388 research outputs found

    Lorenz Population Monotonic Allocation Schemes for TU-games

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    Sprumont (1990) introduces Population Monotonic Allocation Scheme (PMAS) and proves that every assignment game with at least two sellers and two buyers, where each buyer-seller pair derives a positive gain from trade, lacks a PMAS. In particular glove games lacks PMAS. We propose a new cooperative TU-game concept, Lorenz-PMAS, which relaxes some population monotonicity conditions by requiring that the payoff vector of any coalition is Lorenz dominated by the corresponding restricted payoff vector of larger coalitions. We show that every TU-game having a Lorenz-PMAS is totally balanced, but the converse is not true in general. We obtain a class of games having a Lorenz-PMAS, but not PMAS in general. Furthermore, we prove the existence of Lorenz-PMAS for every glove game and for every assignment game with at most five players. Additionally, we also introduce two new notions, Lorenz-PMAS-extendability and Lorenz-PMAS-exactness,and discuss their relationships with the convexity of the game

    The assignment game: core bounds for mixe-pair coalitions

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    In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyerseller exact games and satisfy the condition that each mixedpair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyerseller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixedpair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a 45olattice by means of the core of an assignment game can now be answered.core, exact games, assignment game

    All assignment games with the same core have the same nucleolus

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    There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyerseller exact representative.core, nucleolus, assignment game, kernel

    Uniform-price assignment markets

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    Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolusEls jocs d'assignaciĂł amb preu uniforme sĂłn aquells mercats d'assignaciĂł on el core es redueix a un segment. En aquests casos, per a tots els agents actius en el mercat, els preus competitius varien de forma uniforme, tot i que els productes poden ser no homogenis. En aquest treball es dona una caracteritzaciĂł dels mercats amb preu uniforme a partir de la matriu d'assignaciĂł Els Ășnics mercats on tots els subjocs sĂłn de preu uniforme sĂłn els mercats de cavalls de Bohm-Bawerk. Finalment,provem que en aquests mercats de preu uniforme el kernel, o conjunt de pagaments que s'obtenen a partir d'un procĂ©s de negociaciĂł bilateral i simĂštric, o bĂ© coincideix amb tot core o es redueix al seu punt mig que Ă©s el nucleolus

    Assignment markets with the same core

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    In the framework of bilateral assignment games, we study the set of matrices associated with assignment markets with the same core. We state conditions on matrix entries that ensure that the related assignment games have the same core. We prove that the set of matrices leading to the same core form a join-semilattice with a nite number of minimal elements and a unique maximum. We provide a characterization of the minimal elements. A sucient condition under which the join-semilattice reduces to a lattice is also given.core, semilattice, assignment game

    On the dimension of the core of the assignment game

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    The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.core, assignment game, core dimension

    All assignment games with the same core have the same nucleolus

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    There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representativeExisteixen jocs cooperatius d'utilitat transferible que tot i tenir el mateix core tenen diferent nucleolus. En aquest treball es mostra que aixĂČ no pot passar amb els jocs d'assignaciĂČ Ă©s a dir que, en aquests jocs, el nucleolus ve determinat pel core del joc i per tant dos jocs d'assignaciĂł amb el mateix core tenen forçosament el mateix nucleolus. Per provar-ho mostrem que el nucleolus d'un joc d'assignaciĂł coincideix amb el de l'Ășnic joc que el representa amb la propietat de ser 'buyer-seller' exact

    An alternative proof of the characterization of core stability for the assignment game

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    Solymosi and Raghavan (2001), characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. While their proof makes use of graph-theoretical tools, the alternative proof presented here relies on the notion of the buyer-seller exact representative, as introduced by NĂșñez and Rafels in 2002

