A Bibliography of
Cooperative Games: Value
Theory^{1}
Sergiu
Hart^{2}

Aarts, H. and K. Hoede [1997],
"A Marginalistic Value for Monotonic Set Games,"
International Journal of Game Theory 26, 97112.

Amer, R. and F. Carreras [1995],
"Games and Cooperation Indices,"
International Journal of Game Theory 24, 239258.

Amer, R. and F. Carreras [1997],
"Cooperation Indices and Weighted Shapley Values,"
Mathematics of Operations Research 22, 955968.

Artstein, Z. [1971],
"Values of Games with Denumerably Many Players,"
International Journal of Game Theory 1, 2737.

Aubin, J. [1981],
"Cooperative Fuzzy Games,"
Mathematics of Operations Research 6, 113.

Aumann, R. J. [1964],
"Markets with a Continuum of Traders,"
Econometrica 32, 3950.
 >>
Aumann, R. J. [1975],
"Values of Markets with a Continuum of Traders,"
Econometrica 43, 611646.

Aumann, R. J. [1978],
"Recent Developments in the Theory of the Shapley Value,"
Proceedings of the International Congress of Mathematicians, Helsinki, 9951003.
 >>
Aumann, R. J. [1985],
"An Axiomatization of the NonTransferable Utility Value,"
Econometrica 53, 599612.
 >
Aumann, R. J. [1985],
"On the NonTransferable Utility Value: A Comment on the RothShafer Examples,"
Econometrica 53, 667678.
 >
Aumann, R. J. [1986],
"Rejoinder,"
Econometrica 54, 985989.

Aumann, R. J. [1987],
"Value, Symmetry and Equal Treatment: A Comment on Scafuri and Yannelis,"
Econometrica 55, 14611464.

Aumann, R. J. [1990],
"The Shapley Value,"
in Game Theory and Applications, T. Ichiishi, A. Neyman and Y. Tauman (eds.), Academic Press,
158165.

Aumann, R. J. [1994],
"The Shapley Value,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.),
Kluwer Academic Publishers, 6166.

Aumann, R. J. [1994],
"Economic Applications of the Shapley Value,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 121133.

Aumann, R. J. and J. Drèze [1974],
"Cooperative Games with Coalition Structures,"
International Journal of Game Theory 3, 217237.
 >
Aumann, R. J. and J. Drèze [1986],
"Values of Markets with Satiation or Fixed Prices,"
Econometrica 54, 12711318.

Aumann, R. J., R. J. Gardner and R. W. Rosenthal [1977],
"Core and Value for a Public Goods Economy: An Example,"
Journal of Economic Theory 15, 363365.
 >
Aumann, R. J. and M. Kurz [1977],
"Power and Taxes,"
Econometrica 45, 11371161.

Aumann, R. J. and M. Kurz [1977],
"Power and Taxes in a MultiCommodity Economy,"
Israel Journal of Mathematics 27, 185234.

Aumann, R. J. and M. Kurz [1978],
"Power and Taxes in a MultiCommodity Economy (updated),"
Journal of Public Economics 9, 139161.

Aumann, R. J., M. Kurz and A. Neyman [1983],
"Voting for Public Goods,"
Review of Economic Studies 50, 677693.

Aumann, R. J., M. Kurz and A. Neyman [1987],
"Power and Public Goods,"
Journal of Economic Theory 42, 108127.
 >
Aumann, R. J. and R. B. Myerson [1988],
"Endogenous Formation of Links between Players and of Coalitions: An Application of the Shapley Value,"
in The Shapley Value, A. E. Roth (ed.), Cambridge University Press, 175191.

Aumann, R. J. and U. Rothblum [1977],
"Orderable Set Functions and Continuity III: Orderability and Absolute Continuity,"
SIAM Journal on Control and Optimization 15, 156162.
 >>
Aumann, R. J. and L. S. Shapley [1974],
Values of NonAtomic Games, Princeton University Press.
 >
Banzhaff, J. F. III [1965],
"Weighted Voting Does Not Work: A Mathematical Analysis,"
Rutgers Law Review 19, 317343.
 >
Banzhaff, J. F. III [1968],
"One Man, 3.312 Votes: A Mathematical Analysis of the Electoral College,"
Villanova Law Review 13, 304332.

Beja, A. and I. Gilboa [1990],
"Values for TwoStage Games: Another View of the Shapley Axioms,"
International Journal of Game Theory 19, 1732.

Berbee, H. [1981],
"On Covering Single Points by Randomly Ordered Intervals,"
Annals of Probability 9, 520528.

Bilbao, J.M. [1998],
"Values and Potential of Games with Cooperation Structure,"
International Journal of Game Theory 27, 131145.
 >
Billera, L. J. and D. C. Heath [1982],
"Allocation of Shared Cost: A Set of Axioms Yielding a Unique Procedure,"
Mathematics of Operations Research 7, 3239.
 >
Billera, L. J., D. C. Heath and J. Raanan [1978],
"Internal Telephone Billing Rates  A Novel Application of NonAtomic Game Theory,"
Operations Research 26, 956965.

Billera, L. J., D. C. Heath and J. Raanan [1981],
"A Unique Procedure for Allocating Common Costs from a Production Process,"
Journal of Accounting Research 19, 185196.

Binmore, K. [1987],
"Perfect Equilibria in Bargaining Models,"
in The Economics of Bargaining, K. Binmore and P. Dasgupta (eds.), Blackwell, 77105.

Bolger, E. M. [1982],
"Characterizing the Banzhaf and Shapley Values Assuming Limited Linearity,"
International Journal of Game Theory 11, 112.

