Foundations of Game Theory

Edited by Mary Ann Dimand, Instructor, Department of Economics and Management, Albion College, US and Robert W. Dimand, Professor of Economics, Brock University, Canada

'This collection contains a number of interesting papers which justify reprinting. The editors are to be congratulated on making these available.'

• Introduction by the editorsPart I The Beginnings1. J. Waldegrave ([1713] 1968), ‘Minimax Solution to 2-Person, Zero-Sum Game.’2. F.Y. Edgeworth ([1881] 1967), ‘Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences.’3. J. Bertrand ([1883] 1992), ‘Appendix: Review by Joseph Bertrand of Two Books.’4. F.Y. Edgeworth ([1897] 1925), ‘The Pure Theory of Monopoly.’5. A.L. Bowley (1928), ‘Bilateral Monopoly.’6. F. Zeuthen (1933), ‘Theoretical Remarks on Price Policy: Hotelling’s Case with Variations.’7. A. Smithies and L.J. Savage (1940), ‘A Dynamic Problem in Duopoly.’Part II Mathematical Models of Conflict: Richardson and Lanchester8. L.F. Richardson (1919), ‘Mathematical Psychology of War.’9. F.W. Lanchester ([1916] 1956), ‘Mathematics in Warfare.’Part III Psychological Games Between the Wars10. H. Steinhaus ([1925] 1960), ‘Definitions for a Theory of Games and Pursuit.’11. M. Fréchet (1953), ‘Émile Borel, Initiator of the Theory of Psychological Games and its Application.’12. É. Borel ([1921] 1953), The Theory of Play and Integral Equations with Skew Symmetric Kernels.’13. É. Borel ([1924] 1953), ‘On Games that Involve Chance and the Skill of the Players.’14. É. Borel ([1927] 1953), ‘On Systems of Linear Forms of Skew Symmetric Determinant and the General Theory of Play.’15. M. Fréchet (1953), ‘Commentary on the Three Notes of Émile Borel.’16. J. von Neumann (1953), ‘Communication on the Borel Notes.’17. J. von Neumann (1928), ‘Sur la théorie des jeux.’18. J. von Neumann ([1928] 1959), ‘On the Theory of Games of Strategy’19. (1937), ‘Princeton Scientist Analyzes Gambling: “You Can’t Win”.’20. L. Kalmár (1928-29), ‘Toward a Theory of Abstract Games.’21. R.A. Fisher (1934), ‘Randomisation, and an Old Enigma of Card Play.’22. O. Morgenstern ([1935] 1976), ‘Perfect Foresight and Economic Equilibrium.’23. R. de Possel (1936), ‘Sur la théorie mathématique des jeux de hasard et de réflexion.’24. J. Ville (1938), ‘Sur la théorie générale des jeux ou intervient l’habileté des joueurs.’Part IV The Impact of von Neumann and Morgenstern (1944)25. H.A. Simon (1945), ‘Review of Theory of Games and Economic Behavior.’26. O. Morgenstern (1976), ‘The Collaboration Between Oskar Morgenstern and John von Neumann on the Theory of Games.’27. G.T. Guilbaud (1951), ‘The Theory of Games: Critical Contributions to the Theory of Value.’28. O. Morgenstern (1948), ‘Oligopoly, Monopolistic Competition, and the Theory of Games.’29. O. Morgenstern (1949), ‘Economics and the Theory of Games.’30. L. Hurwicz (1953), ‘What Has Happened to the Theory of Games.’Part V von Neumann’s Later Work on Games31. G.W. Brown and J. von Neumann (1950), ‘Solutions of Games by Differential Equations.’32. J. von Neumann (1953), ‘A Certain Zero-Sum Two-Person Game Equivalent to the Optimal Assignment Problem.’33. D.B. Gillies, J.P. Mayberry and J. von Neumann (1953), ‘Two Variants of Poker.’34. J. von Neumann (1954), ‘A Numerical Method to Determine Optimum Strategy.’35. H.W. Kuhn and A.W. Tucker (1958), ‘John von Neumann’s Work in the Theory of Games and Mathematical Economics.’Part VI Mathematical Reformulation and extension of Minimax Theorem36. A. Wald (1945), ‘Statistical Decision Functions which Minimize the Maximum Risk.’37. A. Wald (1945), ‘Generalization of a Theorem by v. Neumann concerning Zero Sum Two Person Games’38. I. Kaplansky (1945), ‘A Contribution to von Neumann’s Theory of Games.’39. L.H. Loomis (1946), ‘On a Theorem of von Neumann.’40. L.L. Dines (1947), ‘ On a Theorem of von Neumann.’41. H. Weyl (1950), ‘Elementary Proof of a Minimax Theorem due to von Neumann.’42. A. Wald (1950), ‘Note on Zero Sum Two Person Games.’43. A. Dvoretzky, A. Wald and J. Wolfowitz (1950), ‘Elimination of Randomization in Certain Problems of Statistics and of the Theory of Games.’44. A. Dvoretzky, A. Wald and J. Wolfowitz (1951), ‘Elimination of Randomization in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games.’45. A. Wald and J. Wolfowitz (1951), ‘Two Methods of Randomization in Statistics and the Theory of Games.’46. J. Robinson (1951), ‘An Iterative Method of Solving a Game.’47. I.L. Glicksberg (1952), ‘A Further Generalization of the Kakutani Fixed Point Theorem, with Application to Nash Equilibrium Points.’48. K. Fan (1952), ‘Fixed-Point and Minimax Theorems in Locally Convex Topological Linear Spaces.’49. K. Fan (1953), ‘Minimax Theorems.’50. H. Nikaidô (1954), ‘ On von Neumann’s Minimax Theorem.’Name IndexVolume TwoPart I Nash, Bargaining and Equilibrium1. J.F. Nash, Jr. (1950), ‘The Bargaining Problem.’2. J.F. Nash, Jr., (1950), ‘Equilibrium Points in n-Person Games.’3. J.F. Nash and L.S. Shapley (1950), ‘A Simple Three-Person Poker Game.’4. J. Nash (1951), ‘Non-Cooperative Games.’5. J. Nash (1953), ‘Two-Person Cooperative Games.’6. J.P. Mayberry, J.F. Nash and M. Shubik (1953), ‘A Comparison of Treatments of a Duopoly Situation.’7. M. Shubik (1955), ‘A Comparison of Treatments of a Duopoly Problem (Part II).’8. G.K. Kalisch, J. W. Milnor, J.F. Nash and E.D. Nering (1954), ‘Some Experimental n-Person Games.’Part II Game Theory in the 1950s: Formulation and Solution of Games9. R. Bellman and D. Blackwell (1949), ‘Some Two-Person Games Involving Bluffing.’10. R. Bellman (1952), ‘On Games Involving Bluffing.’11. H.W. Kuhn (1950), ‘Extensive Games.’12. D. Gale, H.W. Kuhn and A.W. Tucker (1951), ‘Linear Programming and the Theory of Games.’13. G.V. Dantzig (1951), ‘A Proof of the Equivalence of the Programming Problem and the Game Problem.’14. J.C.C. McKinsey (1952), ‘Some Notions and Problems of Game Theory.’15. M. Shubik (1952), ‘Information, Theories of Competition, and the Theory of Games.’16. M. Shubik (1954), ‘Information, Risk, Ignorance and Indeterminacy.’17. L.S. Shapley (1953), ‘Stochastic Games.’18. H. Raiffa (1953), ‘Arbitration Schemes for Generalized Two-Person Games.’19. R. Isaacs (1955), ‘Rand Reports: ‘Differential Games I: Introduction’ ‘Differential Games II: The Definition and Formulation’ ‘Differential Games III: The Basic Principles of the Solution Process’.’20. J. Milnor (1954), ‘Games Against Nature’21. D. Ellsberg (1956), ‘The Theory of the Reluctant Duelist.’22. L. Friedman (1956), ‘A Competitive-Bidding Strategy.’23. T.C. Schelling (1956), ‘An Essay on Bargaining.’24. T.C. Schelling (1959), ‘For the Abandonment of Symmetry in Game Theory.’25. M. Sion and P. Wolfe (1957), ‘ On a Game Without a Value.’26. A.Y.C. Koo (1959), ‘Recurrent Objections to the Minimax Strategy.’27. D. Ellsberg (1959), ‘Rejoinder’Part III Game Theory in the 1950s: Cooperative Games28. L.S. Shapley (1951), ‘Rand Report: ‘The Noisy Duel: Existence of a Value in the Singular Case’.’29. L.S. Shapley (1951), ‘Rand Report: ‘Notes on the n-Person Game, II: The Value of an N-Person Game’.’30. L.S. Shapley (1952), ‘Rand Report: ‘Notes on the n-Person Game, III: Some Variants of the von Neumann-Morgenstern Definition of Solution’.’31. L.S. Shapley (1955), ‘Rand Report: ‘Markets as Cooperative Games’.’32. R.D. Luce (1954), ‘A Definition of Stability for n-Person