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Bargaining and the Theory of Cooperative Games: John Nash and Beyond
Building on the pioneering work by the Nobel Memorial Laureate, John Nash, Professor Thomson has brought together a broad selection of seminal articles which analyse and discuss bargaining and the theory of cooperative games. Beginning with a distinguished collection of papers discussing the origins of game theory, this volume systematically explores its development as a tool to illuminate economic behaviour. It includes the work of highly accomplished academics whose discoveries over the years have shaped the direction of this subject. With his insightful introduction, the editor has ensured that this indispensable book is suitable for anyone with an interest in cooperative gaming.
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Contributors
Contents
More Information
Building on the pioneering work by the Nobel Memorial Laureate, John Nash, Professor Thomson has brought together a broad selection of seminal articles which analyse and discuss bargaining and the theory of cooperative games. Beginning with a distinguished collection of papers discussing the origins of game theory, this volume systematically explores its development as a tool to illuminate economic behaviour. It includes the work of highly accomplished academics whose discoveries over the years have shaped the direction of this subject. With his insightful introduction, the editor has ensured that this indispensable book is suitable for anyone with an interest in cooperative gaming.
Contributors
51 articles, dating from 1950 to 2004
Contributors include: W. Bossert, Y. Chun, V.P Crawford, E. Kalai, T. Lensberg, H. Moulin, J.F Nash, A.E Roth, A. Rubinstein
Contributors include: W. Bossert, Y. Chun, V.P Crawford, E. Kalai, T. Lensberg, H. Moulin, J.F Nash, A.E Roth, A. Rubinstein
Contents
Contents:
Acknowledgements
Introduction William Thomson
PART I BASIC PAPERS
A Independence
1. 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’
B Monotonicity
7. 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’
C Axioms Pertaining to Operations Performed on Feasible Sets
14. 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’
D Ordinal Invariance
19. 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’
E Non-convex Problems
23. 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 II UNDERSTANDING THE ROLE OF THE DISAGREEMENT POINT
A Monotonocity
25. William Thomson (1987), ‘Monotonicity of Bargaining Solutions with Respect to the Disagreement Point’
B Axioms Pertaining to Operations Performed on Disagreement Points
26. 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 III VARIABLE POPULATION OF AGENTS
A Population Monotonicity
28. 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’
B Consistency and Its Converse
31. 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 IV ENRICHING THE MODEL
A Adding Information About Underlying Set of Physical Alternatives
34. 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’
B Adding Claims
41. Youngsub Chun and William Thomson (1992), ‘Bargaining Problems with Claims’
42. Walter Bossert (1993), ‘An Alternative Solution to Bargaining Problems with Claims’
C Adding Preferences Over Solutions
43. Kim C. Border and Uzi Segal (1997), ‘Preferences Over Solutions to the Bargaining Problem’
PART V STRATEGIC CONSIDERATIONS
A Analyzing Bargaining Problems as Strategic Games
44. 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’
B Manipulation
47. 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’
C Implementation
49. H. Moulin (1984), ‘Implementing the Kalai-Smorodinsky Bargaining Solution’
50. Eiichi Miyagawa (2002), ‘Subgame-Perfect Implementation of Bargaining Solutions’
PART VI EXPERIMENTS
51. M.E. Yaari and M. Bar-Hillel (1984), ‘On Dividing Justly’
Acknowledgements
Introduction William Thomson
PART I BASIC PAPERS
A Independence
1. 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’
B Monotonicity
7. 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’
C Axioms Pertaining to Operations Performed on Feasible Sets
14. 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’
D Ordinal Invariance
19. 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’
E Non-convex Problems
23. 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 II UNDERSTANDING THE ROLE OF THE DISAGREEMENT POINT
A Monotonocity
25. William Thomson (1987), ‘Monotonicity of Bargaining Solutions with Respect to the Disagreement Point’
B Axioms Pertaining to Operations Performed on Disagreement Points
26. 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 III VARIABLE POPULATION OF AGENTS
A Population Monotonicity
28. 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’
B Consistency and Its Converse
31. 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 IV ENRICHING THE MODEL
A Adding Information About Underlying Set of Physical Alternatives
34. 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’
B Adding Claims
41. Youngsub Chun and William Thomson (1992), ‘Bargaining Problems with Claims’
42. Walter Bossert (1993), ‘An Alternative Solution to Bargaining Problems with Claims’
C Adding Preferences Over Solutions
43. Kim C. Border and Uzi Segal (1997), ‘Preferences Over Solutions to the Bargaining Problem’
PART V STRATEGIC CONSIDERATIONS
A Analyzing Bargaining Problems as Strategic Games
44. 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’
B Manipulation
47. 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’
C Implementation
49. H. Moulin (1984), ‘Implementing the Kalai-Smorodinsky Bargaining Solution’
50. Eiichi Miyagawa (2002), ‘Subgame-Perfect Implementation of Bargaining Solutions’
PART VI EXPERIMENTS
51. M.E. Yaari and M. Bar-Hillel (1984), ‘On Dividing Justly’