**William Thomson : Research Page**

### Conferences organized

- Decentralization Conference, University of Minnesota, Minneapolis, 1982.
- Decentralization Conference, University of Rochester, 1987.
- The legacy of Lionel McKenzie, University of Rochester, 1988.
- Buffalo-Cornell-Rochester theory conference, Rochester coordinator. Organizer when it took place in Rochester.
- Second International Conference for Social Choice and Welfare, Rochester, 1994.
- NATO Advanced Research Institute "Game theory and resource allocation: the axiomatic method", Stony Brook, 1997.
- IXth International Game Theory Conference", Stony Brook, 1998.
- Wallis Institute Conference on the Axiomatics of Resource Allocation, Rochester, May 2003.
- Wallis Institute Conference on Game Theory and Social Choice, Rochester, April 2004.
- Wallis Institute Conference on Resource Allocation and Game Theory, Rochester, April 2006.
- "Roth and Sotomayor; twenty years after", (co-organizer), Duke University, May 2010.

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### Books, Monographs

- Axiomatic Theory of Bargaining With a Variable Population (with T. Lensberg), Cambridge University Press, 1989.
- The Legacy of Lionel McKenzie (conference volume coedited with R. Becker, M. Boldrin and R. Jones), Academic Press, 1993.
- A Guide for the Young Economist, M.I.T. Press, Cambridge, 2001.

Chinese Translation, Shanghai University of Finance and Economics Press, 2002.

Japanese Translation, Tokyo Keizai publisher, Tokyo, 2006.

Second edition 2011, includes a new chapter, "Being a graduate student in economics". - Consistent Allocation Rules, unpublished, 2013.
- Bargaining Theory: The Axiomatic Approach, Academic Press, forthcoming 2013.
- The Theory of Fair Allocation, Princeton University Press, forthcoming 2013.
- How To Divide When There Is Not Enough; from the Talmud to Game Theory, unpublished, 2006.

