39 research outputs found

    Adjusting Prices in the Many-to-many Assignment Game

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    Starting with an initial price vector, prices are adjusted in order to eliminate the demand excess and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which sellers should those transfers be made (minimal overdemanded sets) is the key definition in the description of the algorithm. Such approach was previously used by several authors. We introduce a novel distinction by considering multiple sellers owing multiple identical objects and multiple buyers with a quota greater than one consuming at most one unit of each seller’s good. This distinction induces a necessarily more complicated construction of the overdemanded sets than the constructions existing in the literature, even in the simplest case of additive utilities considered here. As the previous papers, our mechanism yields the minimum competitive equilibrium price vector. A procedure to find the maximum competitive equilibrium price vector is also provided.matching; stable payoff; competitive equilibrium payoff; optimal stable payoff; lattice social costs; pure comparative vigilance; super-symmetric rule

    A bargaining set for roommate problems

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    Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result

    Pairing games and markets

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    Pairing Games or Markets studied here are the non-two-sided NTU generalization of assignment games. We show that the Equilibrium Set is nonempty, that it is the set of stable allocations or the set of semistable allocations, and that it has has several notable structural properties. We also introduce the solution concept of pseudostable allocations and show that they are in the Demand Bargaining Set. We give a dynamic Market Procedure that reaches the Equilibrium Set in a bounded number of steps. We use elementary tools of graph theory and a representation theorem obtained here

    A new solution concept for the roommate problem

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    Abstract The aim of this paper is to propose a new solution concept for the roommate problem with strict preferences. We introduce maximum irreversible matchings and consider almost stable matchings (Abraham et al., 2006) and maximum stable matchings (Tan 1990, 1991b). These solution concepts are all core consistent. We find that almost stable matchings are incompatible with the other two concepts. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which we call Q -stable matchings. We construct an efficient algorithm for computing one element of this set for any roommate problem. We also show that the outcome of our algorithm always belongs to an absorbing set (Inarra et al., 2013)

    Strategy-Proofness and Singleton Cores in Generalized Matching Problems

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    We introduce and study the class of generalized matching problems. Two subclasses of this class are marriage problems (Gale and Shapley 1962) and the housing market (Shapley and Scarf 1974). We search for strategy-proof solutions to generalized matching problems. We show that if the core is a singleton and is stable for all problems then it is sstrategy-proof as a solution. We also show that on the class of problems with a non-empty core therre exists a Pareto efficient, individually rational, and sstrategy-proof solution only if the core is a singleton for all problems. Furthermore if such a solution exists, it is the core.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100985/1/ECON427.pd

    The Stability of the Roommate Problem Revisited

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    The lack of stability in some matching problems suggests that alternative solution concepts to the core might be applied to find predictable matchings. We propose the absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts some other matchings when the core is empty. Furthermore, it satisfies an interesting property of outer stability. We also characterize the absorbing sets, determine their number and, in case of multiplicity, we find that they all share a similar structure.roommate problem, core, absorbing sets

    The stability of the roommate problem revisited

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    The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when the core is empty. Furthermore, it satisfies the interesting property of outer stability. We also determine the matchings in absorbing sets and find that in the case of multiple absorbing sets a similar structure is shared by all.roommate problem, core, absorbing sets

    A bargaining set for roommate problems

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    Since stable matchings may not exist, we adopt a weaker notion of stability for solving the roommate problem: the bargaining set. Klijn and Massó (2003) show that the bargaining set coincides with the set of weakly stable and weakly efficient matchings in the marriage problem. First, we show that a weakly stable matching always exists in the roommate problem. However, weak stability is not sufficient for a matching to be in the bargaining set. Second, we prove that the bargaining set is always non-empty. Finally, as Klijn and Massó (2003) get for the marriage problem, we show that the bargaining set coincides with the set of weakly stable and weakly efficient matchings in the roommate problem

    A new solution for the roommate problem

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    The aim of this paper is to propose a new solution for the roommate problem with strict references. We introduce the solution of maximum ir reversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable m atchings (Tan [30] [32]). We find that almost stable matchings are incompatible with the o ther two solutions. Hence, to solve the roommate problem we propose matchings that lie at t he intersection of the maximum irreversible matchings and maximum stable matchings , which are called Q-stable matchings. These matchings are core consistent and we offer an efficient algorithm for computing one of them. The outcome of the algorithm belongs to an ab sorbing set

    Construir el diálogo científico en la Matemática: la búsqueda del equilibrio entre símbolos y palabras en artículos de investigación sobre Teoría de Juegos

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    Maestría en Inglés con Orientación en Lingüística AplicadaMost scientific communication is conducted in English, which may be a difficult task and a source of obstacles for researchers whose primary language is not English (Bitchenera & Basturkmen, 2006; Borlogan, 2009; Duff, 2010; Matsuda & Matsuda, 2010). As a matter of concern for language scholars, this situation requires at least two actions: (1) the development of research focused on the problems faced by researchers when writing in a foreign language, and (2) the design and implementation of pedagogical and didactic programmes or services aimed at providing researchers with the tools to enhance their linguistic and rhetorical skills. In both cases, the ultimate objective of these lines of action is to help researchers integrate into and interact with their knowledge communities in an independent, active and successful way. Considering those needs and the emerging interest in English as a lingua franca or as an international language, many scholars have devoted to studying the features of writing and language use across the world and across disciplines (Hyland, 2004; Matsuda & Matsuda, 2010; Mercado, 2010). However, few have explored the case of Mathematics (Lemke, 2002; Morgan, 2008; O’Halloran, 2005; Schleppegrell, 2007), and even fewer have investigated the discourse of scientific research articles (SRA) in this discipline (Graves & Moghadassi, 2013, 2014). In view of this situation, investigation of the discourse of science in the field of Mathematics (Game Theory - GT) as used in the Institute of Applied Mathematics (IMASL), at the National University of San Luis (UNSL), becomes both an answer to local researchers’ needs and an attempt to contribute to current research in writing, evaluative discourse and use of English as an international language for the communication of science. Thus, the main objective of this work is to conduct a comparative description between unpublished GT SRAs written in English by IMASL researchers and published GT SRAs written in English by international authors, in terms of linguistic features used to build authorship and authorial stance. The exploration of the genre is made from the perspective of the system of Appraisal (Hood, 2010; Martin & White, 2005; White, 2000), with the aid of Corpus Linguistics (CL) tools (Cheng, 2012; Meyer, 2002; Tognini-Bonelli, 2001). The results of this research are expected to be useful for the enhancement of knowledge of language professionals devoted to the teaching of writing as well as translation, proofreading, editing and reviewing services. A further goal is to lay the foundations for the production of didactic material which can potentially be incorporated into writing courses or professional writing, translation, reviewing and proofreading training programmes.Fil: Lucero Arrua, Graciela Beatriz. Universidad Nacional de Córdoba. Facultad de Lenguas; Argentina
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