Bolger, E. M. [1989],
"A Set of Axioms for a Value for Partition Function Games,"
International Journal of Game Theory 18, 3744.

Bolger, E. M. [1993],
"A Value for Games with n Players and r Alternatives,"
International Journal of Game Theory 22, 319334.

Bolger, E. M. [2000],
"A Consistent Value for Games with n Players and r Alternatives,"
International Journal of Game Theory 29, 9399.

Brams, S. J. [1975],
Game Theory and Politics, Free Press, NY.

Brams, S. J., P. J. Affuso and D. M. Kilgour [1989],
"Presidential Power: A GameTheoretic Analysis,"
in The Presidency in the American Politics, P. Brace, C. B. Harrington and G. King (eds.), New York
University Press, 5572.

van den Brink, R. [1997],
"An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure,"
International Journal of Game Theory 26, 2744.

van den Brink, R. and R. P. Gilles [1996],
"Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures,"
Games and Economic Behavior 12, 113126.

Brown, D. and P. A. Loeb [1977],
"The Values of NonStandard Exchange Economies,"
Israel Journal of Mathematics 25, 7186.

Butnariu, D. [1987],
"Values and Cores of Fuzzy Games With Infinitely Many Players,"
International Journal of Game Theory 16, 4368.

Butnariu, D. and E. P. Klement [1993],
Triangular NormBased Measures and Games with Fuzzy Coalitions, Kluwer Academic Publishers.

Butnariu, D. and E. P. Klement [1996],
"Core, Value and Equilibria for Market Games: On a Problem of Aumann and Shapley,"
International Journal of Game Theory 25, 149160.

Calvo, E. and J. C. Santos [1997],
"Potentials in Cooperative TU Games,"
Mathematical Social Science 34, 175190.

Calvo, E. and J. C. Santos [2000],
"Weighted Weak Semivalues,"
International Journal of Game Theory 29, 19.

Carreras, F. [1992],
"Filtrations, Values and Voting Discipline,"
International Journal of Game Theory 20, 357376.

Carreras, F. [1997],
"Automorphisms and Weighted Values,"
International Journal of Game Theory 26, 110.
 >>
Champsaur, P. [1975],
"Cooperation vs. Competition,"
Journal of Economic Theory 11, 394417.

Cheng, H. [1981],
"On Dual Regularity and Value Convergence Theorems,"
Journal of Mathematical Economics 6, 3757.
 Chun, Y. [1989],
"A New Axiomatization of the Shapley Value,"
Games and Economic Behavior 1, 119130.
 Chun, Y. [1991],
"On the Symmetric and Weighted Shapley Values,"
International Journal of Game Theory 20, 183190.

Coleman, J. S. [1986],
Individual Interests and Collective Action: Selected Essays, Cambridge University Press.

Deegan, J. and E. Packel [1979],
"A New Index of Power for Simple nPerson Games,"
International Journal of Game Theory 7, 113123.

Derks, J., H. Haller and H. Peters [2000],
"The Selectoscope for Cooperative Games,"
International Journal of Game Theory 29, 2338.

Derks, J. and H. Peters [1993],
"A Shapley Value for Games with Restricted Coalitions,"
International Journal of Game Theory 21, 351360.

Driessen, T. S. H. [1985],
"The tValue, the Core and Semiconvex Games,"
International Journal of Game Theory 14, 219228.
 >
Dubey, P. [1975],
"On the Uniqueness of the Shapley Value,"
International Journal of Game Theory 4, 131139.

Dubey, P. and A. Neyman [1984],
"Payoffs in Nonatomic Economies: An Axiomatic Approach,"
Econometrica 52, 11291150.
 Dubey, P. and A. Neyman [1994],
"An Axiomatic Approach to the Equivalence Phenomenon,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 135144.

Dubey, P. and A. Neyman [1997],
"An Equivalence Principle for Perfectly Competitive Economies,"
Journal of Economic Theory 75, 314344.

Dubey, P., A. Neyman and R. J. Weber [1981],
"Value Theory without Efficiency,"
Mathematics of Operations Research 6, 122128.

Dubey, P. and L. S. Shapley [1979],
"Mathematical Properties of the Banzhaf Power Index,"
Mathematics of Operations Research 4, 99131.

Einy, E. [1987],
"Semivalues of Simple Games,"
Mathematics of Operations Research 12, 185192.

Einy, E. [1988],
"The Shapley Value on Some Lattices of Monotonic Games,"
Mathematical Social Sciences 15, 110.

Faigle, U. and W. Kern [1992],
"The Shapley Value for Cooperative Games under Precedence Constraints,"
International Journal of Game Theory 21, 249266.

Feinberg, Y. [1998],
"An Incomplete Cooperation Structure for a Voting Game Can Be Strategically Stable,"
Games and Economic Behavior 24, 29.

Felsenthal, D. S. and M. Machover [1995],
"Postulates and Paradoxes of Voting Power  A Critical Reappraisal,"
Theory and Decision 38, 195229.

Felsenthal, D. S. and M. Machover [1996],
"Alternative Forms of the Shapley Value and the ShapleyShubik Index,"
Public Choice 87, 315318.

Felsenthal, D. S. and M. Machover [1997],
"Ternary Voting Games,"
International Journal of Game Theory 26, 335351.

Felsenthal, D. S. and M. Machover [1997],
"The Weighted Voting Rule in the EU Council of Ministers, 19581995: Intentions and Outcomes,"
Electoral Studies 16, 3347.

