilibria with Indivisibilities***by*Martine Quinzii**643 Utility Functions for Debreu's 'Excess Demands'***by*John Geanakoplos**642 On the Disaggregation of Excess Demand Functions***by*John Geanakoplos & Heracles M. Polemarchakis**641 Don't Bet on It***by*John Geanakoplos & James K. Sebenius**640 On Implicit Contracts and Involuntary Unemployment***by*John Geanakoplos & Takatoshi Ito**639 We Can't Disagree Forever***by*John Geanakoplos & Heracles M. Polemarchakis**638 Failure of the Alternation Theorem in Rational Approximations Over C_0(-infinity,infinity)***by*Peter C.B. Phillips**637 The Distribution of Matrix Quotients***by*Peter C.B. Phillips**636 A Bookmaker or Market Type Test for Specification in Discrete Choice Models***by*John J. Beggs**635 Information Processing and Jury Decisionmaking***by*Alvin K. Klevorick & Michael Rothschild & Christopher Winship**634R Revelation of Information in Strategic Market Games: A Critique of Rational Expectations***by*Pradeep Dubey & John Geanakoplos & Martin Shubik**632 Integral Polyhedra in Three Spaces***by*Herbert E. Scarf**631 Inefficiency of Nash Equilibria in a Private Goods Economy***by*Pradeep Dubey & J.D. Rogawski**629 Information About Moves in Extensive Games: II***by*Pradeep Dubey & Mamoru Kaneko**628 Equilibria for a Three-Person Location Problem***by*Martin J. Osborne & Carolyn Pitchik**627 Naval Procurement Problems: Theory and Practice***by*Zvi A. Livne & Martin Shubik**626 On the Exact Distribution of LIML (revised and extended, see CFDP 658)***by*Peter C.B. Phillips**625 Information About Moves in Extensive Games: I***by*Pradeep Dubey & Mamoru Kaneko**624 Stochastic Games II: The Minmax Theorem***by*Curt Alfred Monash**623 Stochastic Games I: Foundations***by*Curt Alfred Monash**622 Inefficiency of Nash Equilibria: I***by*Pradeep Dubey & J.D. Rogawski**621 Exact Small Sample Theory in the Simultaneous Equations Model***by*Peter C.B. Phillips**620 Cores of Partitioning Games***by*Mamoru Kaneko & Myrna Holtz Wooders**619 Approximate Cores of a General Class of Economies: Part II. Set-Up Costs and Firm Formation in Coalition Production Economies***by*Martin Shubik & Myrna Holtz Wooders**618 Approximate Cores of a General Class of Economies. Part I: Replica Games, Externalities, and Approximate Cores***by*Martin Shubik & Myrna Holtz Wooders**617 Small Sample Distribution Theory in Econometric Models of Simultaneous Equations***by*Peter C.B. Phillips**616 Macroeconomics and Fiscal Policy: Paul A. Samuelson and Modern Economics***by*James Tobin**615 How Fast Should We Graze the Global Commons?***by*William D. Nordhaus**614 The Conventionally Stable Sets in Noncooperative Games with Limited Observations: The Application to Monopoly and Oligopoly***by*Mamoru Kaneko**613R Money and Finance in the Macro-Economic Process***by*James Tobin

