Edited by William Thomson, Elmer B. Milliman Professor of Economics, University of Rochester, US

• Contents:AcknowledgementsIntroduction William ThomsonPART IBASIC PAPERS AIndependence1. John F. Nash Jr. (1950), ‘The Bargaining Problem’2. Alvin E. Roth (1977), ‘Individual Rationality and Nash’s Solution to the Bargaining Problem’3. Alvin E. Roth (1977), ‘Independence of Irrelevant Alternatives, and Solutions to Nash’s Bargaining Problem’4. Hans Peters and Peter Wakker (1991), ‘Independence of Irrelevant Alternatives and Revealed Group Preferences’5. Charles Blackorby, Walter Bossert and David Donaldson (1994), ‘Generalized Ginis and Cooperative Bargaining Solutions’6. Efe A. Ok (1998), ‘Inequality Averse Collective Choice’BMonotonicity7. Ehud Kalai and Meir Smorodinsky (1975), ‘Other Solutions to Nash’s Bargaining Problem’8. A.E. Roth (1979), ‘An Impossibility Result Concerning n-Person Bargaining Games’9. Ehud Kalai (1977), ‘Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons’10. Haruo Imai (1983), ‘Individual Monotonicity and Lexicographic Maxmin Solution’11. W. Thomson and R.B. Myerson (1980), ‘Monotonicity and Independence Axioms’12. P.L. Yu (1973), ‘A Class of Solutions for Group Decision Problems’13. Youngsub Chun (1988), ‘The Equal-Loss Principle for Bargaining Problems’CAxioms Pertaining to Operations Performed on Feasible Sets14. Roger B. Myerson (1977), ‘Two-Person Bargaining Problems and Comparable Utility’15. M.A. Perles and M. Maschler (1981), ‘The Super-Additive Solution for the Nash Bargaining Game’16. Roger B. Myerson (1981), ‘Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems’17. Clara Ponsati and Joel Watson (1997), ‘Multiple-Issue Bargaining and Axiomatic Solutions’18. Hans Peters (1986), ‘Simultaneity of Issues and Additivity in Bargaining’DOrdinal Invariance19. Lloyd S. Shapley (1969), ‘Utility Comparison and the Theory of Games’20. Lars Tyge Nielsen (1983), ‘Ordinal Interpersonal Comparisons in Bargaining’21. Yves Sprumont (2000), ‘A Note on Ordinally Equivalent Pareto Surfaces’22. Zvi Safra and Dov Samet (2004), ‘An Ordinal Solution to Bargaining Problems with Many Players’ENon-convex Problems23. John P. Conley and Simon Wilkie (1991), ‘The Bargaining Problem Without Convexity: Extending the Egalitarian and Kalai-Smorodinksy Solutions’24. Lin Zhou (1997), ‘The Nash Bargaining Theory with Non-Convex Problems’PART IIUNDERSTANDING THE ROLE OF THE DISAGREEMENT POINT AMonotonocity25. William Thomson (1987), ‘Monotonicity of Bargaining Solutions with Respect to the Disagreement Point’BAxioms Pertaining to Operations Performed on Disagreement Points26. Hans Peters and Eric van Damme (1991), ‘Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms’27. Youngsub Chun and William Thomson (1990), ‘Bargaining with Uncertain Disagreement Points’PART IIIVARIABLE POPULATION OF AGENTS APopulation Monotonicity28. William Thomson (1983), ‘The Fair Division of a Fixed Supply Among a Growing Population’29. William Thomson (1983), ‘Problems of Fair Division and the Egalitarian Solution’30. William Thomson and Terje Lensberg (1983), ‘Guarantee Structures for Problems of Fair Division’BConsistency and Its Converse31. Terje Lensberg (1987), ‘Stability and Collective Rationality’32. Terje Lensberg (1988), ‘Stability and the Nash Solution’33. Youngsub Chun (2002), ‘The Converse Consistency Principle in Bargaining’PART IVENRICHING THE MODEL AAdding Information About Underlying Set of Physical Alternatives34. Richard E. Kihlstrom, Alvin E. Roth and David Schmeidler (1981), ‘Risk Aversion and Solutions to Nash’s Bargaining Problem’35. Alvin E. Roth and Uriel G. Rothblum (1982), ‘Risk Aversion and Nash’s Solution for Bargaining Games with Risky Outcomes’36. Zvi Safra, Lin Zhou and Itzhak Zilcha (1990), ‘Risk Aversion in the Nash Bargaining Problem with Risky Outcomes and Risky Disagreement Points’37. John E. Roemer (1988), ‘Axiomatic Bargaining Theory on Economic Environments’38. Ariel Rubinstein, Zvi Safra and William Thomson (1992), ‘On the Interpretation of the