On group strategyproof and optimal object allocation
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On group strategyproof and optimal object allocation Conan Mukherjee1 Received: 16 January 2020 / Accepted: 4 June 2020 © Society for the Advancement of Economic Theory 2020
Abstract We consider a two-agent, single indivisible object allocation problem. We focus on continuous mechanisms that satisfy agent sovereignty, and investigate implications of group strategyproofness. In particular, we provide an explicit characterization of the strategyproof mechanisms and show that there are non-affine maximizer mechanisms that do not belong to the class characterized by Roberts (North-Holland, 1979). Further, we show that there are no budget-balanced strategyproof mechanisms. Also, we obtain an impossibility for existence of strong group strategyproof mechanism. We find that this impossibility goes away upon relaxing our notion of group strategyproofness, and consequently, present a class of weak group strategyproof mechanisms. Finally, we completely characterize the class of feasible strategyproof mechanisms satisfying individual rationality, and show that there are no optimal strategyproof expected revenue maximizing mechanisms under a general class of well behaved type distributions. Keywords Group strategyproofness · Budget balance · Optimal mechanism JEL classification C72 · C78 · D71 · D63
1 Introduction We consider the standard object allocation model where a single indivisible object is allocated among two agents who have private non-negative valuations for the object and quasi-linear preferences over the object and money. An example of such a situation could be a bilateral bargaining setting where two agents, a seller and a buyer, negotiate over when and how to trade an indivisible object. Similar examples can I would like to thank the associate editor and the anonymous referee, as well as Professors Tommy Andersson, Debasis Mishra and Manipushpak Mitra for their comments. I would also thank Parikshit De for discussions. Any remaining errors are mine. * Conan Mukherjee [email protected] 1
Economics Group, Indian Institute of Management Calcutta, Kolkata, India
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also be seen in situations where a license, a house, a plot of land or an airport landing right, etc. is to allotted. We focus on reasonable mechanisms in the sense that they are well behaved (satisfying a mild notion of continuity) and satisfy agent sovereignty (which requires that every agent have some ability to affect the allocation outcome of mechanism). In the class of such mechanisms, we provide an explicit complete characterization of the strategyproof mechanisms, similar to that obtained in Roberts (1979). However, unlike Roberts (1979), this class contains non-affine maximizer mechanisms. This is clearly because in the present setting there are only two alternatives and the domain of valuations is restricted. We then look for stronger notions of non-manipulability, in terms of strong and weak (pairwise) group strategyproofness, that eliminate group level incentives to misreport. We find that the
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