### 1981

**612 The Epsilon Core of a Large Game***by*Myrna Holtz Wooders**611 Macroconfusion: The Dilemmas of Economic Policy***by*William D. Nordhaus**610 Payoffs in Non-Atomic Economies: An Axiomatic Approach***by*Pradeep Dubey & Abraham Neyman**609 Marginal Densities of Instrumental Variable Estimators in the General Single Equation Case***by*Peter C.B. Phillips**608 A New Approach to Small Sample Theory***by*Peter C.B. Phillips**607 Some Remarks on the Folk Theorem in Game Theory***by*Mamoru Kaneko**606 Game Theory: The Language of Strategy?***by*Martin Shubik**605 Asset Markets, General Equilibrium and the Neutrality of Money***by*Christophe Chamley & Heracles M. Polemarchakis**604 Economic Policy in the Face of Declining Productivity Growth***by*William D. Nordhaus**603 Schumpeterian Dynamics II. Technological Progress, Firm Growth and 'Economic Selection'***by*Katsuhito Iwai**602 Schumpeterian Dynamics I. An Evolutionary Model of Innovation and Imitation***by*Katsuhito Iwai**601 The Conventionally Stable Sets in Noncooperative Games with Limited Observations: Definitions and Introductory Arguments***by*Mamoru Kaneko**600 Algorithms for the Linear Complementarity Problem Which Allow an Arbitrary Starting Point***by*Dolf A.J.J. Talman & Ludo Van der Heyden**599 The Optimal Progressive Income Tax -- The Existence and the Limit Tax Rates***by*Mamoru Kaneko**598 On the Infinite Welfare Cost of Inflation and Other Second Order Effects***by*Christophe Chamley**597 Estimated Effects of Relative Prices on Trade Shares***by*Ray C. Fair**596 Arbitrage Pricing Theory in a Finite Economy***by*John J. Beggs**595 Approximate Equilibria with Bounds Independent of Preferences***by*Robert M. Anderson & M. Ali Khan & Salim Rashid**594 Mandatory Retirement Saving and Capital Formation***by*Walter Dolde & James Tobin**593 Market Structure in the 'Research and Development Phase'***by*John J. Beggs**592 Estimated Output, Price, Interest Rate, and Exchange Rate Linkages Among Countries***by*Ray C. Fair**591 Efficient Stationary Taxation and Intertemporal General Equilibrium***by*Christophe Chamley & Douglas Downing**590 Strong Core Theorems with Nonconvex Preferences***by*Robert M. Anderson**589 Interest Rate Policies and Informational Efficiency***by*Laurence Weiss**588 The Dynamic Interaction Between Industry Level Profits and Research and Development***by*John J. Beggs**587 Ratio Equilibrium in an Economy with an Externality***by*Yozo Ito & Mamoru Kaneko**586 Marginal Cost Pricing, Taxation and Subsidies in Urban Transport***by*John J. Beggs**585 Properties of Manipulative Government Forecasts***by*John J. Beggs**584 The Demand for Telephone Services in Australia and the Welfare Implications of Alternative Pricing Policies***by*John J. Beggs**583 An Empirical Note on the Disposition of U.S. Corporations to Undertake Research and Development Expenditures***by*John J. Beggs**582 Cake Slicing and Revealed Government Preference***by*John J. Beggs & Samuel Strong**581 Existence of Equilibrium in a Hyperfinite Exchange Economy: I and II***by*Donald J. Brown & Lucinda M. Lewis**580 Entrepreneurial Abilities and Liabilities in a Model of Self-Selection***by*Christophe Chamley**579 Equilibria of a Two-Person Non-Zero Sum Noisy Game of Timing***by*Carolyn Pitchik**578 Core Theory with Strongly Convex Preferences***by*Robert M. Anderson**577 Society, Land, Love or Money (A Strategic Model of How to Glue the Generations Together)***by*Martin Shubik**576 Duopoly with Differentiated Products and Entry Barriers***by*Kofi O. Nti & Martin Shubik**551 Incentive Arbitration and Time-Related Bargaining Costs***by*Zvi A. Livne**550 An Extension of the Nash Bargaining Problem: Introducing Time-Related Bargaining Costs***by*Zvi A. Livne