Felsenthal, D. S., M. Machover and W. Zwicker [1998],
"The Bicameral Postulates and Indices of a priori Voting Power,"
Theory and Decision 44, 83116.

Felsenthal, D. S. and M. Machover [1998],
"The Product Paradox of Voting Power,"
Public Choice 96, 8192.

Felsenthal, D. S. and M. Machover [1998],
The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes, Edward Elgar.

Felsenthal, D. S. and M. Machover [1998],
"Minimizing the Mean Majority Deficit: the Second SquareRoot Rule,"
Mathematical Social Sciences 37, 2537.

Feltkamp, V. [1995],
"Alternative Axiomatic characterizations of the Shapley and Banzhaf Values,"
International Journal of Game Theory 24, 179186.

Fogelman, F. and M. Quinzii [1980],
"Asymptotic Values of Mixed Games,"
Mathematics of Operations Research 5, 8693.
 Gardner, R. J. [1977],
"Shapley Value and Disadvantageous Monopolies,"
Journal of Economic Theory 16, 513517.

Gardner, R. J. [1981],
"Wealth and Power in a Collegiate Polity,"
Journal of Economic Theory 25, 353366.

Gardner, R. J. [1983],
"lTransfer Value and FixedPrice Equilibrium in TwoSided Markets,"
in Social Choice and Welfare, P. K. Pattanaik and M. Salles (eds.), NorthHolland, 301323.

Gardner, R. J. [1984],
"Power and Taxes in a OneParty State: The USSR, 19251929,"
International Economic Review 25, 743755.

Gilboa, I. and D. Monderer [1991],
"Quasivalues on Subspaces of Games,"
International Journal of Game Theory 19, 353363.
 >
Gomes, A., S. Hart and A. MasColell [1999],
"Finite Horizon Bargaining and the Consistent Field,"
Games and Economic Behavior 27, 204228.

Guesnerie, R. [1977],
"Monopoly, Syndicate, and Shapley Value: About Some Conjectures,"
Journal of Economic Theory 15, 235251.
 >
Gul, F. [1989],
"Bargaining Foundations of Shapley Value,"
Econometrica 57, 8195.
 >
Gul, F. [1999],"Efficiency and Immediate Agreement: A Reply to Hart and Levy,"
Econometrica 67, 913915.

Haimanko, O. [1998],
"NonSymmetric Values of Finite Games,"
The Hebrew University of Jerusalem, Center for Rationality DP167.

Haimanko, O. [1998],"NonSymmetric Values of NonAtomic and Mixed Games,"
The Hebrew University of Jerusalem, Center for Rationality DP168.

Haimanko, O. [1998],
"Partially Symmetric Values,"
The Hebrew University of Jerusalem, Center for Rationality DP169.

Haimanko, O. [1999],
"Payoffs in NonDifferentiable Perfectly Competitive Economies,"
The Hebrew University of Jerusalem, Center for Rationality DP197.

Haimanko, O. [1999],
"Payoffs in NonDifferentiable Perfectly Competitive Economies,"
The Hebrew University of Jerusalem, Center for Rationality DP205.

Haller, H. [1994],
"Collusion Properties of Values,"
International Journal of Game Theory 23, 261282.

Hamiache, G. [1999],
"A Value with Incomplete Communication,"
Games and Economic Behavior 26, 5978.
 Harsanyi, J. C. [1959],
"A Bargaining Model for the Cooperative nPerson Games,"
in Contributions to the Theory of Games IV (Annals of Mathematics Studies 40), A. W. Tucker and R. D. Luce (eds.), Princeton University Press, 325356.
 >>
Harsanyi, J. C. [1963],
"A Simplified Bargaining Model for the nPerson Cooperative Game,"
International Economic Review 4, 194220.

Harsanyi, J. C. [1977],
Rational Behavior and Bargaining Equilibrium in Games and Social Situations,
Cambridge University Press.
 Harsanyi, J. C. [1980],
"Comments on Roth's Paper, 'Values for Games Without Side Payments',"
Econometrica 48, 477.

Harsanyi, J. C. [1985],
"The Shapley Value and the Risk Dominance Solutions of Two Bargaining Models for CharacteristicFunction Games,"
in Essays in Game Theory and Mathematical Economics, R. J. Aumann et al (eds.), Bibliographisches Institut Mannheim, 4368.

Hart, O. and J. Moore [1990],
"Property Rights and the Nature of the Firm,"
Journal of Political Economy 98, 11191157.

Hart, S. [1973],
"Values of Mixed Games,"
International Journal of Game Theory 2, 6985.

Hart, S. [1976],
"A Note on the Edges of the nCube,"
Discrete Mathematics 14, 157163.
 >>
Hart, S. [1977],
"Asymptotic Value of Games with a Continuum of Players,"
Journal of Mathematical Economics 4, 5780.
 >>
Hart, S. [1977],
"Values of NonDifferentiable Markets with a Continuum of Traders,"
Journal of Mathematical Economics 4, 103116.
Reprinted in Game and Economic Theory, S. Hart and A. Neyman (eds.), The University of Michigan Press [1995], 321334.

Hart, S. [1979],
"Values of Large Market Games,"
in Applied Game Theory, S. J. Brams, A. Schotter and G. Schwödiauer (eds.), PhysicaVerlag, 187197.

Hart, S. [1980],
"MeasureBased Values of Market Games,"
Mathematics of Operations Research 5, 197228.
 >>
Hart, S. [1985],
"An Axiomatization of Harsanyi's NonTransferable Utility Solution,"
Econometrica 53, 12951313.
 >
Hart, S. [1985],
"NonTransferable Utility Games and Markets: Some Examples and the Harsanyi Solution,"
Econometrica 53, 14451450.

