388 research outputs found
Lorenz Population Monotonic Allocation Schemes for TU-games
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
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
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
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 són de preu uniforme són 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 procés de negociació bilateral i simÚtric, o bé coincideix amb tot core o es redueix al seu punt mig que és el nucleolus
Assignment markets with the same core
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
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
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
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
A jĂĄtĂ©kelmĂ©let kĂŒlönbözĆ 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 elĆadĂĄsban is bemutattuk. Legfontosabb eredmĂ©nyeink: âą Megmutattuk, hogy a Nash-fĂ©le alkuproblĂ©mĂĄkra ismert implementĂĄciĂłs modellek ĂĄtalakĂtĂĄsĂĄval megkaphatĂł a limit-Nash megoldĂĄs is. âą 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. âą Megmutattuk, hogy a hozzĂĄrendelĂ©si piacokon bĂĄrmelyik szereplĆ eredmĂ©nyesen tudja manipulĂĄlni a âfair egyensĂșlyiâ, illetve a nukleolusz allokĂĄciĂłs mechanizmust, ugyanakkor Ă©les felsĆ korlĂĄtokat is megadtunk ennek mĂ©rtĂ©kĂ©re. âą KarakterizĂĄltuk a stabil halmazokat az egy-eladĂłs hozzĂĄrendelĂ©si jĂĄtĂ©kokban. âą KĂŒlönfĂ©le jĂĄtĂ©kosztĂĄlyokon megvizsgĂĄltuk a Shapley-Ă©rtĂ©k fĆbb karakterizĂĄciĂłjainak Ă©rvĂ©nyessĂ©gĂ©t. Erre alapozva javasoltuk a Shapley-Ă©rtĂ©k âmĂ©rĂ©si eszközkĂ©ntâ valĂł hasznĂĄlatĂĄt a regressziĂłs modellekben, az ĂĄltalĂĄnosĂtott szavazĂĄsi helyzetekben, illetve a rizikĂł allokĂĄciĂłs problĂ©mĂĄkban. âą Megmutattuk, hogy nincsen univerzĂĄlis topologikus tĂpustĂ©r, a HarsĂĄnyi-program ilyen tĂpusterekben tehĂĄt nem mƱködik. Ugyanakkor matematikailag megalapoztunk egy ilyen jellegƱ, a mĂ©rhetĆ 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: âą We adjusted various implementation models designed for Nash bargaining problems to obtain the limit-Nash solution as well. âą 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. âą We showed that in assignment markets each agent can manipulate the âfair equilibriumâ and the nucleolus allocation mechanisms to his benefit, but established sharp upper bounds to its extent. âą We characterized stable sets in assignment games with one-seller. âą 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 âmeasurementâ tool in regression models, in generalized weighted voting situations, and in risk allocation problems. âą 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
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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