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Economics Department Faculty

William Thomson

Professor of Economics
Phone: (585) 275-2236
Email: wth2 at mail.rochester.edu

Ph.D. Stanford, 1976

My CV is available in in pdf

Link to the research page of Prof. Thomson

Research Interests: Game Theory, Mechanism Design, Theory of Equity

Selected Papers and Publications:

• "The fair division of a fixed supply among a growing population," Mathematics of Operations Research, 8 (1983), 319-326.
• "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, 46 (1988), 237-254.
• Axiomatic Theory of Bargaining With a Variable Population (with T.Lensberg), Cambridge University Press, 1989.
• "Can everyone benefit from growth? Two difficulties" (with H. Moulin), Journal of Mathematical Economics (1988), 339-345.
• "No-envy and consistency in economies with indivisible goods" (with K. Tadenuma), Econometrica, 59 (1991) 1755-1767.
• "Population-monotonic solutions to the problem of fair division when preferences are single-peaked," Economic Theory, 5 (1995), 229-246.
• A Guide for the Young Economist, M.I.T. Press, 2001.
  Book consisting of three pedagogical essays entitled:
  1. "Writing papers"
  2. "Giving talks"
  3. "Writing referee reports"

Forthcoming Publications and Recent papers:

• "Let them cheat!", Rochester Center for Economic Research Working Paper, last revised July 2009.
  
  Abstract

  We consider the problem of fairly allocating a bundle of infinitely divisible commodities among a group of agents with "classical" preferences. We propose to measure an agent's "sacrifice" at an allocation by the size of the set of feasible bundles that the agent prefers to her consumption. As a solution, we select the allocations at which sacrifices are equal across agents and this common sacrifice is minimal. We then turn to the manipulability of this solution. In the tradition of Hurwicz (1972, Decision and Organization, U. Minnesota Press), we identify the equilibrium allocations of the manipulation game associated with this solution when all commodities are normal: (i) for each preference profile, each equal-division constrained Walrasian allocation is an equilibrium allocation; (ii) conversely, each equilibrium allocation is equal-division constrained Walrasian. (iii) Furthermore, we show that if normality of goods is dropped, then equilibrium allocations may not be efficient.

  Available in PDF format.
  
  
• "Borrowing-proofness", Rochester Center for Economic Research Working Paper, last revised January 2009.
  
  Abstract

  We formulate and study the requirement on an allocation rule that no agent should be able to benefit by augmenting his endowment through borrowing resources from the outside world (alternatively, by simply exaggerating it). We show that the Walrasian rule is not "borrowing-proof" even on standard domains. More seriously, no efficient selection from the endowments-lower-bound correspondence, or from the no-envy-in-trades correspondence, or from the egalitarian-equivalent-in-trades correspondence is borrowing-proof. These impossibilities hold even on the domain of economies with homothetic preferences.

  Available in PDF format.
  
  
• "Fair Allocation Rules", Rochester Center for Economic Research Working Paper, last revised December 2007.
  
  Available in PDF format.



• "Lorenz rankings of rules for the adjudication of conflicting claims", Rochester Center for Economic Research Working Paper, last revised December 2007.
  
  Abstract For the problem of adjudicating conflicting claims, we offer simple criteria to compare rules on the basis of the Lorenz order. These criteria pertain to three families of rules. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules (Thomson, 2007a). The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. The third family consists of consistent rules (Young, 1987). We also address the issue whether certain operators on the space of rules preserve the Lorenz order.
  Available in PDF format.



• "Cost allocation and airport problems", Rochester Center for Economic Research Working Paper, last revised December 2007.
  
  Abstract We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the need they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the "airport problem", the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions.
  Available in PDF format.

Surveys:

• "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.
• "Welfare-domination under preference-replacement: a survey and open questions", Social Choice and Welfare 16 (1999), 373-394.
• "On the axiomatic method and its recent applications to game theory and resource allocation", Social Choice and Welfare, 18 (2001), 327- 387.
• "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey", Mathematical Social Sciences, 45 (2003), 249-297.
• "Consistency and its converse: an elementary introduction", University of Rochester Rochester Center for Economic Research Working Paper, 2004.
• "Airport problems and cost allocation", Rochester Center for Economic Research Working Paper, 2006.
• "Fair Allocation Rules", in Handbook of Social Choice and Welfare (K. Arrow, A. Sen, and K. Suzumura, eds), North-Holland, Amsterdam, New York, forthcoming, 2008.