Hart, S. [1985],
"Axiomatic Approaches to Coalitional Bargaining,"
in Game Theoretic Models of Bargaining, A. E. Roth (ed.), Cambridge University Press, 305319.

Hart, S. [1987],
"Shapley Value,"
in The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate and P. Newman (eds.),
Macmillan Press, vol. 4, 318320.
Reprinted in Game Theory, J. Eatwell, M. Milgate and P. Newman (eds.), Macmillan Press [1989], 210216.

Hart, S. [1990],
"Advances in Value Theory,"
in Game Theory and Applications, T. Ichiishi, A. Neyman and Y. Tauman (eds.), Academic Press, 166175.
 >
Hart, S. [1994],
"On Prize Games,"
in Essays in Game Theory, N. Megiddo (ed.), SpringerVerlag, 111121.

Hart, S. [1994],
"The Harsanyi Value,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 105111.

Hart, S. [1994],
"Value Equivalence Theorems: The TU and NTU Cases,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 113120.

Hart, S. [1997],
"Classical Cooperative Theory II: ValueLike Solutions,"
in Cooperation: Game Theoretic Approaches, S. Hart and A. MasColell (eds.), SpringerVerlag, 4349.
 >
Hart, S. and M. Kurz [1983],
"On the Endogenous Formation of Coalitions,"
Econometrica 51, 12951313.

Hart, S. and M. Kurz [1984],
"Stable Coalition Structures,"
in Coalitions and Collective Actions, M. J. Holler (ed.), PhysicaVerlag, 235258.
 >
Hart, S. and Z. Levy [1999],
"Efficiency Does Not Imply Immediate Agreement,"
Econometrica 67, 909912.
 >
Hart, S. and A. MasColell [1988],
"The Potential of the Shapley Value,"
in The Shapley Value, A. E. Roth (ed.), Cambridge University Press, 127137.
 >>
Hart, S. and A. MasColell [1989],
"Potential, Value and Consistency,"
Econometrica 57, 589614.
 Hart, S. and A. MasColell [1992],
"A NonCooperative Interpretation of Value and Potential,"
in Rational Interaction, R. Selten (ed.), SpringerVerlag, 8393.
 >
Hart, S. and A. MasColell [1995],
"Egalitarian Solutions of Large Games: I. A Continuum of Players,"
Mathematics of Operations Research 20, 9591002.
 >
Hart, S. and A. MasColell [1995],
"Egalitarian Solutions of Large Games: II. The Asymptotic Approach,"
Mathematics of Operations Research 20, 10031022.
 >>
Hart, S. and A. MasColell [1996],
"Harsanyi Values of Large Economies: NonEquivalence to Competitive Equilibria,"
Games and Economic Behavior 13, 7499.
 >>
Hart, S. and A. MasColell [1996],
"Bargaining and Value,"
Econometrica 64, 357380.
Reprinted in Recent Developments in Game Theory, E. S. Maskin (ed.), Elgar Publishing [1999], 440463.

Hart, S. and D. Monderer [1997],
"Potential and Weighted Values of Nonatomic Games,"
Mathematics of Operations Research 22, 619630.

Hart, S. and A. Neyman [1988],
"Values of NonAtomic Vector Measure Games: Are They Linear Combinations of the Measures?,"
Journal of Mathematical Economics 17, 3140.

Holzman, R., E. Lehrer and N. Linial [1988],
"Some Bounds for the Banzhaf Index and Other Semivalues,"
Mathematics of Operations Research 13, 358363.

Hsiao, C.R. and T. E. S. Raghavan [1992],
"Monotonicity and Dummy Free Property for MultiChoice Cooperative Games,"
International Journal of Game Theory 21, 301312.

Hsiao, C.R. and T. E. S. Raghavan [1993],
"Shapley Value for MultiChoice Cooperative Games, I,"
Games and Economic Behavior 5, 240256.

Hsiao, C.R. [1995],
"A Value for ContinuouslyManyChoice Cooperative Games,"
International Journal of Game Theory 24, 273292.

Imai, H. [1983],"Voting, Bargaining, and Factor Income Distribution,"
Journal of Mathematical Economics 11, 211233.

Imai, H. [1983],
"On Harsanyi's Solution,"
International Journal of Game Theory 12, 161179.

Iņarra, E. and J. M. Usategui [1993],
"The Shapley Value and Average Convex Games,"
International Journal of Game Theory 22, 1330.
 >
Kalai, E. and D. Samet [1985],
"Monotonic Solutions to General Cooperative Games,"
Econometrica 53, 307327.

Kalai, E. and D. Samet [1987],
"On Weighted Shapley Values,"
International Journal of Game Theory 16, 205222.
 Kannai, Y. [1966],
"Values of Games with a Continuum of Players,"
Israel Journal of Mathematics 4, 5458.

Kern, R. [1985],
"The Shapley Transfer Value Without Zero Weights,"
International Journal of game Theory 14, 7392.

Khmelnitskaya, A. B. [1999],
"Marginalist and Efficient Values for TU Games,"
The Hebrew University of Jerusalem, Center for Rationality DP188; Mathematical Social Sciences (forthcoming).

Khmelnitskaya, A. B. [1999],
"Power Indices Without the Transfer Axiom,"
in Logic, Game Theory and Social Choice, H. de Swart (ed.), Tilburg University Press, 208213.

Kleinberg, N. and J. H. Weiss [1985],
"Equivalent NPerson games and the Null Space of the Shapley Value,"
Mathematics of Operations Research 10, 233243.

