
on Economic Design 
By:  Hiroki Shinozaki; Tomoya Kazumura; Shigehiro Serizawa 
Abstract:  We consider the problem of allocating multiple units of an indivisible object among agents and collecting payments. Each agent can receive multiple units of the object, and his (consumption) bundle is a pair of the units he receives and his payment. An agent's preference over bundles may be nonquasilinear, which accommodates income effects or soft budget constraints. We show that the generalized Vickrey rule is the only rule satisfying efficiency, strategyproofness, individual rationality, and no subsidy for losers on rich domains with nondecreasing marginal valuations. We further show that if a domain is minimally rich and includes an arbitrary preference exhibiting both decreasing marginal valuations and a positive income effect, then no rule satisfies the same four properties. Our results suggest that in nonquasilinear environments, the design of an efficient multiunit auction mechanism is possible only when agents have nondecreasing marginal valuations. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1097&r=all 
By:  Parag A. Pathak; Tayfun S\"onmez; M. Utku \"Unver; M. Bumin Yenmez 
Abstract:  COVID19 has revealed several limitations of existing mechanisms for rationing scarce medical resources under emergency scenarios. Many argue that they abandon various ethical values such as equity by discriminating against disadvantaged communities. Illustrating that these limitations are aggravated by a restrictive choice of mechanism, we formulate pandemic rationing of medical resources as a new application of market design and propose a reserve system as a resolution. We develop a general theory of reserve design, introduce new concepts such as cutoff equilibria and smart reserves, extend previouslyknown ones such as sequential reserve matching, and relate these concepts to current debates. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.00374&r=all 
By:  Rouzbeh Ghouchani (Concordia University); Szilvia Pápai (Concordia University) 
Abstract:  We study the aggregation of a couple's preferences over their respective jobs when they enter a centralized labor market jointly, such as the market for assigning hospital residencies to medical students. Usually in such markets couples need to submit joint preferences over pairs of jobs. Starting from two individual preference orderings over jobs, we first study the Lexicographic and the RankBased Leximin aggregation rules, and then propose a family of aggregation rules, the kLexiPairing rules, and provide an axiomatic characterization of these rules. The parameter k indicates the degree of selfishness for one partner (and altruism for the other partner), with the least selfish RankBased Leximin rule at one extreme and the most selfish Lexicographic rule at the other extreme. Since couples care about geographic proximity, we also identify a simple parametric family of preference aggregation rules which build on the kLexiPairing rules and reflect the couple's preference for togetherness. 
Keywords:  matching with couples; preference aggregation; leximin; compromise; togetherness 
JEL:  D71 D47 
Date:  2020–08–05 
URL:  http://d.repec.org/n?u=RePEc:crd:wpaper:20006&r=all 
By:  Alex Suzdaltsev 
Abstract:  A seller chooses a reserve price in a secondprice auction to maximize worstcase expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. We prove that it is always optimal to set the reserve price to seller's own valuation. However, the maxmin reserve price may not be unique. If the number of bidders is sufficiently high, all prices below the seller's valuation, including zero, are also optimal. A secondprice auction with the reserve equal to seller's value (or zero) is an asymptotically optimal mechanism (among all mechanisms) as the number of bidders grows without bound. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.01618&r=all 
By:  Fabra, Natalia; Llobet, Gerard 
Abstract:  The energy transition will imply a change in the competitive paradigm of electricity markets. Competitionwise, one distinguishing feature of renewables versus fossilfuels is that their marginal costs are known but their available capacities are uncertain. Accordingly, in order to understand competition among renewables, we analyze a uniformprice auction in which bidders are privately informed about their random capacities. Renewable plants partially mitigate market power as compared to conventional technologies, but producers are still able to charge positive markups. In particular, firms exercise market power by either withholding output when realized capacities are large, or by raising their bids above marginal costs when realized capacities are small. Since markups are decreasing in realized capacities, a positive capacity shock implies that firms offer to supply more at reduced prices, giving rise to lower but also more volatile market prices. An increase in capacity investment depresses market prices, which converge towards marginal cost when total installed capacity is sufficiently large, or when the market structure is sufficiently fragmented. 
Keywords:  Electricity markets; Forecasts; Multiunit auctions; renewables 
Date:  2019–10 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:14060&r=all 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Peter Sudhölter (Department of Business and Economics  SDU  University of Southern Denmark) 
Abstract:  A balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T) to any feasible T that is not contained in S. It turns out that outvoting is transitive and the set M of maximal elements with respect to outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a superstable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core superstability is equivalent to vital extendability, requiring that each vital coalition is extendable. 
Abstract:  Un jeu à utilité transférable équilibré (N,v) a un coeur stable si son coeur est externalement stable, c'estàdire si chaque imputation hors du coeur est dominée par un élément du coeur. Etant donné deux paiements x et y, on dit que x surclasse y via une coalition S d'un ensemble réalisable si x dominie y via S et si x alloue au moins v(T) à toute coalition réalisable T qui n'est pas contenue dans S. Il s'ensuit que la relation de surclassement est transitive et que l'ensemble M des éléments maximaux par rapport au surclassement coïncide avec le coeur si et seulement si une certaine condition emboîtée d'équilibrage est vérifiée. Ainsi, on peut vérifier en un nombre fini d'étapes si un jeu équilibré à un coeur stable. On dit qu'un jeu a un coeur superstable si tout vecteur de paiement qui alloue moins que v(S) à une coalition S est dominé par un élément du coeur, et nous prouvons que la superstabilité du coeur est équivalente à l'étendabilité vitale, qui requiert que toute coalition vitale soit étendable. 
Keywords:  Domination,stable set,core,TU game,ensemble stable,coeur,jeux TU 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs02900564&r=all 
By:  Burak Can (Department of Data Analytics and Digitalisation, Maastricht University); Jens Leth Hougaard (Department of Food and Resource Economics, University of Copenhagen; Economics, NYUShanghai); Mohsen Pourpouneh (Department of Food and Resource Economics, University of Copenhagen) 
Abstract:  This paper proposes a conceptual framework for the analysis of reward sharing schemes in mining pools, such as those associated with Bitcoin. The framework is centered around the reported shares in a pool instead of agents and results in two new fairness criteria, absolute and relative redistribution. These criteria impose that the addition of a share to the pool affects all previous shares in the same way, either in absolute amount or in relative ratio. We characterize two large classes of economically viable reward sharing schemes corresponding to each of these fairness criteria in turn. We further show that the intersection of these classes brings about a generalization of the the wellknown proportional scheme, which also leads to a new characterization of the proportional scheme as a corollary. 
Keywords:  blockchain, bitcoin, fairness, mining pools, resource allocation, mechanism design 
JEL:  D63 G20 L86 D31 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:foi:wpaper:2020_09&r=all 