### 1980

**575 A Path Following Procedure for Finding a Point in the Core of a Balanced N-Person Game***by*Ludo Van der Heyden**574 Additively Decomposed Quasiconvex Functions***by*Gerard Debreu & Tjalling C. Koopmans**573 On the Consistency of Non-Linear FIML***by*Phillips, Peter C.B.**572 A Market Value Approach to Approximate Equilibria***by*Robert M. Anderson**571 Housing Market with Indivisibility***by*Mamoru Kaneko**570 National Savings, Economic Welfare, and the Structure of Taxation***by*Alan J. Auerbach & Lawrence Kotlikoff**569 The Adequacy of Savings***by*Lawrence Kotlikoff & Avia Spivak & Lawrence H. Summers**568 On the Behavior of Inconsistent Instrumental Variable Estimators***by*Esfandier Maasoumi & Peter C.B. Phillips**567 Characteristic Functions and the Tail Behavior of Probability Distributions***by*Peter C.B. Phillips**566 A Necessary and Sufficient Condition for the Nonemptiness of the Cores of Partitioning Games***by*Mamoru Kaneko**565 Thinking About Carbon Dioxide: Theoretical and Empirical Aspects of Optimal Control Strategies***by*William D. Nordhaus**564 Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models***by*Ray C. Fair & John B. Taylor**563 The Central Assignment Game and the Assignment Markets***by*Mamoru Kaneko**562 Best Uniform Approximation to Probability Densities in Econometrics***by*Peter C.B. Phillips**561 The Characteristic Function of the F Distribution***by*Peter C.B. Phillips**560 On a Lemma of Amemiya***by*Peter C.B. Phillips**559 Perfect or Robust Noncooperative Equilibrium: A Search for the Philosophers Stone?***by*Martin Shubik**558 Heterogeneous Information and the Theory of the Business Cycle***by*Sanford Grossman & Laurence Weiss**557 Intergenerational Political Economy (A Game Theoretic Model of How to Glue the Generations Together)***by*Martin Shubik**556 Extension of a Dynamical Model of Political Equilibrium***by*Gerald H. Kramer**555 Policy Responses to the Productivity Slowdown***by*William D. Nordhaus**554 Optimal Intertemporal Taxation and the Public Debt***by*Christophe Chamley**553 The Welfare Cost of Capital Income Taxation in a Growing Economy***by*Christophe Chamley**552 A Model of Output, Employment, Capital Formation and Inflation***by*R.W. Bailey & V.B. Hall & Peter C.B. Phillips**549 An Application of the Khachian-Shor Algorithm to a Class of Linear Complementary Problems***by*Ilan Adler & Richard P. McLean & J. Scott Provan**548 A Model of U.S. Financial and Nonfinancial Economic Behavior***by*David Backus & William C. Brainard & Gary Smith & James Tobin**547 Weakly Democratic Regular Tax Equilibria in a Local Public Goods Economy with Perfect Consumer Mobility***by*Donald K. Richter**546 Output Supply, Employment, and Intra-Industry Wage Dispersion***by*Philip H. Dybvig & Gerald David Jaynes**545 Inequality, Exploitation, Justice and Socialism: A Theoretical-Historical Approach***by*John E. Roemer**544 Rawlsian Justice as the Core of a Game***by*Roemer, John E. Roemer & Roger Howe**543 Exploitation and Class: Part II, Capitalist Economy***by*John E. Roemer**542 Linear Complementarity and the Degree of Mappings***by*Roger Howe

### 1979

**541R A Multicountry Econometric Model***by*Ray C. Fair**540 Some Relationships Between Discrete and Continuous Models of an Urban Economy***by*Richard P. McLean & Thomas J. Muench**539 Morse Programs***by*Okitsugu Fujiwara**538 On the Tendency Toward Convexity of the Vector Sum of Sets***by*Roger Howe**537 An Algorithm for FIML and 3SLS Estimation of Large Nonlinear Models***by*William R. Parke**536 The Spending Behavior of Wealth- and Liquidity-Constrained Consumers***by*Kim Kowalewski & Gary Smith**535 Disequilibrium Models of Financial Institutions***by*Gary Smith & William C. Brainard**534 The Energy Crisis and Macroeconomic Policy***by*William D. Nordhaus**533 Tax-Based Incomes Policies: A Better Mousetrap?***by*William D. Nordhaus**532 How Should We Revise Our Beliefs About Nuclear Power Safety After Three Mile Island?***by*William D. Nordhaus**531 Competitive Bidding and Proprietary Information***by*Richard Engelbrecht-Wiggans & Robert J. Webber**530 On the Relation of Various Reliability Measures to Each Other and to Game Theoretic Values***by*Richard Engelbrecht-Wiggans & David R. Strip**529 The Design of Distributed Service Systems***by*David R. Strip & Richard Engelbrecht-Wiggans**528 Information Aggregation and Policy***by*Laurence Weiss**527 The ALEP Definition of Complementarity and Least Concave Utility Functions***by*Yakar Kannai**526 Production Sets with Indivisibilities: Generalities and the Case of Two Variables***by*Herbert E. Scarf**525 Stochastic Games, Oligopoly Theory and Competitive Resource Allocation***by*Martin Shubik & Matthew J. Sobel**524 Most Convex Functions are Smooth***by*Roger Howe**523 On the Non-Existence of Multiplicative Equilibrium Bidding Strategies***by*Engelbrecht-Wiggans & Robert J. Weber**522 The Short-Run Macroeconomics of Floating Exchange Rates: An Exposition***by*James Tobin & Jorge B. de Macedo**521 A Strategic Market Game with Price and Quantity Strategies***by*Pradeep Dubey & Martin Shubik**520 Price-Quantity Strategic Market Games***by*Pradeep Dubey**519 Full Information Estimates of a Nonlinear Macroeconometric Model***by*Ray C. Fair & William R. Parke**518 An Even More Elementary `Calculus' Proof of the Brouwer Fixed Point Theorem***by*Yakar Kannai**517 Cooperative Game Solutions: Australian, Indian and U.S. Opinions***by*Martin Shubik**516 An Index Theorem for General Equilibrium Models with Production***by*Timothy J. Kehoe**515 Subjectivity in the Valuation of Games***by*Robert J. Weber**514 Market Induced Welfare Optima***by*Rolf R. Mantel**513 Value Theory without Efficiency***by*Pradeep Dubey & Abraham Neyman & Robert J. Weber**500R Bidding in Auctions with Multiplicative Lognormal Errors: An Example***by*Richard Engelbrecht-Wiggans**496R Auctions and Bidding Models: A Survey***by*Richard Engelbrecht-Wiggans