Kleinberg, N. and J. H. Weiss [1986],
"The Orthogonal Decomposition of Games and an Averaging Formula for the Shapley Value,"
Mathematics of Operations Research 11, 117124.
 >
Krishna, V. and R. Serrano [1995],
"Perfect Equilibria of a Model of NPerson Noncooperative Bargaining,"
International Journal of Game Theory 24, 259272.

Kohlberg, E. [1973],
"On NonAtomic Games: Conditions for f °m Ė pNA,"
International Journal of Game Theory 2, 8798.

Kurz, M. [1977],
"Distortion of Preferences, Income Distribution and the Case for a Linear Income Tax,"
Journal of Economic Theory 14, 291298.

Kurz, M. [1980],
"Income Distribution and Distortion of Preferences: the lCommodity Case,"
Journal of Economic Theory 22, 99106.

Lefèvre, F. [1994],
"The Shapley Value of a Perfectly Competitive Market May Not Exist,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 95104.

Lehrer, E. [1988],
"An Axiomatization of the Banzhaf Value,"
International Journal of Game Theory 17, 8999.

Lemaire, J. [1973],
"A New Value for Games without Transferable Utilities,"
International Journal of Game Theory 2, 205214.

Leviatan, S. [1998],
"Consistent Values and the Core in Continuum Market Games with Two Types,"
The Hebrew University of Jerusalem, Center for Rationality DP171.

Levy, A. and R. P. McLean [1989],
"Weighted Coalition Structure Values,"
Games and Economic Behavior 1, 234249.

Levy, A. and R. P. McLean [1991],
"An Axiomatization of the Weighted NTU Value,"
International Journal of Game Theory 19, 339352.

Littlechild, S. C. and G. Owen [1973],
"A Simple Expression for the Shapley Value in a Special Case,"
Management Science 20, 99107.

Lucas, W. F. [1983],
"Measuring Power in Weighted Voting Systems,"
in Political and Related Models, S. J. Brams, W. F. Lucas and P. D. Straffin (eds.), SpringerVerlag.

Mann, I. and L. S. Shapley [1960],
"Values of Large Games, IV: Evaluating the Electoral College by MonteCarlo Techniques,"
The Rand Co. RM2651PR, Santa Monica, CA.

Mann, I. and L. S. Shapley [1962],
"Values of Large Games, VI: Evaluating the Electoral College Exactly,"
The Rand Co. RM3158PR, Santa Monica, CA.

Maschler, M. [1982],
"The Worth of a Cooperative Enterprise to Each Member,"
in Games, Economic Dynamics and Time Series Analysis, M. Diestler, F. Fürst and G. Schwödiauer (eds.), PhysicaVerlag, 6773.
 >>
Maschler, M. and G. Owen [1989],
"The Consistent Shapley Value for Hyperplane Games,"
International Journal of Game Theory 18, 389407.
 >>
Maschler, M. and G. Owen [1992],
"The Consistent Shapley Value for Games without Side Payments,"
in Rational Interaction, R. Selten (ed.), SpringerVerlag, 512.

Maschler, M., G. Owen and B. Peleg [1988],
"Paths Leading to the Nash Set,"
in The Shapley Value, A. E. Roth (ed.), Cambridge University Press, 321330.
 >>
MasColell, A. [1977],
"Competitive and Value Allocations of Large Exchange Economies,"
Journal of Economic Theory 14, 419438.

MasColell [1980],
"Remarks on the GameTheoretic Analysis of a Simple Distribution of Surplus Problem,"
International Journal of Game Theory 9, 125140.

>
MasColell, A. [1988],
"Algunos Comentarios sobre la Teoria Cooperativa de los Juegos,"
Cuadernos Economicos 40, 143161.

MasColell, A. [1997],
"Bargaining Games,"
in Cooperation: Game Theoretic Approaches, S. Hart and A. MasColell (eds.), SpringerVerlag, 4349.

McLean, R. P. [1991],
"Random Order Coalition Structure Values,"
International Journal of Game Theory 20, 109127.

Mertens, J.F. [1980],
"Values and Derivatives,"
Mathematics of Operations Research 5, 523552.

Mertens, J.F. [1988],
"The Shapley Value in the NonDifferentiable Case,"
International Journal of Game Theory 17, 165.
 >
Mertens, J.F. [1988],
"Nondifferentiable TU Markets: The Value,"
in The Shapley Value, A. E. Roth (ed.), Cambridge University Press, 235264.

Mertens, J.F. [1994],
"The TUValue: The NonDifferentiable Case,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 8194.

Milchtaich, I. [1995],
"The Value of Nonatomic Games Arising from Certain Noncooperative Congestion Games,"
The Hebrew University of Jerusalem, Center for Rationality DP87.

Milchtaich, I. [1998],
"Vector Measure Games Based on Measures with Values in an Infinite Dimensional Vector Space,"
Games and Economic Behavior 24, 2546.

Milnor, J. W. and L. S. Shapley [1978],
"Values of Large Games II: Oceanic Games,"
Mathematics of Operations Research 3, 290307.

Mirman, L. J. and A. Neyman [1983],
"Prices for Homogeneous Cost Functions,"
Journal of Mathematical Economics 12, 257273.

Mirman, L. J. and A. Neyman [1984],"Diagonality of Cost Allocation Prices,"
Mathematics of Operations Research 9, 6674.

Mirman, L. J., J. Raanan and Y. Tauman [1982],
"A Sufficient Condition on f for f°m to be in pNAD,"
Journal of Mathematical Economics 9, 251257.