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### Articles

- "Maximin strategies and elicitation of preferences," in Aggregation and Revelation of Preferences, (J.-J. Laffont, ed.), North-Holland, 1979, 245-268.
- "On allocations attainable through Nash equilibria, A comment," in Aggregation and Revelation of Preferences, (J.-J. Laffont, ed.), North- Holland, 1979, 420-431.
- "Eliciting production possibilities from a well-informed manager," Journal of Economic Theory, 20 (1979), 360-380.
- "Monotonicity and independence axioms," (with R.B. Myerson), International Journal of Game Theory, 9 (1980), 37-49.
- "Two characterizations of the Raiffa solution," Economics Letters, 6 (1980), 225-231.
- "Nashs bargaining solution and utilitarian choice rules," Econometrica, 49 (1981), 535-538.
- "Independence of irrelevant expansions," International Journal of Game Theory, 10 (1981), 107-114.
- "A class of solutions to bargaining problems," Journal of Economic Theory, 25 (1981), 431-441.
- "An informationally efficient equity criterion," Journal of Public Economics, 18 (1982), 243-263.
- "Incentives and information in labor-managed economies," Journal of Comparative Economics, 6 (1982), 248-268.
- "Collective guarantee structures," Economics Letters, 11 (1983), 63-68.
- "Equity in exchange economies," Journal of Economic Theory, 29 (1983), 217-244.
- "The fair division of a fixed supply among a growing population," Mathematics of Operations Research, 8 (1983), 319-326.
- "Guarantee structures for problems of fair division," (with T. Lensberg), Mathematical Social Sciences, 4 (1983), 205-218.
- "Problems of fair division and the egalitarian principle," Journal of Economic Theory, 31 (1983), 211-226.
- "Truncated egalitarian solutions," Social Choice and Welfare, 1 (1984), 25-32.
- "The manipulability of resource-allocation mechanisms," Review of Economic Studies, 51 (1984), 447-460.
- "Monotonicity, stability and egalitarianism," Mathematical Social Sciences, 8 (1984), 15-18.
- "Axiomatic theory of bargaining with a variable population: a survey of recent results," Chapter 11 of Game Theoretic Models of Bargaining (A.E. Roth, ed.), Cambridge University Press (1985), 233-258.
- "Theories of justice based on symmetry," (with H. Varian) Chapter 4 of Social Goals and Social Organization, volume in memory of E. Pazner (L. Hurwicz, D. Schmeidler and H. Sonnenschein, eds.), Cambridge University Press (1985), 107-129.
- "Replication invariance of bargaining solutions," International Journal of Game Theory, 15 (1986), 59-63.
- "Reversal of asymmetries of economic mechanisms under manipulation," Economics Letters, 21 (1986), 227-230.
- "The Walrasian mechanism from equal division is not monotonic with respect to variations in the number of consumers" (with G. Chichilnisky), Journal of Public Economics, 32 (1987), 119-124.
- "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, 42 (1987), 50-58.
- "The vulnerability to manipulative behavior of economic mechanisms designed to select equitable and efficient outcomes," Chapter 14 of Information, Incentives and Economic Mechanisms, T. Groves, R. Radner and S. Reiter (eds.), University of Minnesota Press (1987), 375-396.
- "Individual and collective opportunities," International Journal of Game Theory, 16 (1987), 245-252.
- "Monotonicity properties of bargaining solutions when applied to economics,"(with Y. Chun), Mathematical Social Sciences, 15 (1988), 1-27.
- "The manipulability of the Shapley-value," International Journal of Game Theory, 17 (1988), 101-127.
- "Characterizing the Nash bargaining solution without Pareto-optimality"(with T. Lensberg), Social Choice and Welfare, 5 (1988), 247-259.
- "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, 46 (1988), 237-254.
- "Can everyone benefit from growth? Two difficulties" (with H. Moulin), Journal of Mathematical Economics, 17 (1988), 339-345.
- "Bargaining solutions and relative guarantees" (with Y. Chun), Mathematical Social Sciences, 17 (1989), 285-295.
- "A refinement and extension of the no-envy concept" (with D. Diamantaras) Economics Letters, 33 (1990), 217-222.
- "Bargaining problems with uncertain disagreement points" (with Y. Chun), Econometrica, 58 (1990), 951-959.
- "Egalitarian solutions and uncertain disagreement points" (with Y. Chun), Economics Letters, 33 (1990), 29-33.
- "Nash solution and uncertain disagreement points" (with Y. Chun), Games and Economic Behavior, 2 (1990), 213-223.
- "On the non-existence of envy-free and egalitarian-equivalent allocations in economies with indivisibilities," Economics Letters, 34 (1990), 227-229.
- "The consistency principle," in Game Theory and Applications, Proceedings of the 1987 International Conference, Ohio State University, Columbus, Ohio (T. Ichiishi, A. Neyman and Y. Tauman, eds.), Academic Press (1990) 187-215.
- "Iterative planning procedures with a finite memory," (with L. Hurwicz), in Theoretical Foundations of Development Planning (B. Dahiya, ed.), Jan Tinbergen Educational Foundation Trust.
- "No-envy and consistency in economies with indivisible goods" (with K. Tadenuma), Econometrica, 59 (1991) 1755-1767.
- "Bargaining problems with claims" (with Y. Chun), Mathematical Social Sciences, 24 (1992) 19-33.
- "On the fair division of a heterogeneous commodity" (with M. Berliant and K. Dunz), Journal of Mathematical Economics, 21 (1992) 201-216.
- "The fair allocation of an indivisible good when monetary compensations are possible," (with K. Tadenuma), Mathematical Social Sciences, 25 (1993) 117-132.
- "Consistent allocation rules in atomless economies," (with L. Zhou), Econometrica, 61 (1993) 575-587.
- "The replacement principle in public good economies with single-peaked preferences", Economics Letters, 42 (1993), 31-36.
- "Labsence denvie: une introduction", Recherches Economiques de Louvain, 60 (1994) 43-61.
- "Notions of equal, or equivalent, opportunities," Social Choice and Welfare, 11 (1994), 137-156.
- "Resource-monotonic solutions to the problem of fair division when preferences are single-peaked," Social Choice and Welfare, 11 (1994), 205-223.
- "Consistent solutions to the problem of fair division when preferences are single-peaked," Journal of Economic Theory, 63 (1994), 219-245.
- "Consistent extensions," Mathematical Social Sciences, 28 (1994) 35-49.
- "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications (R. Aumann and S. Hart, eds.), North Holland, 1994, 1237-1284.
- "Population-monotonic solutions to the problem of fair division when preferences are single-peaked," Economic Theory, 5 (1995), 229-246.
- "Population-monotonic allocation rules", Chapter 4 in Social Choice, Welfare, and Ethics (W. Barnett, H.Moulin, M. Salles and N. Schofield, eds) Cambridge University Press, 1995, 79-124.
- "Games of fair division" (with K. Tadenuma), Games and Economic Behavior, 9 (1995), 191-204.
- "Refinements of the no-envy solution in economies with indivisible goods," (with K. Tadenuma), Theory and Decision 39 (1995), 189-206.
- "Concepts of implementation", Japanese Economic Review 47 (1996), 133-143.
- "Cooperative theory of bargaining: the classical model", in Cooperation: Game Theoretic Approach , (S. Hart and A. Mas-Colell, eds), Springer-Verlag, 1997, 9-24.
- "Cooperative theory of bargaining: modern developments", in Cooperation: Game Theoretic Approach , (S. Hart and A. Mas-Colell, eds), Springer-Verlag, 1997, 25-33.
- "The replacement principle in private good economies with singlepeaked preferences", Journal of Economic Theory, 76 (1997), 145-168.
- "Two derivations of the uniform rule and an application to bankruptcy",(with James Schummer), Economics Letters, 55 (1997), 145-168.
- "Axiomatic analysis of resource allocation", (with H. Moulin), in Social Choice reexamined, (K. Arrow, A. Sen and K. Suzumura, eds), London: McMillan 1997, 101-120.
- "The replacement principle in economies with indivisible goods," Social Choice and Welfare, 15 (1998), 57-66.
- "A comment on Bossert, Blackorby and Donaldson", in Social Choice reexamined, (K. Arrow, A. Sen and K. Suzumura, eds), London: McMillan.
- "The young persons guide to writing economic theory", Journal of Economic Literature, 37 (1999) 157-183.

