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on Economic Design |
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Issue of 2023‒05‒22
nine papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Jorge Alcalde-Unzu; Marc Vorsatz |
| Abstract: | We establish that all strategy-proof social choice rules in strict preference domains follow necessarily a two-step procedure. In the first step, agents are asked to reveal some specific information about their preferences. Afterwards, a subrule that is dictatorial or strategy-proof of range 2 must be applied, and the selected subrule may differ depending on the answers of the first step. As a consequence, the strategy-proof rules that have been identified in the literature for some domains can be reinterpreted in terms of our procedure and, more importantly, this procedure serves as a guide for determining the structure of the strategy-proof rules in domains that have not been explored yet. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.12843&r=des |
| By: | Pinaki Mandal |
| Abstract: | This paper studies the stability and strategy-proofness aspect of the two-sided one-to-one matching market. Agents have single-peaked preferences on trees. In this setting, we characterize all rich anonymous tree-single-peaked domains where a stable and (weakly group) strategy-proof matching rule exists. We also show that whenever there exists a stable and strategy-proof matching rule on a rich anonymous tree-single-peaked domain, one or both of the deferred acceptance rules (Gale and Shapley, 1962) satisfy stability and weak group strategy-proofness on that domain. Finally, we show that for markets with a size of at least five, there is no rich anonymous domain where a stable and non-bossy matching rule exists. As a corollary, we show incompatibility between stability and group strategy-proofness on rich anonymous tree-single-peaked domains for markets with a size of at least five. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.11494&r=des |
| By: | Ata Atay; Sylvain Funck; Ana Mauleon; Vincent Vannetelbosch |
| Abstract: | We adopt the notion of the farsighted stable set to determine which matchings are stable when agents are farsighted in matching markets with couples. We show that a singleton matching is a farsighted stable set if and only if the matching is stable. Thus, matchings that are stable with myopic agents remain stable when agents become farsighted. Examples of farsighted stable sets containing multiple non-stable matchings are provided for markets with and without stable matchings. For couples markets where the farsighted stable set does not exist, we propose the DEM farsighted stable set to predict the matchings that are stable when agents are farsighted. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.12276&r=des |
| By: | Orhan Aygün; Günnur Ege Bilgin |
| Abstract: | We analyze an extension of the many-to-one placement problem, where some doctors are exogenously guaranteed a seat at a program, which defines a lower bound on their assignment. Respecting assignment guarantees, combined with the limited capacities of programs often violates fairness and leaves more preferred doctors unemployed. In pursuance of restoring fairness, a designer often has to deviate from the target capacities of programs, and imposing the traditional notion of fairness results in excessive deviations from the target capacities. In order to prevent excessive deviations, we introduce two notions that are tailored to the environment: q-fairness and avoiding unnecessary slots. Furthermore, we introduce the Assignment-Guarantees-Adjusted Mechanism (AGAM) and show that it is the unique strategy-proof mechanism that satisfies q-fairness and avoids unnecessary slots whilst respecting assignment guarantees. Furthermore, among the mechanisms that satisfy q-fairness and respect guarantees, AGAM minimizes the deviation from the target capacities. |
| Keywords: | many-to-one matching, assignment guarantees, flexible capacities, q-fairness |
| JEL: | C78 D47 D78 D82 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_417&r=des |
| By: | Ostrovsky, Michael (Stanford U); Skrzypacz, Andy (Stanford U) |
| Abstract: | We revisit the classic result on the (non-)existence of pure-strategy Nash equilibria in the Generalized First-Price Auction for sponsored search advertising and show that the conclusion may be reversed when ads are ranked based on the product of stochastic quality scores and bid amounts, rather than solely on the latter. Moreover, the expected revenue in the pure strategy equilibrium of the Generalized First-Price Auction may substantially exceed that of the Generalized Second-Price Auction. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:4043&r=des |
| By: | Alfred Galichon; Yu-Wei Hsieh; Maxime Sylvestre |
| Abstract: | We propose monotone comparative statics results for maximizers of submodular functions, as opposed to maximizers of supermodular functions as in the classical theory put forth by Veinott, Topkis, Milgrom, and Shannon among others. We introduce matrons, a natural structure that is dual to sublattices that generalizes existing structures such as matroids and polymatroids in combinatorial optimization and M-sets in discrete convex analysis. Our monotone comparative statics result is based on a natural order on matrons, which is dual in some sense to Veinott's strong set order on sublattices. As an application, we propose a deferred acceptance algorithm that operates in the case of divisible goods, and we study its convergence properties. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.12171&r=des |
| By: | Sarah Auster; Nicola Pavoni |
| Abstract: | We study the delegation problem between a principal and an agent, who not only has better information about the performance of the available actions but also superior awareness of the set of actions that are actually feasible. We provide conditions under which the agent finds it optimal to leave the principal unaware of relevant options. By doing so, the agent increases the principal’s cost of distorting the agent’s choices and increases the principal’s willingness to grant him higher information rents. We further show that the principal may use the option of renegotiation as a tool to implement actions that are not describable to her at the contracting stage. If the agent renegotiates, his proposal signals information about the payoff state. Due to her limited awareness, the principal makes a coarse inference from the agent’s recommendations and, as a result, accepts a large number of the agent’s proposals, which ultimately benefits both. |
| Keywords: | Unawareness, optimal delegation, strategic disclosure |
| JEL: | D82 D83 D86 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_256v3&r=des |
| By: | Ziwei Wang; Jiabin Wu |
| Abstract: | We present a model that investigates preference evolution with endogenous matching. In the short run, individuals' subjective preferences simultaneously determine who they are matched with and how they behave in the social interactions with their matched partners, which results in material payoffs for them. Material payoffs in turn affect how preferences evolve in the long run. To properly model the "match-to-interact" process, we combine stable matching and equilibrium concepts. Our findings emphasize the importance of parochialism, a preference for matching with one's own kind, in shaping our results. Under complete information, the parochial efficient preference type -- characterized by a weak form of parochialism and a preference for efficiency -- stands out in the evolutionary process, because it is able to force positive assortative matching and efficient play among individuals carrying this preference type. Under incomplete information, the exclusionary efficient preference type -- characterized by a stronger form of parochialism and a preference for efficiency -- prevails, as it provides individuals with an incentive to engage in self-sorting through rematching in any matching outcomes that involve incomplete information and inefficient play. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.11504&r=des |
| By: | Jian Yang |
| Abstract: | We are concerned with the stability of a coalitional game, i.e., a transferable-utility (TU) cooperative game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings. This principle of consensual blocking, as well as the traditional core-defining principle of unilateral blocking and one straddling in between, can all be applied to partition-allocation pairs. Each such pair is made up of a partition of the grand coalition and a corresponding allocation vector whose components are individually rational and efficient for the various constituent coalitions of the given partition. For the resulting strong, medium, and weak stability concepts, the first is core-compatible in that the traditional core exactly contains those allocations that are associated through this strong stability concept with the all-consolidated partition consisting of only the grand coalition. Probably more importantly, the latter medium and weak stability concepts are universal. By this, we mean that any game, no matter how ``poor'' it is, has its fair share of stable solutions. There is also a steepest ascent method to guide the convergence process to a mediumly stable partition-allocation pair from any starting partition. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.10651&r=des |