Mirman, L. J., D. Samet and Y. Tauman [1983],
"An Axiomatic Approach to the Allocation of Fixed Cost through Prices,"
Bell Journal of Economics 14, 139151.

Mirman, L. J. and Y. Tauman [1982],
"The Continuity of the AumannShapley Price Mechanism,"
Journal of Mathematical Economics 9, 235249.
 >
Mirman, L. J. and Y. Tauman [1982],
"Demand Compatible Equitable CostSharing Prices,"
Mathematics of Operations Research 7, 4056.

Monderer, D. [1986],
"Measure Based Values of NonAtomic Games,"
Mathematics of Operations Research 11, 321335.

Monderer, D. [1988],
"A Probabilistic Problem Arising in Economics,"
Journal of Mathematical Economics 17, 321338.

Monderer, D. [1988],
"Values and Semivalues on Subspaces of Finite Games,"
International Journal of Game Theory 17, 321338.

Monderer, D. [1989],
"Asymptotic Measure Based Values of Nonatomic Games,"
Mathematics of Operations Research 14, 737744.

Monderer, D. [1989],
"Weighted Majority Games Have Many mValues,"
International Journal of Game Theory 18, 321325.

Monderer, D. [1990],
"A Milnor Condition for NonAtomic Lipschitz Games and its Applications,"
Mathematics of Operations Research 15, 714723.

Monderer, D. and A. Neyman [1988],
"Values of Smooth Nonatomic Games: The Method of Multilinear Approximation,"
in The Shapley Value, A. E. Roth (ed.), Cambridge University Press, 217234.

Monderer, D., D. Samet and L. S. Shapley [1992],
"Weighted Shapley Values and the Core,"
International Journal of Game Theory 21, 2739.

Monderer, D. and W. H. Ruckle [1990],
"On the Symmetry Axiom for Values of NonAtomic Games,"
International Journal Mathematics and Mathematical Sciences 13, 165170.

Myerson, R. B. [1976],
"Values of Games in Partition Function Form,"
International Journal of Game Theory 6, 2331.
 >
Myerson, R. B. [1977],
"Graphs and Cooperation in Games,"
Mathematics of Operations Research 2, 225229.
 >
Myerson, R. B. [1980],
"Conference Structures and Fair Allocation Rules,"
International Journal of Game Theory 9, 169182.

Myerson, R. B. [1992],
"FictitiousTransfer Solutions in Cooperative Game Theory,"
in Rational Interaction, R. Selten (ed.), SpringerVerlag, 1333.
 >
Nash, J. [1950],
"The Bargaining Problem,"
Econometrica 18, 155162.

Neyman, A. [1977],
"Continuous Values are Diagonal,"
Mathematics of Operations Research 2, 338342.

Neyman, A. [1977],
"Values for NonTransferable Utility Games with a Continuum of Players,"
Cornell University, S.O.R.I.E. TR351.

Neyman, A. [1979],
"Asymptotic Values of Mixed Games,"
in Game Theory and Related Topics, O. Moeschlin and D. Pallaschke (eds.), NorthHolland, 7181.

Neyman, A. [1981],
"Singular Games Have Asymptotic Values,"
Mathematics of Operations Research 6, 205212.

Neyman, A. [1982],
"Renewal Theory for Sampling without Replacement,"
Annals of Probability 10, 464481.

Neyman, A. [1985],
"SemiValues of Political Economic Games,"
Mathematics of Operations Research 10, 390402.

Neyman, A. [1988],
"Weighted Majority Games Have Asymptotic Values,"
Mathematics of Operations Research 13, 556580.
 >>
Neyman, A. [1989],
"Uniqueness of the Shapley Value,"
Games and Economic Behavior 1, 116118.
 >
Neyman, A. [1994],
"Values of Games with a Continuum of Players,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 6779.

Neyman, A. [1998],
"Values of NonAtomic Vector Measure Games,"
The Hebrew University of Jerusalem, Center for Rationality DP183.

Neyman, A. and Y. Tauman [1976],
"The Existence of Nondiagonal Axiomatic Values,"
Mathematics of Operations Research 1, 246250.

Neyman, A. and Y. Tauman [1979],
"The Partition Value,"
Mathematics of Operations Research 4, 236264.

Nowak, A. S. [1997],
"Note on the Axiomatization of the Banzhaf Value without the Additivity Axiom,"
International Journal of Game Theory 26, 137146.

Nowak, A. S. and T. Radzik [1994],
"A Solidarity Value for nPerson Transferable Utility Games,"
International Journal of Game Theory 23, 261282.

Nowak, A. S. and T. Radzik [1994],
"The Shapley Value for nPerson Games in Generalized Characteristic Function Form,"
Games and Economic Behavior 6, 150161.

Nowak, A. S. and T. Radzik [1995],
"On Axiomatizations of the Weighted Shapley Values,"
Games and Economic Behavior 8, 389405.
 Orshan, G. [1992],
"The Consistent Shapley Value in Hyperplane Games from a Global Standpoint,"
International Journal of Game Theory 21, 112.

Osborne, M. J. [1984],
"Why Do Some Goods Bear Higher Taxes than Others?,"
Journal of Economic Theory 32, 301316.

Otten, G.J., P. Borm and S. Tijs [1996],
"A Note on the Characterizations of the Compromise Value,"
International Journal of Game Theory 25, 427436.

Owen, G. [1968],
"A Note on the Shapley Value,"
Management Science 14, 731732.

Owen, G. [1971],
"Political Games,"
Naval Research Logistics Quarterly 18, 345355.

Owen, G. [1972],
"Multilinear Extensions of Games,"
Management Science 18, 6479.

