20 research outputs found
Manipulation of Stable Matchings using Minimal Blacklists
Gale and Sotomayor (1985) have shown that in the Gale-Shapley matching
algorithm (1962), the proposed-to side W (referred to as women there) can
strategically force the W-optimal stable matching as the M-optimal one by
truncating their preference lists, each woman possibly blacklisting all but one
man. As Gusfield and Irving have already noted in 1989, no results are known
regarding achieving this feat by means other than such preference-list
truncation, i.e. by also permuting preference lists.
We answer Gusfield and Irving's open question by providing tight upper bounds
on the amount of blacklists and their combined size, that are required by the
women to force a given matching as the M-optimal stable matching, or, more
generally, as the unique stable matching. Our results show that the coalition
of all women can strategically force any matching as the unique stable
matching, using preference lists in which at most half of the women have
nonempty blacklists, and in which the average blacklist size is less than 1.
This allows the women to manipulate the market in a manner that is far more
inconspicuous, in a sense, than previously realized. When there are less women
than men, we show that in the absence of blacklists for men, the women can
force any matching as the unique stable matching without blacklisting anyone,
while when there are more women than men, each to-be-unmatched woman may have
to blacklist as many as all men. Together, these results shed light on the
question of how much, if at all, do given preferences for one side a priori
impose limitations on the set of stable matchings under various conditions. All
of the results in this paper are constructive, providing efficient algorithms
for calculating the desired strategies.Comment: Hebrew University of Jerusalem Center for the Study of Rationality
discussion paper 64
The shared assignment game and applications to pricing in cloud computing
ABSTRACT We propose an extension to the Assignment Gam
Social Games: Matching and the Play of Finitely Repeated Games
We examine a new class of games, which we call social games, where players not only choose strategies but also choose with whom they play. A group of players who are dissatisfied with the play of their current partners can join together and play a new equilibrium. This imposes new refinements on equilibrium play, where play depends on the relative populations of players in different roles, among other things. We also examine finite repetitions of games where players may choose to rematch in any period. Some equilibria of fixed-player repeated games cannot be sustained as equilibria in a repeated social game. Conversely, the set of repeated matching (or social) equilibria also includes some plays that are not part of any subgame perfect equilibrium of the corresponding fixed-player repeated games. We explore existence under different equilibrium definitions, as well as the relationship to renegotiation-proof equilibrium. It is possible for repeated matching equilibria to be completely distinct from renegotiation-proof equilibria, and even to be Pareto inefficient.Social games, Matching, Games, Repeated games, Renegotiation
Social Games: Matching and the Play of Finitely Repeated Games
We examine a new class of games, which we call social games, where players not only choose strategies but also choose with whom they play. A group of players who are dissatisfied with the play of their current partners can join together and play a new equilibrium. This imposes new refinements on equilibrium play, where play depends on the relative populations of players in different roles, among other things. We also examine finite repetitions of games where players may choose to rematch in any period. Some equilibria of fixed-player repeated games cannot be sustained as equilibria in a repeated social game. Conversely, the set of repeated matching (or social) equilibria also includes some plays that are not part of any subgame perfect equilibrium of the corresponding fixed-player repeated games. We explore existence under different equilibrium definitions, as well as the relationship to renegotiation-proof equilibrium. It is possible for repeated matching equilibria to be completely distinct from renegotiation-proof equilibria, and even to be Pareto inefficient.Social Games, Matching, Games, Repeated Games, Renegotiation
Social Games: Matching and the Play of Finitely Repeated Games
We examine a new class of games, which we call social games, where players not only choose strategies but also choose with whom they play. A group of players who are dissatisfied with the play of their current partners can join together and play a new equilibrium. This imposes new refinements on equilibrium play, where play depends on the relative populations of players in different roles, among other things. We also examine finite repetitions of games where players may choose to rematch in any period. Some equilibria of fixed-player repeated games cannot be sustained as equilibria in a repeated social game. Conversely, the set of repeated matching (or social) equilibria also includes some plays that are not part of any subgame perfect equilibrium of the corresponding fixed-player repeated games. We explore existence under different equilibrium definitions, as well as the relationship to renegotiation-proof equilibrium. It is possible for repeated matching equilibria to be completely distinct from renegotiationproof equilibria, and even to be Pareto inefficient
Construir el diĂĄlogo cientĂfico en la MatemĂĄtica: la bĂșsqueda del equilibrio entre sĂmbolos y palabras en artĂculos de investigaciĂłn sobre TeorĂa de Juegos
MaestrĂa en InglĂ©s con OrientaciĂłn en LingĂŒĂstica 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; OâHalloran, 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 researchersâ 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 CĂłrdoba. Facultad de Lenguas; Argentina