Regular Population Monotonic Allocation Schemes and the Core

A subclass of games with population monotonic allocation schemes is studied, namely games with regular population monotonic allocation schemes (rpmas). We focus on the properties of these games and we prove the coincidence between the core and both the Davis-Maschler bargaining set and the Mas-Colell bargaining set.rpmas, bargaining set, pmas, tu-game

On the coincidence between the Shimomuras bargaining sets and the core

A necessary condition for the coincidence of the bargaining sets dened by Shimomura (1997) and the core of a cooperative game with transferable utility is provided. To this aim, a set of payo vectors, called max-payo vectors, are introduced. This necessary condition simply checks whether these vectors are core elements of the game.max-payo vectors, core, bargaining set, cooperative games

On bargaining sets of supplier-firm-buyer games

We study a special three-sided matching game, the so-called supplier-firm-buyer game, in which buyers and sellers (suppliers) trade indirectly through middlemen (firms). Stuart (1997) showed that all supplier-firm-buyer games have non-empty core. We show that for these games the core coincides with the classical bargaining set (Davis and Maschler, 1967), and also with the Mas-Colell bargaining set (Mas-Colell, 1989)

Mas-Colell Bargaining Set of Large Games

We study the equivalence between the MB-set and the core in the general context of games with a measurable space of players. In the first part of the paper, we study the problem without imposing any restriction on the class of games we consider. In the second part, we apply our findings to specific classes of games for which we provide new equivalence results. These include non-continuous convex games, exact non-atomic market games and non-atomic non-exact games. We also introduce, and characterize, a new class of games, which we call thin games. For these, we show not only that the MB-set is equal to the core, but also that it is the unique stable set in the sense of von Neumann and Morgenstern. Finally, we study the relation between thin games, market games and convex games.Mas-Colell Bargaining Set, maximal excess game, core-equivalence, thin games, market games, convex games.

Regular population monotonic allocation schemes and the core

A subclass of games with population monotonic allocation schemes is studied, namely games with regular population monotonic allocation schemes (rpmas). We focus on the properties of these games and we prove the coincidence between the core and both the Davis-Maschler bargaining set and the Mas-Colell bargaining set- En aquest article s'estudia una subclase dels jocs cooperatius amb esquemes de distribució monótons des del punt de vista poblacional, i que anomenem jocs amb esquemes de distribució regulars. L'anàlisi es centra en les propietats d'aquests jocs i, com a resultat principal, es demostra que el nucli del joc coincideix amb el conjunt de negociació de Davis-Maschler, així com també amb el conjunt de negociació de Mas-Colell

Játékelmélet = Game Theory

A kutatás főbb eredményeit 8 folyóiratcikkben és 14 konferencia-előadáson ismertettük. - "Játékelmélet" címmel elkészítettünk és elektronikusan elérhetővé tettünk egy tankönyvet, amely bemutatja a klasszikus játékelmélet legfontosabb témáit és eredményeit. - Megmutattuk, hogy a legtöbb kétszemélyes alkuproblémára (például azokra, amelyek lehetséges kimenetel halmaza poliéder) az L-Nash megoldást implementálni lehet bármilyen olyan nem kooperatív alkujátékkal, amely magát a Nash-megoldást is implementálja. - Azonosítottuk a lánc mentén összefüggő additív játékoknak azt a részosztályát, amelyen a mag az egyetlen stabil halmaz a Neumann-Morgenstern-i értelemben. - A mag illetve a szűkmag esetén jellemeztük azokat a koalíciókat, amelyek feltétlenül szükségesek, illetve amelyek mindenképpen elhagyhatók az adott megoldás megadásához. - Megmutattuk, hogy a hozzárendelési játékokra a nukleolusz rendelkezik a páronkénti monotonitási tulajdonsággal. - Megmutattuk, hogy topologikus feltevések nélkül, csak tisztán mérhető paramétertérre alapozva is bizonyítható a nem teljes információs játékok elemzésére Harsányi által javasolt egyetemes típustér létezése. Általánosítottuk a mértékterek inverz rendszerére vonatkozó Kolmogorov-féle Kiterjesztési Tételt. - Megállapítottuk, hogy a Shapley-érték használata regressziós modellek magyarázó változóinak értékelésére egy axiomatikusan megalapozható, jól interpretálható módszer. | Our main contributions have been published in a total of 8 articles and 14 conference presentations. - We have written and made electronically available a textbook covering the classical main topics and results of Game Theory. - We have shown that for most two-person bargaining problems (e.g. those with polyhedral outcome sets) the L-Nash solution is implementable by any non-cooperative bargaining game which implements the Nash solution itself. - We characterized the chain-component additive games for which the core is the unique von Neumann-Morgenstern stable set. - With respect to the core and the least-core, we identified which types of coalitions are always necessary and which ones can always be neglected in the determination of the given solution. - We proved that the nucleolus is pairwise-monotonic on assignment games. - We proved that a universal type space (the concept suggested by Harsányi to model situations with incomplete information) can be built upon a purely measurable parameter space, without any kind of topological assumptions. We generalized Kolmogoroff's Extension Theorem concerning the inverse systems of measure spaces. - We concluded that using the Shapley-value for measuring the explanatory effects of variables in regression models is an axiomatically sound, easily interpretable method