    Jåtékelméleti kutatåsok = Investigations in Game Theory

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    A jĂĄtĂ©kelmĂ©let kĂŒlönbözƑ kĂ©rdĂ©sköreiben vĂ©gzett kutatĂĄsaink eredmĂ©nyeit eddig 9 nemzetközi Ă©s 5 hazai folyĂłiratban, valamint 2 szerkesztett kötetben mĂĄr megjelent cikkben közöltĂŒk (Ă©s tovĂĄbbi 2-4 nemzetközi cikkre szĂĄmĂ­tunk). EredmĂ©nyeinket több mint 30 nemzetközi, illetve hazai konferencia elƑadĂĄsban is bemutattuk. Legfontosabb eredmĂ©nyeink: ‱ Megmutattuk, hogy a Nash-fĂ©le alkuproblĂ©mĂĄkra ismert implementĂĄciĂłs modellek ĂĄtalakĂ­tĂĄsĂĄval megkaphatĂł a limit-Nash megoldĂĄs is. ‱ BevezettĂŒk a puha korrelĂĄlt egyensĂșly fogalmĂĄt. Bemutattuk, hogy ez az Ășj korrelĂĄlt egyensĂșly több modellben Pareto-Ă©rtelemben jobb megoldĂĄst eredmĂ©nyez, mint mĂĄs korrelĂĄlt egyensĂșlyok. ‱ Megmutattuk, hogy a hozzĂĄrendelĂ©si piacokon bĂĄrmelyik szereplƑ eredmĂ©nyesen tudja manipulĂĄlni a ’fair egyensĂșlyi’, illetve a nukleolusz allokĂĄciĂłs mechanizmust, ugyanakkor Ă©les felsƑ korlĂĄtokat is megadtunk ennek mĂ©rtĂ©kĂ©re. ‱ KarakterizĂĄltuk a stabil halmazokat az egy-eladĂłs hozzĂĄrendelĂ©si jĂĄtĂ©kokban. ‱ KĂŒlönfĂ©le jĂĄtĂ©kosztĂĄlyokon megvizsgĂĄltuk a Shapley-Ă©rtĂ©k fƑbb karakterizĂĄciĂłjainak Ă©rvĂ©nyessĂ©gĂ©t. Erre alapozva javasoltuk a Shapley-Ă©rtĂ©k ’mĂ©rĂ©si eszközkĂ©nt’ valĂł hasznĂĄlatĂĄt a regressziĂłs modellekben, az ĂĄltalĂĄnosĂ­tott szavazĂĄsi helyzetekben, illetve a rizikĂł allokĂĄciĂłs problĂ©mĂĄkban. ‱ Megmutattuk, hogy nincsen univerzĂĄlis topologikus tĂ­pustĂ©r, a HarsĂĄnyi-program ilyen tĂ­pusterekben tehĂĄt nem mƱködik. Ugyanakkor matematikailag megalapoztunk egy ilyen jellegƱ, a mĂ©rhetƑ tĂ­pusterekre vonatkozĂł pozitĂ­v eredmĂ©nyt. | We have investigated various topics in game theory and published so far 9 articles in international journals (and expect to have 2-4 more), 5 articles in domestic journals, 2 papers in an edited volume. We have also presented our results in more than 30 talks at international and domestic conferences. Our main contributions include (but not limited to) the following: ‱ We adjusted various implementation models designed for Nash bargaining problems to obtain the limit-Nash solution as well. ‱ We introduced a new correlation protocol. We demonstrated in several settings that this new (called soft) correlated equilibrium can give Pareto-better outcomes than what other correlated equilibria can. ‱ We showed that in assignment markets each agent can manipulate the ’fair equilibrium’ and the nucleolus allocation mechanisms to his benefit, but established sharp upper bounds to its extent. ‱ We characterized stable sets in assignment games with one-seller. ‱ We examined several characterizations of the Shapley value on various classes of games. Based on these results, we proposed using the Shapley-value as a ’measurement’ tool in regression models, in generalized weighted voting situations, and in risk allocation problems. ‱ We have demonstrated that the HarsĂĄnyi program does not work in topological type spaces, therefore no universal topological type space exists. We have laid the mathematical foundation of a positive result on measurable type spaces

    A survey on assignment markets

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    The assignment game is a two-sided market, say buyers and sellers, where demand and supply are unitary and utility is transferable by means of prices. This survey is structured in three parts: a first part, from the introduction of the assignment game by Shapley and Shubik (1972) until the publication of the book of Roth and Sotomayor (1990), focused on the notion of core; the subsequent investigations that broaden the scope to other notions of solution for these markets; and its extensions to assignment markets with multiple sides or multiple partnership. These extended two-sided assignment markets, that allow for multiple partnership, better represent the situation in a labour market or an auction
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