Russian translation, 2005. - "Monotonic extensions on economic domains", Review of Economic Design, 4 (1999), 13-33.
- "Economies with public goods: an elementary geometric exposition", Journal of Public Economic Theory 1 (1999), 139-176.
- "Welfare-domination under preference-replacement: a survey and open questions", Social Choice and Welfare 16 (1999), 373-394.
- "R`egles dallocation monotones en ressources: une revue de la litt´erature", Revue Economique 50 (1999), 757-796.
- "On the fairness literature: a comment" (with M. Berliant and K. Dunz), Southern Journal of Economics 67 (2000), 479-484.
- "On the axiomatic method and its recent applications to game theory and resource allocation", Social Choice and Welfare, 18 (2001), 327- 387.
- "Constrained egalitarianism: a new solution for claims problems" (with Y. Chun and J. Schummer), Seoul Journal of Economics, 14 (2002), 269-297.
- "Group order preservation and the proportional rule for the adjudication of conflicting claims", (with C. Chambers), Mathematical Social Sciences 44 (2002), 235-252.
- "Nash bargaining theory: fifty years later", in Game Theory: a Festschrift in Honor of John Nash (C. Kottaridi and G. Siourounis, eds), University of Athens, 2002.
- "Claims problems and weighted generalizations of the Talmud rule", (with T. Hokari), Economic Theory, 21 (2003), 241-261.
- "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey", Mathematical Social Sciences, 45 (2003), 249-297.
- "On monotonicity in economies with indivisible goods", Social Choice and Welfare, 21 (2003), 195-205.
- "Convergence under replication of rules to adjudicate conflicting claims", (with Y. Chun), Games and Economic Behavior, 50 (2005), 129-142.
- "Divide-and-permute", Games and Economic Behavior, 52 (2005), 186-200.
- "A new solution to the problem of adjudicating conflicting claims", (with D. Dominguez), Economic Theory, 28 (2006), 283-307.
- "Children crying at birthday parties; Why?", Economic Theory, 31 (2007), 501-521.
- "On the existence of consistent rules to resolve conflicting claims: a geometric approach", Review of Economic Design, 11 (2007), 225-251.
- "The two-agent claims-truncated proportional rule has no consistent extension: a constructive proof", Economics Letters, 98 (2008), 59-65.
- "Fair allocation", in The New Palgrave Dictionary of Economics Second Edition. (S. Durlauf and L. Blume, eds), 2008
- "On properties of division rules lifted by bilateral consistency", (with T. Hokari), 2000, Journal of Mathematical Economics, 44 (2008), 1057-1071.
- "Two families of rules for the adjudication of conflicting claims", Social Choice and Welfare 31 (2008), 667-692.
- "Operators for the adjudication of conflicting claims", (with Chun-Hsien Yeh) Journal of Economic Theory 143 (2008), 177-198.
- "Implementation of solutions to the problem of fair division when preferences are single-peaked", Review of Economic Design 14 (2010), 1-15.
- "Bargaining and the theory of cooperative games: John Nash and beyond", (Introduction to collection of reprints of classic papers on bargaining theory in book of the same title, Edward Elgar Publishing Ltd, Camberly, Northampton, MA), 2010.
- "Fair allocation rules", in Handbook of Social Choice and Welfare (K. Arrow, A. Sen, and K. Suzumura, eds), North-Holland, Amsterdam, New York, 2010, 393-506.
- "Borrowing-proofness of the Lindahl rule in Kolm triangle economies", in Social Ethics and Normative Economics: Essays in Honour of Serge-Christophe Kolm, (M. Fleurbaey, M. Salles, and J. Weymark, eds), Springer, 2011, 169-191.
- "Consistency and its converse: an introduction", Review of Economic Design 15 (2011), 257-291.
- "Let them cheat!", (with R. Velez), Games and Economic Behavior 75 (2012), 948-963.
- "Lorenz rankings of rules for the adjudication of conflicting claims", Economic Theory 50 (2012), 547-569.
- "On the axiomatics of resource allocation: Interpreting the consistency principle", Economics and Philosophy 28 (2012), 385-421.
- "Game-theoretic analysis of bankruptcy and taxation problems: recent advances", International Game Theory Review, forthcoming, 2013.
- "New variable-population paradoxes for resource allocation", Social Choice and Welfare, forthcoming, 2013.
- "A characterization of a family of rules for the adjudication of conflicting claims", Games and Economic Behavior, forthcoming, 2013.
- "Population-monotonic solutions in public good economies with singlepeaked preferences", (with S. Ching), University of Rochester Working Paper, Social Choice and Welfare, forthcoming.