Les ensembles du Marchandage de Mas-Colell et de Zhou en Fonction d'effectivité

Nous définissons les ensembles du marchandage au sens de Mas-Colell et de Zhou dans les fonctions d'effectivité. Une fonction d'effectivité est marchandage stable si son ensemble de marchandage est non vide pour tout profil de préférences. Après quelques discussions sur les interprétations de ces nouvelles formes de stabilité, nous discutons de quelques propriétés des marchandages stabilités, mais ce travail a pour objet d'identifier les classes de fonctions d'effectivité pour lesquelles les stabilités au sens du marchandage et la stabilité au sens du cœur sont équivalentes

The Nucleolus, the Kernel, and the Bargaining Set: An Update

One of David Schmeidler’s many important contributions in his distinguished career was the introduction of the nucleolus, one of the central single-valued solution concepts in cooperative game theory. This paper is an updated survey on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set. As a first approach to these concepts, we refer the reader to the great survey by Maschler (1992); see also the relevant chapters in Peleg and Sudholter (2003). Building on the notes of four lectures on the nucleolus and the kernel delivered by one of the authors at the Hebrew University of Jerusalem in 1999, we have updated Maschler’s survey by adding more recent contributions to the literature. Following a similar structure, we have also added a new section that covers the bargaining set. The nucleolus has a number of desirable properties, including nonemptiness, uniqueness, core selection, and consistency. The first way to understand it is based on an egalitarian principle among coalitions. However, by going over the axioms that characterize it, what comes across as important is its connection with coalitional stability, as formalized in the notion of the core. Indeed, if one likes a single-valued version of core stability that always yields a prediction, one should consider the nucleolus as a recommendation. The kernel, which contains the nucleolus, is based on the idea of “bilateral equilibrium” for every pair of players. And the bargaining set, which contains the kernel, checks for the credibility of objections coming from coalitions. In this paper, section 2 presents preliminaries, section 3 is devoted to the nucleolus, section 4 to the kernel, and section 5 to the bargaining set.Iñarra acknowledges research support from the Spanish Government grant ECO2015-67519-P, and Shimomura from Grant-in-Aid for Scientific Research (A)18H03641 and (C)19K01558

Régulation et Contrôle du Pouvoir<br />dans un Système Pluraliste

Ce travail fait partie des recherches du programme DELICOM (ANR JC-JC 05)Les interprétations que je propose dans les exemples et illustrations ont été inspirées du travail commun de E. Picavet \& D. Razafimahatolotra.Les théories institutionnelles se sont développées autour de la polarisation de la société en individus et institutions. La recherche d'un compromis sur la convergence de ces deux pôles devient alors la tâche principale de cette classe de théories. Ce travail qui s'inscrit dans l'institutionnalisme tente d'entrer au cœur du problème de la rationalité et de la sélection del'issue sociale en posant en même temps des questions épistémiques autour de la fonction d'effectivité. C'est est un début d'un essai sur la théorie pure du pouvoir, une théorie alternative aux théories institutionnelles existantes