(Minimally) ?-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities

We consider competitive and budget-balanced allocation rules for problems where a number of indivisible objects and a fixed amount of money is allocated among a group of agents. In "small" economies, we identify under classical preferences each agent's maximal gain from manipulation. Using this result we find the competitive and budget-balanced allocation rules which are minimally manipulable for each preference profile in terms of any agent's maximal gain. If preferences are quasi-linear, then we can find a competitive and budget-balanced allocation rule such that for any problem, the maximal utility gain from manipulation is equalized among all agents.

[1]  William Thomson,et al.  Claims problems and weighted generalizations of the Talmud rule , 2003 .

[2]  Flip Klijn,et al.  An algorithm for envy-free allocations in an economy with indivisible objects and money , 2000, Soc. Choice Welf..

[3]  D. Gale,et al.  Fair Allocation of Indivisible Goods and Criteria of Justice , 1991 .

[4]  Tommy Andersson,et al.  Budget-Balance, Fairness and Minimal Manipulability , 2014 .

[5]  Alexander Kovalenkov,et al.  Simple Strategy-Proof Approximately Walrasian Mechanisms , 2002, J. Econ. Theory.

[6]  Enriqueta Aragones,et al.  A derivation of the money Rawlsian solution , 1995 .

[7]  Lars-Gunnar Svensson.  Large Indivisibles: An analysis with respect to price equilibrium and fairness , 1983 .

[8]  Tommy Andersson,et al.  Non-manipulable assignment of individuals to positions revisited , 2008, Math. Soc. Sci..

[9]  Kate Larson,et al.  Randomised Room Assignment-Rent Division , 2011 .

[10]  D. J. Roberts,et al.  THE INCENTIVES FOR PRICE-TAKING BEHAVIOR IN LARGE EXCHANGE ECONOMIES , 1976 .

[11]  Hans Peters,et al.  Minimal manipulability: anonymity and unanimity , 2007, Soc. Choice Welf..

[12]  Ning Sun,et al.  A General Strategy Proof Fair Allocation Mechanism , 2003 .

[13]  Hans Peters,et al.  Anonymous voting and minimal manipulability , 2007, J. Econ. Theory.

[14]  Matthias G. Raith,et al.  Bidding for envy-freeness: A procedural approach to n-player fair-division problems , 2002, Soc. Choice Welf..

[15]  R. Aumann,et al.  Game theoretic analysis of a bankruptcy problem from the Talmud , 1985 .

[16]  William Thomson,et al.  Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey , 2003, Math. Soc. Sci..

[17]  Fuad Aleskerov,et al.  Degree of manipulability of social choice procedures , 1999 .

[18]  Flip Klijn,et al.  Asymmetrically fair rules for an indivisible good problem with a budget constraint , 2012, Soc. Choice Welf..

[19]  Parag A. Pathak,et al.  School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation. NBER Working Paper No. 16783. , 2011 .

[20]  Jerry R. Green,et al.  Incentives in public decision-making , 1979 .

[21]  M. Jackson,et al.  Approximately competitive equilibria in large finite economies , 1997 .

[22]  Lars-Gunnar Svensson,et al.  Coalitional strategy-proofness and fairness , 2009 .

[23]  Yuji Fujinaka,et al.  Maximal Manipulation in Fair Allocation , 2012 .

[24]  M. Jackson.  Incentive compatibility and competitive allocations , 1992 .