Owen, G. [1972],
"A Value for Games Without Side Payments,"
International Journal of Game Theory 1, 95109.

Owen, G. [1975],
"Evaluation of a Presidential Election Game,"
American Political Science Review 69, 947953.
 >
Owen, G. [1977],
"Values of Games with a priori Unions,"
in Essays in Mathematical Economics and Game Theory, R. Henn and O. Moeschlin (eds.), SpringerVerlag, 7688.

Owen, G. [1986],
"Values of GraphRestricted Games,"
SIAM Journal of Algebra and Discrete Mathematics 7, 210220.

Owen, G. [1994],
"The NonConsistency and NonUniqueness of the Inductive Value,"
in Essays in Game Theory, N. Megiddo (ed.), SpringerVerlag, 155162.

Owen, G. and L. S. Shapley [1989],
"Optimal Location of Candidates in Ideological Space,"
International Journal of Game Theory 18, 339356.

Owen, G. and E. Winter [1992],
"The Multilinear Extension and the Coalition Value,"
Games and Economic Behavior 4, 582587.

Pallaschke, D. and J. Rosenmüller [1995],
"The Shapley Value for Countably Many Players,"
University of Bielefeld, Institute of Mathematical Economics WP240.

Pechersky, S. and A. Sobolev [1995],
"SetValued Nonlinear Analogues of the Shapley Value,"
International Journal of Game Theory 24, 5778.

Peck, R. M. [1986],
"Power and Linear Income Taxation: An Example,"
Econometrica 54, 8794.

Peck, R. M. [1988],
"Power, Majority Voting and Linear Income Tax Schedules,"
Journal of Public Economics 36, 5367.

PerezCastrillo, D. and D. Wettstein [1999],
"Bidding for the Surplus: A NonCooperative Approach to the Shapley Value,"
BenGurion University, Monaster Center for Economic Research DP 997.

Riker, W. and L. S. Shapley [1968],
"Weighted Voting: A Mathematical Analysis for Instrumental Judgements,"
in Representation: Nomos X, J. R. Pennock and J. W. Chapman (eds.), Atherton, 199216.

Rosenmüller, J. [1977],
"Remark on the Transfer Operator and the ValueEquilibrium Equivalence Hypothesis,"
in Mathematical Economics and Game Theory, R. Henn and O. Moeschlin (eds.), SpringerVerlag, 108127.

Rosenmüller, J. [1981],
"Values of NonSidepayment Games and Their Application in the Theory of Public Goods,"
in Essays in Game Theory and Mathematical Economics, R. J. Aumann et al (eds.), Bibliographisches Institut Mannheim, 111129.

Rosenmüller, J. [1984],
"Selection of Values for NonSidepayment Games,"
Methods of Operations Research 48, 339398.

Rosenthal, R.W. [1976],
"Lindahl Solutions and Values for a Public Goods Example,"
Journal of Mathematical Economics 3, 3741.

Rosenthal, R.W. [1990],
"Monotonicity of the Core and Value in Dynamic Cooperative Games,"
International Journal of Game Theory 19, 4558.
 >
Roth, A. E. [1977],
"The Shapley Value as a von NeumannMorgenstern Utility,"
Econometrica 45, 657664.
 >
Roth, A. E. [1980],
"Values of Games without Side Payments: Some Difficulties with Current Concepts,"
Econometrica 48, 457465.
 >
Roth, A. E. [1986],
"On the NonTransferable Utility Value: A Reply to Aumann,"
Econometrica 54, 981984.

Roth, A. E. (ed.) [1988],
The Shapley Value,
Cambridge University Press.

Rothblum, U. [1973],
"On Orderable Set Functions and Continuity I,"
Israel Journal of Mathematics 16, 375397.

Rothblum, U. [1977],
"Orderable Set Functions and Continuity II: Set Functions with Infinitely Many Null Points,"
SIAM Journal on Control and Optimization 15, 144155.

Ruckle, W. H. [1982],
"Projections in Certain Spaces of Set Functions,"
Mathematics of Operations Research 7, 314318.

Ruckle, W. H. [1982],
"An Extension of the AumannShapley Value Concept to Functions on Arbitrary Banach Spaces,"
International Journal of Game Theory 11, 105116.

Ruiz, L. M., F. Valenciano and J. M. Zarzuelo [1998],
"The Family of Least Squares Values for Transferable Utility Games,"
Games and Economic Behavior 24, 109130.

Samet, D., Y. Tauman and I. Zang [1984],
"An Application of the AumannShapley Prices to the Transportation Problems,"
Mathematics of Operations Research 9, 2542.

Santos, J. C. and J. M. Zarzuelo [1998],
"Mixing Weighted Values of NonAtomic Games,"
International Journal of Game Theory 27, 331342.

Scafuri, A. J. and N. Yannelis [1984],
"NonSymmetric Cardinal Value Allocations,"
Econometrica 52, 13651368.
 >
Shafer, W. [1980],
"On the Existence and Interpretation of Value Allocations,"
Econometrica 48, 467477.

Shapiro, N. Z. and L. S. Shapley [1978],
"Values of Large Games I: A Limit Theorem,"
Mathematics of Operations Research 3, 19.

Shapley, L. S. [1953],
"Additive and NonAdditive Set Functions,"
Ph.D. thesis, Princeton University.
 >>
Shapley, L. S. [1953],
"A Value for nPerson Games,"
in Contributions to the Theory of Games II (Annals of Mathematics Studies 28), H. W. Kuhn and A. W. Tucker (eds.), Princeton University Press, 307317.

