## KAROL FLORES-SZWAGRZAK - Papers

*Strategy-Proof Assignment Of Multiple Resources*(with Albin Erlanson) Journal of Economic Theory, 2015, Volume 159 Pages 137-162 (preprint) (published paper) We examine the strategy-proof allocation of multiple resources; an application is the assignment of packages of tasks, workloads, and compensations among the members of an organization. In the domain of multidimensional single-peaked preferences, we find that any allocation mechanism obtained by maximizing a separably concave function over a polyhedral extension of the set of Pareto-efficient allocations is strategy-proof. Moreover, these are the only strategy-proof, unanimous, consistent, and resource-monotonic mechanisms.These mechanisms generalize the parametric rationing mechanisms [Young in Math. Operations Res. 12, 1987, 398-414], some of which date back to the Babylonian Talmud.*Priority Classes And Weighted Constrained Equal Awards Rules For The Claims Problem*Journal of Economic Theory, 2015, Volume 160 Pages 36-55 (preprint) (published paper)

We revisit the ``claims problem" (Oneill, MSS 1982), where a group of individuals have claims on a resource but there is not enough of it to honor all of the claims. We characterize the rules satisfying three well-known invariance axioms: consistency, composition up, and claims truncation invariance. They are priority-augmented versions of the standard weighted constrained equal awards rules, also known as weighted gains methods (Moulin, Econometrica 2000): individuals are sorted into priority classes; the resource is distributed among the individuals in the first priority class using a weighted constrained equal awards rule; if some of the resource is left over, then it is distributed among the individuals in the second priority class, again using a weighted constrained equal awards rule; the distribution carries on in this way until the resource is exhausted.

Our characterization extends to a generalized version of the claims problem where there are multiple divisible and indivisible resources and individuals have claims on each of these.*Efficient, Fair, and Strategy-proof (re)allocation under network constraints*

Social Choice and Welfare, forthcoming, (preprint) (published paper)

We study the (re)allocation of workloads among a group of workers with different skill sets. A network connects workers to the tasks requiring their skills. We assume a tentative initial workload allocation. However, the task processing times can turn out to be greater or lesser than expected. As a result, the initial workload allocation may need to be updated to ensure completion. Moreover, the initial workloads may also be unsatisfactory: some employees would prefer larger workloads, others smaller ones, and there may be unused opportunities to balance these mismatches. We prove that ruling out Pareto-improvements involving exactly two agents is equivalent to full Pareto-efficiency, no matter how complex the network encoding skills is. We propose a version of the most relevant fairness notion in economies with initial allocations, ``fair net trades" [Schmeidler, D. and K. Vind. 1972. Fair net trades. Econometrica, 40, 637-642]. Strikingly, there is a unique strategy-proof and efficient allocation rule satisfying this fairness notion. This rule is in fact group strategy-proof.*The replacement principle in networked economies with single-peaked preferences*

Social Choice and Welfare, forthcoming, (preprint)

We study the transfer of a resource from a group of suppliers to a group of demanders through links in a network. The analysis is relevant to situations where institutional constraints bar the use of the price mechanism: the allo- cation of workloads under fixed salaries, a commodity under disequilibrium prices, etc. In these contexts suppliers and demanders naturally have single- peaked preferences. We evaluate transfer rules on the basis of the “replacement principle” (Thomson, 1997; Moulin, 1987), the requirement that a change in an agent’s preferences affects all other agents in the same direction in terms of welfare. We find that the only Pareto-efficient, participation-compatible, replication-invariant, and envy-free rule satisfying an appropriate formulation of the replacement principle is the “egalitarian rule” introduced by Bochet et al. (2012).

Working Papers

- Teamwork and individual productivity (with Rafael Treibich)
- Matching supply and demand in networks We study the problem of matching the supplies of a resource to demands on it under constraints that can be modeled by networks. Network connections model necessary conditions for a supplier of the resource to transfer an amount of it to a demander. These conditions may include information, trust, relationship-specific skills, contracts, or tissue-blood type compatibility in the assignment of organs for transplant. As is common in the matching literature, we model situations where institutional constraints bar the use of the price mechanism. Natural assumptions on production possibilities or preferences imply that suppliers and demanders have single-peaked preferences over their transfers. We identify a class of Pareto-efficient, individually rational, and strategy-proof allocation rules matching supply and demand. These rules specify the amount transferred from each supplier and to each demander. All of these rules are, in fact, group strategy-proof and elicit a truthful report of each agent's connections in the network when these cannot be publicly observed.
- Strategy-Proof Market Clearing Mechanisms

Consider a market for a resource under disequilibrium prices where suppliers and demanders are privately informed about their optimal supply and consumption levels. Strategy-proof market clearing mechanisms give suppliers and demanders dominant strategy incentives to truthfully reveal this information. We describe the class of strategy-proof and efficient mechanisms responding well to changes in supplies and demands, as formalized by the “replacement principle" [Thomson, 2011, Fair allocation rules, Handbook of Social Choice and Welfare]. Since no symmetry or anonymity conditions are imposed, these mechanisms can implement a wide array of distributional objectives in both indivisible and divisible resource allocation situations. These mechanisms apply to allocation problems involving network constraints modeling necessary conditions for a transfer of the resource from a supplier to a demander. The class of mechanisms contains the egalitarian rules of Bochet, Ilkilic, and Moulin [2013, J. Econ. Theory, 148, 535–562] and Bochet, Ilkilic, Moulin, and Sethuraman [2012, Theoretical Economics, 7, 395-423]. In the simple ``non-networked" and one-sided version of the problem, our family coincides with the ``sequential-allotment rules" [Barbera S., M. Jackson and A. Neme. 1997. Strategy-proof allotment rules. Games Econ. Behavior, 18, 1-21]. - Coherent resource allocation in networks A commodity is to be transferred from a group of suppliers to a group of demanders by means of a network. Monetary compensations are ruled out and agents are equipped with single-plateaued or single-peaked preferences over their assignments. Our objective is to identify allocation rules satisfying normatively and strategically appealing properties. We are concerned with the behavior of Pareto-efficient solutions in response to changes in the set of efficient allocations. We propose the following principle: if an agent's preferences change and, as a result, the set of efficient allocations shrinks but the allocation originally recommended is still Pareto-efficient, then this allocation is still chosen. We call this property ``contraction invariance." It is a basic notion of social rationality akin to a central axiom in choice theory [Chernoff, H. 1954. Rational selection of decision functions. Econometrica, 22, 422-443] and ``independence of irrelevant alternatives" in the axiomatic theory of bargaining [Nash, J.F. 1950. The bargaining problem. Econometrica, 18,155-162]. Based on this criterion, and considering the domain of single-peaked preferences, we provide alternative characterizations of the egalitarian rules proposed by Bochet, Ilkilic, Moulin, and Sethuraman [2012, Theoretical Economics, 7, 395-423] and Bochet, Ilkilic, and Moulin [2013, J. Econ. Theory, 148, 535–562]. Moreover, we establish connections between contraction invariance and group strategy-proofness.