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### Book reviews

- Thomas Schelling, "Choice and Consequence," Harvard University Press, Journal of Economic Literature, 23 (1985), 616-617.
- William Baumol, "Superfairness," M.I.T. Press, American Political Science Review, 81 (1987), 1425-1426.
- Herv´e Moulin, "Axioms of Cooperative Decision Making," Cambridge University Press (1989), Economica, (1990) 543-545.
- Alvin E. Roth (editor), "The Shapley Value. Essays in Honor of Lloyd S. Shapley," Cambridge University Press (1988), Economica, 58 (1990) 123-124.
- Tatsuro Ichiishi, "The Cooperative Nature of the Firm", Cambridge University Press, Journal of Economic Literature, 33 (1995), 1980-1981.
- Serge-Christophe Kolm, "Justice and Equity", M.I.T Press, Journal of Economic Literature, 67 (2000), 479-484.

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### Research papers

- "The equilibrium allocations of Walras and Lindahl manipulation games," University of Minnesota, Center for Economic Research Discussion Paper No. 790-111, July 1979.
- "Recovering von Neumann-Morgenstern preferences from the acceptance frontier," (with P. Dybvig), Harvard Institute of Economic Research Discussion Paper No. 959, January 1983.
- "On the Nash bargaining solution," University of Rochester mimeo, 1985.
- "Can everyone benefit from growth? Another impossibility," University of Rochester mimeo, May 1987.
- "Monotonic allocation rules," University of Rochester Discussion Paper No. 116, December 1987, revised 1995.
- "Monotonic allocation rules in economies with public goods," University of Rochester Discussion Paper No. 117, December 1987, revised 1995.
- "Manipulation and implementation of solutions to the problem of fair division when preferences are single-peaked," University of Rochester mimeo, December 1990.
- "On the computational implications of converse consistency," University of Rochester mimeo, December 1991.
- "Consistency in exchange economies", University of Rochester mimeo, 1992.
- ""Bargaining"; an etymological note", University of Rochester mimeo, 1990, revised 1995.
- "Phantom voters and calibration points, a terminological note", 1999.
- "The case for "implementation", a terminological note", 1999.
- "Endowment monotonicities in economies with single-peaked preferences", October 1995.
- "Option monotonicity", mimeo, revised 2004.
- "Airport problems and cost allocation", revised 2013.
- "Borrowing-proofness", mimeo, revised 2013.
- "Borrowing-proofness in public good economies", mimeo, June 2005
- "Borrowing-proofness in economies with indivisible goods", (with Murat Atlamaz), mimeo, June 2010.
- "Where should you daughter go to college? An axiomatic analysis", mimeo, revised 2013.
- "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update", July 2013.
- "A consistent compromise between the proportional and constrained equal awards rules", December 2011, revised May 2013.
- "On the extension of the uniform rule to multiple commodities: existence and maximality-of-domains results", (With J. Cho), June 2011, revised July 2013.
- "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update", mimeo, revised August 2013.

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