Games.’33. J.C. Harsanyi (1956), ‘Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen’s, Hicks’, and Nash’s Theories.’34. J.C. Harsanyi (1959), ‘A Bargaining Model for the Cooperative n-Person Game.’35. R.J. Aumann (1959), ‘Acceptable Points in General Cooperative n-Person Games.’36. R.J. Aumann (1960), ‘Linearity of Unrestrictedly Transferable Utilities.’37. R.J. Aumann and B. Peleg (1960), ‘Von Neumann-Morgenstern Solutions to Co-operative Games Without Side Payments.’38. D.B. Gillies (1959), ‘Solutions to General Non-Zero-Sum Games.’Name IndexVolume ThreePart I Game Theory in the 1950s: Games of Indefinite or Infinite Length1. D. Gale and F.M. Stewart (1953), ‘Infinite Games with Perfect Information.’2. H. Everett (1957). ‘Recursive Games.’3. J. Milnor and L.S. Shapley (1957), ‘On Games of Survival.’4. H.E. Scarf (1957), ‘On Differential Games with Survival Payoff.’Part II Game Theory in the 1950s: War and Peace5. D.W. Blackett (1954), ‘Some Blotto Games.’6. O.G. Haywood, Jr. (1954), ‘Military Decision and Game Theory.’7. T.E. Caywood and C.J. Thomas (1955), ‘Applications of Game Theory in Fighter Versus Bomber Combat.’8. T.C. Schelling (1957), ‘Bargaining, Communication, and Limited War.’9. H.K. Weiss (1959), ‘Some Differential Games of Tactical Interest and the Value of a Supporting Weapon System.’Part III Beginnings of Experimental Games10. E.H. Chamberlin (1948), ‘An Experimental Imperfect Market.’11. W.E. Vinacke and A. Arkoff (1957), ‘An Experimental Study of Coalitions in the Triad.’12. M.M. Flood (1958), ‘Some Experimental Games.’13. J.J. Stone (1958), ‘An Experiment in Bargaining Games.’14. A. Scodel, J.S. Minas, P. Ratoosh and M. Lipetz (1959), ‘Some Descriptive Aspects of Two-Person Non-Zero-Sum Games.’15. J.S. Minas, A. Scodel, D. Marlowe and H. Rawson (1960), ‘Some Descriptive Aspects of Two-Person Non-Zero-Sum Games II.’16. A. Rapoporte and C. Orwant (1962), ‘Experimental Games: A Review.’Part IV Some Economic and Business Applications Beyond Market Structure17. H. Steinhaus (1948), ‘The Problem of Fair Division.’18. M. Shubik (1952), ‘A Business Cycle Model with Organized Labor Considered.’19. K. Midutani (1955), ‘The Maximum Expansion of Bank Credit and the Theory of Games.’20. G.K. Chacko (1956), ‘Certain Game Situations in Regional Economic Development.’21. G.J. Glasser (1958), ‘Personnel Decisions and the Theory of Games.’22. L. Friedman (1958), ‘Game-Theory Models in the Allocation of Advertising Expenditures.’23. I. Hale (1960), ‘The Theory of “Games” in Stock Selection ....how it might be applied to Security Analysis.’Part V Applications Beyond Economics24. J. Bernard (1954), ‘The Theory of Games of Strategy as a Modern Sociology of Conflict.’25. R.B. Braithwaite ([1954] 1963), ‘Theory of Games as a Tool for the Moral Philosopher.’26. L.S. Shapley and M. Shubik (1954), ‘A Method for Evaluating the Distribution of Power in a Committee System.’27. K.W. Deutsch (1954), ‘Game Theory and Politics: Some Problems of Application.’28. R.C. Snyder (1955), ‘Game Theory and the Analysis of Political Behavior.’29. R.D. Luce and A.A. Rogow (1956), ‘A Game Theoretic Analysis of Congressional Power Distributions for a Stable Two-Party System.’30. H.A. Simon, (1956), ‘A Comparison of Game Theory and Learning Theory.’31. S. Siegel (1959), ‘Theoretical Models of Choice and Strategy Behavior: Stable State Behavior in the Two-Choice Uncertain Outcome Situation.’32. F. Barth (1959), ‘Segmentary Opposition and the Theory of Games: A Study of Pathan Organization.’33. R.C. Lewontin (1961), ‘Evolution and the Theory of Games.’Part VI Bibliography34. D.M. Thompson and G.L. Thompson (1959), ‘A Bibliography of Game Theory.’Name Index