Shapley, L. S. [1962],
"Values of Games with Infinitely Many Players,"
in Recent Advances in Game Theory, M. Maschler (ed.), Ivy Curtis Press, Philadelphia, 113118;
also The Rand Co. RM2912, Santa Monica, CA.
 >>
Shapley, L. S. [1964],
"Values of Large Games VII: A General Exchange Economy with Money,"
The Rand Co. RM4248PR, Santa Monica, CA.
 >>
Shapley, L. S. [1969],
"Utility Comparison and the Theory of Games,"
in La Décision, Editions du CNRS, Paris, 251263.

Shapley, L. S. [1977],
"A Comparison of Power Indices and a Nonsymmetric Generalization,"
The Rand Co. P5872, Santa Monica, CA.
 >
Shapley, L. S. [1981],
"Discussant's Comments on R. D. Banker's 'Equity Considerations in Traditional Full Cost Allocation Practices: An Axiomatic Perspective',"
in Joint Cost Allocations, S. Moriarty (ed.), University of Oklahoma Press, 131136.
 >>
Shapley, L. S. and M. Shubik [1954],
"A Method for Evaluating the Distribution of Power in a Committee System,"
American Political Science Review 48, 787792.

Shapley, L. S. and M. Shubik [1969],
"Pure Competition, Coalitional Power, and Fair Division,"
International Economic Review 24, 139.

Sroka, J. J. [1993],
"The Value of Certain pNA Games through InfiniteDimensional Banach Spaces,"
International Journal of Game Theory 22, 123139.

Straffin, P. D. [1977],
"Homogeneity, Independence and Power Indices,"
Public Choice 30, 107118.

Straffin, P. D. [1994],
"Power and Stability in Politics,"
Hanbook of Game Theory with Economic Applications, Vol. II, R. J. Aumann and S. Hart (eds.), NorthHolland, 11271151.

Straffin, P. D. and J. P. Heaney [1981],
"Game Theory and the Tennessee Valley Authority,"
International Journal of Game Theory 10, 3543.

Suzuki, M. and M. Nakayama [1976],
"The Cost Assignment of Cooperative Water Resource Development: A Game Theoretic Approach,"
Management Science 22, 10811086.

Tauman, Y. [1977],
"A Nondiagonal Value on a Reproducing Space,"
Mathematics of Operations Research 2, 331337.

Tauman, Y. [1979],
"Value on the Space of all Scalar Integrable Games,"
in Game Theory and Related Topics, O. Moeschlin and D. Pallaschke (eds.), NorthHolland, 107115.

Tauman, Y. [1981],
"Value on a Class of NonDifferentiable Market Games,"
International Journal of Game Theory 10, 155162.

Tauman, Y. [1981],
"Values of Market Games with a Majority Rule,"
in Game Theory and Mathematical Economics, O. Moeschlin and D. Pallaschke (eds.), NorthHolland, 103122.

Tauman, Y. [1982],
"A Characterization of Vector Measures Games in pNA,"
Israel Journal of Mathematics 43, 7596.

Thomson, W. [1988],
"The Manipulability of the Shapley Value,"
International Journal of Game Theory 17, 101128.

Ui, T. [2000],
"A Shapley Value Representation of Potential Games,"
Games and Economic Behavior 31, 121135.

Weber, R. J. [1988],
"Probabilistic Values for Games,"
in The Shapley Value, A. E. Roth (ed.), Cambridge University Press.

Willson, S. J. [1993],
"A Value for Partially Defined Cooperative Games,"
International Journal of Game Theory 21, 371384.

Winter, E. [1989],
"A Value for Games with Level Structures,"
International Journal of Game Theory 18, 227242.

Winter, E. [1991],
"A Solution for NonTransferable Utility Games with Coalition Structure,"
International Journal of Game Theory 20, 5363.

Winter, E. [1992],
"The Consistency and the Potential for Values with Games with Coalition Structure,"
Games and Economic Behavior 4, 132144.

Winter, E. [1994],
"The Demand Commitment Bargaining and Snowballing Cooperation,"
Economic Theory 4, 255273.

Wooders, M. [1994],
"Large Games and Economies with Effective Small Groups,"
in GameTheoretic Methods in General Equilibrium Analysis, J.F. Mertens and S. Sorin (eds.), Kluwer Academic Publishers, 145206.

Wooders, M. and W. R. Zame [1987],
"Large Games: Fair and Stable Outcomes,"
Journal of Economic Theory 42, 5993.

Wooders, M. and W. R. Zame [1987],
"NTU Values of Large Games,"
Stanford University, I.M.S.S.S. TR503.
 >>
Young, H. P. [1985],
"Monotonic Solutions of Cooperative Games,"
International Journal of Game Theory 14, 6572.

Young, H. P. (ed.) [1985],
Cost Allocation: Methods, Principles, Applications,
NorthHolland.
 >
Young, H. P. [1994],
"Cost Allocation,"
in Handbook of Game Theory with Economic Applications, Vol. II, R. J. Aumann and S. Hart (eds.), NorthHolland, 11931235.
Footnotes:
^{1}
Prepared for lectures given at the 1999 Jerusalem Summer School in Economic
Theory.
Papers discussed during the lectures are marked >>;
other relevant papers are marked >.
Heinrich Nax is keeping an updated list at
https://gametheory.online/project_show/31
^{2}
Center for Rationality and Interactive Decision Theory; Department of
Economics; and Department of Mathematics; The Hebrew University of
Jerusalem, Feldman Building, Givat Ram, 91904 Jerusalem, Israel.
File translated from
T_{E}X by
T_{T}H,
version 2.30.
Last updated: