1,709 research outputs found

    Cooperative Games with Overlapping Coalitions

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    In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions--or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

    Convex Fuzzy Games and Participation Monotonic Allocation Schemes

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    AMS classifications: 90D12; 03E72Convex games;Core;Decisionmaking;Fuzzy coalitions;Fuzzy games;Monotonic allocation schemes;Weber set

    Az erƑs,a gyenge, meg a ravasz: Hatalom Ă©s stratĂ©giai viselkedĂ©s szavazĂĄsi jĂĄtĂ©kokban = The Strong, the Weak and the Cunning: Power and Strategy in Voting Games

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    KutatĂĄsi eredmĂ©nyeink hĂĄrom tĂ©ma körĂ© csoportosĂ­thatĂłk. Ezek közĂŒl az elsƑ a stratĂ©giai megfontolĂĄsok vizsgĂĄlata. Megmutatjuk, hogy a szavazĂłk növelhetik befolyĂĄsukat, ha veszekednek mĂĄs szavazĂłkkal Ă©s a stratĂ©giai hatalmi indexek jĂłl definiĂĄltak a jĂĄtĂ©kok bizonyos osztĂĄlyaira. Egy mĂĄsik vonal a kooperatĂ­v jĂĄtĂ©kok olyan kulcsfontossĂĄgĂș tulajdonsĂĄgait vizsgĂĄlja, mint a konvexitĂĄs, vagy az egzaktsĂĄg. Bizonyos esetekben a nyerƑ koalĂ­ciĂłk halmaza kĂŒlsƑ okok miatt korlĂĄtozott: erre a leggyakoribb pĂ©lda, mikor egy hĂĄlĂłzaton elhelyezkedƑ csĂșcsok helyzeti befolyĂĄsĂĄt vizsgĂĄljuk. A csĂșcsok csak az Ƒket összekötƑ Ă©lek mentĂ©n kommunikĂĄlhatnak Ă©s csak szomszĂ©daikkal. Több Ă©rtĂ©k Ă©s index is kiterjesztĂ©sre, illetve bevezetĂ©sre kerĂŒl ilyen hĂĄlĂłzati jĂĄtĂ©kokra, illetve az Ă©rtĂ©kekhez axiomatikus karakterizĂĄciĂłt adunk. VĂ©gĂŒl a hatalmi indexeket olyan jĂĄtĂ©kokra is kiterjesztjĂŒk, ahol egyes szavazĂłk hiĂĄnyozhatnak. A nem stratĂ©giai hiĂĄnyzĂĄst vizsgĂĄljuk Ă©s a Shapley Ă©rtĂ©ket teljesen karakterizĂĄljuk az ĂĄltalĂĄnosĂ­tott sĂșlyozott szavazĂĄsi jĂĄtĂ©kok osztĂĄlyĂĄn. ModellĂŒnket kĂŒlönbözƑ parlamentekre alkalmazzuk, illetve az elmĂ©leti mĂłdszerek több egyĂ©b alkalmazĂĄsĂĄt is vizsgĂĄltuk, Ășgymint a Lisszaboni SzerzƑdĂ©s hatĂĄsĂĄt a Miniszterek TanĂĄcsĂĄban folyĂł sĂșlyozott szavazĂĄs hatalmi viszonyaira. | The results of the project centre around three themes. The first is strategic considerations. We have shown that voters are able to increase their power by strategic quarrelling and the strategic power indices are well defined for certain classes of games. Additional papers provide tests on key properties, such as convexity and exactness of cooperative games. In some situations the set of feasible (winning) coalitions is restricted exogenously. The most common example is to study positional power over a network where the voters are located at the nodes and can only communicate with their neighbours. Several values and indices are introduced and characterised for games over networks. At last we generalised power indices to weighted voting games where representatives may be absent. We study non-strategic absenteeism and characterise the Shapley value for the class of generalised weighted voting games. We have also studied applications studying the effect of absent voters in various national parliaments or the effect of the Lisbon Treaty of the European Union to the power balance in the Council of Ministers

    The efficiency of the non-profit enterprise: constitutional ideology, conformist preferences and reputation

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    According to one thesis the non profit enterprise (in short NPE) is able to attract ideological entrepreneurs and workers (Rose-Ackerman 1996). In fact I prove that without the ideological element, a simple game between the entrepreneur, worker and beneficiary is condemned to an opportunistic equilibrium, beneficial to the internal members of the organization but detrimental to the beneficiary. Thus the NPE does not better than its for profit counterpart. In my model ideologues, both entrepreneurs and workers, share a principle of justice seen as the constitutional ideology of the NPE, agreed upon in an hypothetical ex ante bargaining game. The constitutional principle provides an independent source of motivation (a source of utility) of the players, in so far as they believe in the reciprocity of conformity to the ideology by all the participants. I call this conformity-based utility “ideological”, and I see it as the representation of a preference for expected conformity to the given constitutional principle. The philosophical underpinnings of this reform of the players' utility functions in worked out by distinguishing two concepts of preferences of the Self: consequentialist preferences and conformist preferences. The latter are preferences for those actions that are part of states of affairs described in terms of interdependent actions conforming to an abstract norm or principle, which become effective once the preferences' holder does expect that the other players do they part in that state of affairs and they do expect that himself do his part in the same state of affairs. What result is that a player's ideological utility depends on the expectation of deontological modes of behaviour followed by all the participants, himself included. On this basis it is possible to overcome personal incentives to embrace opportunistic behaviour, so that the proper Non-profit Enterprise emerges. It is proved that in the “social enterprise game” amongst the member of the organisation there exists an organisational equilibrium minimising transaction costs to the beneficiaries. At last, this equilibrium rests on the emergence of an expectations system of reciprocal conformity to the constitutional ideology. As the existence - not even the selection – of the internal organizational equilibrium rests heavily on the existence of the appropriate system of reciprocal expectation, the problem of how we can justify the emergence of the appropriate system of beliefs must be underlined. Here is where the explicit moral codes of the NPE enters the scene. I see the code of ethics as the building block for deriving a reputation equilibrium between the NPE as a whole and its external stakeholders within a repeated game, whose stage-game is the typical game of trust played under incomplete knowledge and unforeseen contingencies. At last the conformist-motivation model and the reputation model under unforeseen contingencies are shown to play together in a mutually supporting explanation of the efficiency of the NPE.

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

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    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

    Cooperative games with overlapping coalitions

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    In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

    Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.

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    The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.
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