Incentive Compatible Allocation and Exchange of Discrete Resources

Abstract

Allocation and exchange of discrete resources such as kidneys, school seats, and many other resources for which agents have single-unit demand is conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns in designing such mechanisms. We show that a mechanism is individually strategy-proof and always selects the efficient outcome with respect to some Arrovian social welfare function if and only if the mechanism is group strategy-proof and Pareto efficient. We construct the full class of these mechanisms and show that each of them can be implemented by endowing agents with control rights over resources.This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange.We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms strictly Lorenz dominate all previously known mechanisms.

Ordinal Efficiency, Fairness, and Incentives in Large Markets

“…A similar argument shows that uniform randomizations over fixed-endowment Hierarchical Exchange mechanisms of Pápai (2000) and their counterpart among Trading Cycles of Pycia and Ünver (2016) (extended to the setting with object copies by Pycia and Ünver (2011)) are regular provided the number of object copies satisfies condition (3).…”

“…For instance, Pathak and Sethuraman (2010) describe the deliberations of policymakers 6 For instance, all uniform randomizations over any Trading Cycle mechanisms of Pycia and Ünver (2016) (extended to the setting with copies by Pycia and Ünver, 2011) are asymptotically efficient.…”

“…To define the asymptotic counterpart of this efficiency concept let us say that, for any ϵ > 0, a random allocation µ is ϵ-efficient with respect to a preference profile ≻ iff (i) for no n ≥ 2 there is a cycle of agents i 1 , ..., i n and objects a 1 , ..., a n such that µ (i k , a k ) > ϵ and a k+1 ≻ i k a k for all k = 1, ..., n (that is no agents i 1 , ..., i n can 17 See footnote 25 in Pycia and Ünver (2016) for an extension of Pápai's fixed-endowment idea. 18 This concept is also known as stochastic-dominance efficiency because the efficiency of an allocation µ is equivalent to the lack of another allocation that first order stochastically dominates µ.…”

Serial Dictatorship: The Unique Optimal Allocation Rule When Information is Endogenous

“…Second, in addition to ownership there is a new form of control called brokerage. Brokerage was introduced by Pycia and Ünver (2013). Third, a trading and braiding mechanism might terminate with a braid.…”

“…Pycia and Ünver (2013) and Bade (2014) characterize the very large set of all such mechanisms. Lots of room remains to impose additional requirements to select among these mechanisms.…”