Nash Bargaining Solution and its Extension to Non-Expected Utility Preferences’39. Zvi Safra and Itzhak Zilcha (1993), ‘Bargaining Solutions without the Expected Utility Hypothesis’40. Simon Grant and Atsushi Kajii (1995), ‘A Cardinal Characterization of the Rubinstein-Safra-Thomson Axiomatic Bargaining Theory’BAdding Claims41. Youngsub Chun and William Thomson (1992), ‘Bargaining Problems with Claims’42. Walter Bossert (1993), ‘An Alternative Solution to Bargaining Problems with Claims’CAdding Preferences Over Solutions43. Kim C. Border and Uzi Segal (1997), ‘Preferences Over Solutions to the Bargaining Problem’PART VSTRATEGIC CONSIDERATIONS AAnalyzing Bargaining Problems as Strategic Games44. John Nash (1953), ‘Two-Person Cooperative Games’45. Eric van Damme (1986), ‘The Nash Bargaining Solution is Optimal’46. Ariel Rubinstein (1982), ‘Perfect Equilibrium in a Bargaining Model’BManipulation47. Vincent P. Crawford and Hal R. Varian (1979), ‘Distortion of Preferences and The Nash Theory of Bargaining’48. Joel Sobel (1981), ‘Distortion of Utilities and the Bargaining Problem’CImplementation49. H. Moulin (1984), ‘Implementing the Kalai-Smorodinsky Bargaining Solution’50. Eiichi Miyagawa (2002), ‘Subgame-Perfect Implementation of Bargaining Solutions’PART VIEXPERIMENTS 51. M.E. Yaari and M. Bar-Hillel (1984), ‘On Dividing Justly’

Edited by William Thomson, Elmer B. Milliman Professor of Economics, University of Rochester, US

• Contents:AcknowledgementsIntroduction William ThomsonPART IBASIC PAPERS AIndependence1. John F. Nash Jr. (1950), ‘The Bargaining Problem’2. Alvin E. Roth (1977), ‘Individual Rationality and Nash’s Solution to the Bargaining Problem’3. Alvin E. Roth (1977), ‘Independence of Irrelevant Alternatives, and Solutions to Nash’s Bargaining Problem’4. Hans Peters and Peter Wakker (1991), ‘Independence of Irrelevant Alternatives and Revealed Group Preferences’5. Charles Blackorby, Walter Bossert and David Donaldson (1994), ‘Generalized Ginis and Cooperative Bargaining Solutions’6. Efe A. Ok (1998), ‘Inequality Averse Collective Choice’BMonotonicity7. Ehud Kalai and Meir Smorodinsky (1975), ‘Other Solutions to Nash’s Bargaining Problem’8. A.E. Roth (1979), ‘An Impossibility Result Concerning n-Person Bargaining Games’9. Ehud Kalai (1977), ‘Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons’10. Haruo Imai (1983), ‘Individual Monotonicity and Lexicographic Maxmin Solution’11. W. Thomson and R.B. Myerson (1980), ‘Monotonicity and Independence Axioms’12. P.L. Yu (1973), ‘A Class of Solutions for Group Decision Problems’13. Youngsub Chun (1988), ‘The Equal-Loss Principle for Bargaining Problems’CAxioms Pertaining to Operations Performed on Feasible Sets14. Roger B. Myerson (1977), ‘Two-Person Bargaining Problems and Comparable Utility’15. M.A. Perles and M. Maschler (1981), ‘The Super-Additive Solution for the Nash Bargaining Game’16. Roger B. Myerson (1981), ‘Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems’17. Clara Ponsati and Joel Watson (1997), ‘Multiple-Issue Bargaining and Axiomatic Solutions’18. Hans Peters (1986), ‘Simultaneity of Issues and Additivity in Bargaining’DOrdinal Invariance19. Lloyd S. Shapley (1969), ‘Utility Comparison and the Theory of Games’20. Lars Tyge Nielsen (1983), ‘Ordinal Interpersonal Comparisons in Bargaining’21. Yves Sprumont (2000), ‘A Note on Ordinally Equivalent Pareto Surfaces’22. Zvi Safra and Dov Samet (2004), ‘An Ordinal Solution to Bargaining Problems with Many Players’ENon-convex Problems23. John P. Conley and Simon Wilkie (1991), ‘The Bargaining Problem Without Convexity: Extending the Egalitarian and Kalai-Smorodinksy Solutions’24. Lin Zhou (1997), ‘The Nash Bargaining Theory with Non-Convex Problems’PART IIUNDERSTANDING THE ROLE OF THE DISAGREEMENT POINT AMonotonocity25. William Thomson (1987), ‘Monotonicity of Bargaining Solutions with Respect to the Disagreement Point’BAxioms Pertaining to Operations Performed on Disagreement Points26. Hans Peters and Eric van Damme (1991), ‘Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms’27. Youngsub Chun and William Thomson (1990), ‘Bargaining with Uncertain Disagreement Points’PART IIIVARIABLE POPULATION OF AGENTS APopulation Monotonicity28. William Thomson (1983), ‘The Fair Division of a Fixed Supply Among a Growing Population’29. William Thomson (1983), ‘Problems of Fair Division and the Egalitarian Solution’30. William Thomson and Terje Lensberg (1983), ‘Guarantee Structures for Problems of Fair Division’BConsistency and Its Converse31. Terje Lensberg (1987), ‘Stability and Collective Rationality’32. Terje Lensberg (1988), ‘Stability and the Nash Solution’33. Youngsub Chun (2002), ‘The Converse Consistency Principle in Bargaining’PART IVENRICHING THE MODEL AAdding Information About Underlying Set of Physical Alternatives34. Richard E. Kihlstrom, Alvin E. Roth and David Schmeidler (1981), ‘Risk Aversion and Solutions to Nash’s Bargaining Problem’35. Alvin E. Roth and Uriel G. Rothblum (1982), ‘Risk Aversion and Nash’s Solution for Bargaining Games with Risky Outcomes’36. Zvi Safra, Lin Zhou and Itzhak Zilcha (1990), ‘Risk Aversion in the Nash Bargaining Problem with Risky Outcomes and Risky Disagreement Points’37. John E. Roemer (1988), ‘Axiomatic Bargaining Theory on Economic Environments’38. Ariel Rubinstein, Zvi Safra and William Thomson (1992), ‘On the Interpretation of the Nash Bargaining Solution and its Extension to Non-Expected Utility Preferences’39. Zvi Safra and Itzhak Zilcha (1993), ‘Bargaining Solutions without the Expected Utility Hypothesis’40. Simon Grant and Atsushi Kajii (1995), ‘A Cardinal Characterization of the Rubinstein-Safra-Thomson Axiomatic Bargaining Theory’BAdding Claims41. Youngsub Chun and William Thomson (1992), ‘Bargaining Problems with Claims’42. Walter Bossert (1993), ‘An Alternative Solution to Bargaining Problems with Claims’CAdding Preferences Over Solutions43. Kim C. Border and Uzi Segal (1997), ‘Preferences Over Solutions to the Bargaining Problem’PART VSTRATEGIC CONSIDERATIONS AAnalyzing Bargaining Problems as Strategic Games44. John Nash (1953), ‘Two-Person Cooperative Games’45. Eric van Damme (1986), ‘The Nash Bargaining Solution is Optimal’46. Ariel Rubinstein (1982), ‘Perfect Equilibrium in a Bargaining Model’BManipulation47. Vincent P. Crawford and Hal R. Varian (1979), ‘Distortion of Preferences and The Nash Theory of Bargaining’48. Joel Sobel (1981), ‘Distortion of Utilities and the Bargaining Problem’CImplementation49. H. Moulin (1984), ‘Implementing the Kalai-Smorodinsky Bargaining Solution’50. Eiichi Miyagawa (2002), ‘Subgame-Perfect Implementation of Bargaining Solutions’PART VIEXPERIMENTS 51. M.E. Yaari and M. Bar-Hillel (1984), ‘On Dividing Justly’

Edited by William Thomson, Elmer B. Milliman Professor of Economics, University of Rochester, US

• Contents:AcknowledgementsIntroduction William ThomsonPART IBASIC PAPERS AIndependence1. John F. Nash Jr. (1950), ‘The Bargaining Problem’2. Alvin E. Roth (1977), ‘Individual Rationality and Nash’s Solution to the Bargaining Problem’3. Alvin E. Roth (1977), ‘Independence of Irrelevant Alternatives, and Solutions to Nash’s Bargaining Problem’4. Hans Peters and Peter Wakker (1991), ‘Independence of Irrelevant Alternatives and Revealed Group Preferences’5. Charles Blackorby, Walter Bossert and David Donaldson (1994), ‘Generalized Ginis and Cooperative Bargaining Solutions’6. Efe A. Ok (1998), ‘Inequality Averse Collective Choice’BMonotonicity7. Ehud Kalai and Meir Smorodinsky (1975), ‘Other Solutions to Nash’s Bargaining Problem’8. A.E. Roth (1979), ‘An Impossibility Result Concerning n-Person Bargaining Games’9. Ehud Kalai (1977), ‘Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons’10. Haruo Imai (1983), ‘Individual Monotonicity and Lexicographic Maxmin Solution’11. W. Thomson and R.B. Myerson (1980), ‘Monotonicity and Independence Axioms’12. P.L. Yu (1973), ‘A Class of Solutions for Group Decision Problems’13. Youngsub Chun (1988), ‘The Equal-Loss Principle for Bargaining Problems’CAxioms Pertaining to Operations Performed on Feasible Sets14. Roger B. Myerson (1977), ‘Two-Person Bargaining Problems and Comparable Utility’15. M.A. Perles and M. Maschler (1981), ‘The Super-Additive Solution for the Nash Bargaining Game’16. Roger B. Myerson (1981), ‘Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems’17. Clara Ponsati and Joel Watson (1997), ‘Multiple-Issue Bargaining and Axiomatic Solutions’18. Hans Peters (1986), ‘Simultaneity of Issues and Additivity in Bargaining’DOrdinal Invariance19. Lloyd S. Shapley (1969), ‘Utility Comparison and the Theory of Games’20. Lars Tyge Nielsen (1983), ‘Ordinal Interpersonal Comparisons in Bargaining’21. Yves Sprumont (2000), ‘A Note on Ordinally Equivalent Pareto Surfaces’22. Zvi Safra and Dov Samet (2004), ‘An Ordinal Solution to Bargaining Problems with Many Players’ENon-convex Problems23. John P. Conley and Simon Wilkie (1991), ‘The Bargaining Problem Without Convexity: Extending the Egalitarian and Kalai-Smorodinksy Solutions’24. Lin Zhou (1997), ‘The Nash Bargaining Theory with Non-Convex Problems’PART IIUNDERSTANDING THE ROLE OF THE DISAGREEMENT POINT AMonotonocity25. William Thomson (1987), ‘Monotonicity of Bargaining Solutions with Respect to the Disagreement Point’BAxioms Pertaining to Operations Performed on Disagreement Points26. Hans Peters and Eric van Damme (1991), ‘Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms’27. Youngsub Chun and William Thomson (1990), ‘Bargaining with Uncertain Disagreement Points’PART IIIVARIABLE POPULATION OF AGENTS APopulation Monotonicity28. William Thomson (1983), ‘The Fair Division of a Fixed Supply Among a Growing Population’29. William Thomson (1983), ‘Problems of Fair Division and the Egalitarian Solution’30. William Thomson and Terje Lensberg (1983), ‘Guarantee Structures for Problems of Fair Division’BConsistency and Its Converse31. Terje Lensberg (1987), ‘Stability and Collective Rationality’32. Terje Lensberg (1988), ‘Stability and the Nash Solution’33. Youngsub Chun (2002), ‘The Converse Consistency Principle in Bargaining’PART IVENRICHING THE MODEL AAdding Information About Underlying Set of Physical Alternatives34. Richard E. Kihlstrom, Alvin E. Roth and David Schmeidler (1981), ‘Risk Aversion and Solutions to Nash’s Bargaining Problem’35. Alvin E. Roth and Uriel G. Rothblum (1982), ‘Risk Aversion and Nash’s Solution for Bargaining Games with Risky Outcomes’36. Zvi Safra, Lin Zhou and Itzhak Zilcha (1990), ‘Risk Aversion in the Nash Bargaining Problem with Risky Outcomes and Risky Disagreement Points’37. John E. Roemer (1988), ‘Axiomatic Bargaining Theory on Economic Environments’38. Ariel Rubinstein, Zvi Safra and William Thomson (1992), ‘On the Interpretation of the Nash Bargaining Solution and its Extension to Non-Expected Utility Preferences’39. Zvi Safra and Itzhak Zilcha (1993), ‘Bargaining Solutions without the Expected Utility Hypothesis’40. Simon Grant and Atsushi Kajii (1995), ‘A Cardinal Characterization of the Rubinstein-Safra-Thomson Axiomatic Bargaining Theory’BAdding Claims41. Youngsub Chun and William Thomson (1992), ‘Bargaining Problems with Claims’42. Walter Bossert (1993), ‘An Alternative Solution to Bargaining Problems with Claims’CAdding Preferences Over Solutions43. Kim C. Border and Uzi Segal (1997), ‘Preferences Over Solutions to the Bargaining Problem’PART VSTRATEGIC CONSIDERATIONS AAnalyzing Bargaining Problems as Strategic Games44. John Nash (1953), ‘Two-Person Cooperative Games’45. Eric van Damme (1986), ‘The Nash Bargaining Solution is Optimal’46. Ariel Rubinstein (1982), ‘Perfect Equilibrium in a Bargaining Model’BManipulation47. Vincent P. Crawford and Hal R. Varian (1979), ‘Distortion of Preferences and The Nash Theory of Bargaining’48. Joel Sobel (1981), ‘Distortion of Utilities and the Bargaining Problem’CImplementation49. H. Moulin (1984), ‘Implementing the Kalai-Smorodinsky Bargaining Solution’50. Eiichi Miyagawa (2002), ‘Subgame-Perfect Implementation of Bargaining Solutions’PART VIEXPERIMENTS 51. M.E. Yaari and M. Bar-Hillel (1984), ‘On Dividing Justly’