### 1978

**512 Fiscal and Monetary Policies, Capital Formation, and Economic Activity***by*Willem H. Buiter & James Tobin**511 An Estimate of the Uncertainty of Policy Effects in a Macro-economic Model***by*Ray C. Fair**510 Balance of Payments and the Foreign Exchange Market: A Dynamic Partial Equilibrium Model***by*Pentti J.K. Kouri**509 A Model of Stochastic Equilibrium in a Quasi-Competitive Industry***by*John Sutton**508R Finiteness and Inefficiency of Nash Equilibria***by*Pradeep Dubey**507 The Capital Stock Modified Competitive Equilibrium***by*Martin Shubik**506 A Proposal for International Monetary Reform***by*James Tobin**505 Economics among the Sciences***by*Tjalling C. Koopmans**504 Equity, Efficiency and Increasing Returns***by*Donald J. Brown & Geoffrey M. Heal**503 The Optimal Payment of Unemployment Insurance Benefits over Time***by*Steven Shavell & Laurence Weiss**502 Government Deficits and Capital Accumulation***by*James Tobin**501 Nash Equilibria of Market Games: II. Finiteness***by*Pradeep Dubey**499 A Model of International Trade and Finance***by*Laurence Weiss**498 Comparison of Public Choice Systems***by*Robert J. Weber**497 Debt Neutrality: A Brief Review of Doctrine and Evidence***by*Willem H. Buiter & James Tobin**495 A Model for the Distribution of the Number of Bidders in an Auction***by*Richard Engelbrecht-Wiggans**494 An Example of a Multi-Object Auction Game***by*Richard Engelbrecht-Wiggans**493 An Integrated Model of Household Flow-of-Funds Allocations***by*David Backus & Douglas D. Purvis**492 An Analysis of the Accuracy of Four Macroeconometric Models***by*Ray C. Fair**491 The Role for Active Monetary Policy in a Rational Expectations Model***by*Laurence Weiss**490 Profitability and Growth in a Small Open Economy***by*Pentti J.K. Kouri**489 Systems Defense Games: Colonel Blotto, Command and Control***by*Martin Shubik & Robert J. Weber**488 Exchange Rates and the International Adjustment Process***by*Pentti J.K. Kouri & Jorge B. de Macedo**487 A Note on the Saddlepoint Approximation in the First Order Non-Circular Autoregression***by*Peter C.B. Phillips**486 The Transition from Exhaustible to Renewable or Inexhaustible Resources***by*Tjalling C. Koopmans**485 The Structure of Neutral Monotonic Social Functions***by*Julian H. Blau & Donald J. Brown**484 On 'On the Foundations of the Theory of Monopolistic Competition'***by*Pradeep Dubey & Martin Shubik**483 A Theory of Money and Financial Institutions. Part 37. The Profit Maximizing Firm: Managers and Stockholders***by*Pradeep Dubey & Martin Shubik**482 Competitive Valuation of Cooperative Games***by*Martin Shubik & Robert J. Weber**481 Myopic Economic Agents***by*Donald J. Brown & Lucinda M. Lewis**480 Estimating the Expected Predictive Accuracy of Econometric Models***by*Ray C. Fair**479 A Model of the Jury Decision Process***by*Alvin K. Klevorick & Michael Rothschild**478 The Nucleolus as a Noncooperative Game Solution***by*Martin Shubik & H. Peyton Young**472R The Effects of Money Supply on Economic Welfare***by*Weiss, Laurence Weiss

### 1977

**477 Modelling the Choice of Residential Location***by*Daniel McFadden**476 Game Theory Models and Methods in Political Economy***by*Martin Shubik**475 Nash Equilibria of Market Games: I. Existence and Convergence***by*Pradeep Dubey**474 Quantitative Methods for Analyzing Travel Behaviour of Individuals: Some Recent Developments***by*Daniel McFadden**473 The Computation of Equilibrium Prices: An Exposition***by*Herbert E. Scarf**471R Probabilistic Values for Games***by*Robert J. Weber**471 Probabilistic Values for Games***by*Pradeep Dubey & Robert J. Weber**470 Sealed Bid Auctions with Non-Additive Bid Functions***by*Richard Englebrecht-Wiggans**469 The Greedy Heuristic Applied to a Class of Set Partitioning and Subset Selection Problems***by*Richard Engelbrecht-Wiggans**468 The Long Run Implications of an IS-LM Simulation Model***by*Gary Smith**467 Information Conditions, Communication and General Equilibrium***by*Pradeep Dubey & Martin Shubik**466 The Long Run Implications of a Two Sector Model with Immobile Capital***by*Gary Smith**465 On Modeling the Economic Linkages among Countries***by*Ray C. Fair**464 The Long Run Consequences of Monetary and Fiscal Policies When the Governments Budget Is Not Balanced***by*Gary Smith**463 Deficit Spending and Crowding Out in Shorter and Longer Runs***by*James Tobin**462 A Theory of Money and Financial Institutions***by*Martin Shubik**461 Equilibrium and Disequilibrium Interpretations of the IS-LM Model***by*Gary Smith**460R Strategic Market Games: A Sketch of an Approach to the Theory of Money and Financial Institutions. Together with an Informal Guide to Some Papers***by*Martin Shubik**459 An Analysis of a Macroeconometric Model with Rational Expectationsin the Bond and Stock Markets***by*Ray C. Fair**458 How Dead is Keynes?***by*James Tobin**457 Modeling Technological Change: Use of Mathematical Programming Models in the Energy Sector***by*William D. Nordhaus & Ludo Van der Heyden**456 Monetary Policies and the Economy -- The Transmission Mechanism***by*James Tobin**455 A Theory of Money and Financial Institutions. Part 22. A Price-Quantity Buy-Sell Market with and without Contingent Bids***by*Martin Shubik**454 A Theory of Money and Financial Institutions. Part 36. The Money Rate of Interest (A Multiperiod Nonatomic Trading and Production Economy with Outside Money, Inside Money and Optimal Bankruptcy Rules)***by*Pradeep Dubey & Martin Shubik**453 An Observation on the Structure of Production Sets with Indivisibilities***by*Herbert E. Scarf**452 Policy Effects in a Model of the Balance of Payments***by*Ray C. Fair**451 A Model of the Balance of Payments***by*Ray C. Fair**450 A Shortrun Macroeconomic Model of an Open Economy***by*Gary Smith**449 What is the Value of Advanced Nuclear Power?***by*William D. Nordhaus**448 A Theory of Money and Financial Institutions. Part 35. Bankruptcy and Optimality in a Closed Trading Mass Economy Modelled as a Noncooperative Game***by*Pradeep Dubey & Martin Shubik**447 Noncooperative Exchange with a Continuum of Traders***by*Pradeep Dubey & Lloyd S. Shapley**446 The Sensitivity of Fiscal-Policy Effects to Assumptions about the Behavior of the Federal Reserve***by*Ray C. Fair

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