STABLE COALITION STRUCTURES UNDER RESTRICTED COALITIONAL CHANGES

In this paper, we examine whether farsighted players form the efficient grand coalition structure in coalition formation games. We propose a stability concept for a coalition structure, called sequentially stability, when only bilateral mergers of two separate coalitions are feasible because of high negotiation costs. We provide an algorithm to check the sequential stability of the grand coalition structure as well as sufficient conditions for which the efficient grand coalition structure is sequentially stable. We also illustrate out results by means of common pool resource games and Cournot oligopoly games.

Download Full-text

COALITION FORMATION IN GAMES WITHOUT SYNERGIES

International Game Theory Review ◽

10.1142/s0219198906000813 ◽

2006 ◽

Vol 08 (01) ◽

pp. 111-126 ◽

Cited By ~ 8

Author(s):

SERGIO CURRARINI ◽

MARCO A. MARINI

Keyword(s):

Coalition Formation ◽

Sufficient Conditions ◽

Coalition Structure ◽

Strategic Complementarity ◽

Form Game ◽

Stable Coalition ◽

Unanimity Game

This paper establishes sufficient conditions for the existence of a stable coalition structure in the "coalition unanimity" game of coalition formation, first defined by Hart and Kurz (1983) and more recently studied by Yi (1997, 2003). Our conditions are defined on the strategic form game used to derive the payoffs of the game of coalition formation. We show that if no synergies are generated by the formation of coalitions, a stable coalition structure always exists provided that players are symmetric and either the game exhibits strategic complementarity or, if strategies are substitutes, the best reply functions are contractions.

Download Full-text

STABILITY AND ALLOCATION IN A THREE-PLAYER GAME

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595913400149 ◽

2013 ◽

Vol 30 (03) ◽

pp. 1340014

Author(s):

LEQIN WU ◽

XIN CHEN ◽

YE LU ◽

YA-XIANG YUAN

Keyword(s):

Cooperative Game ◽

Grand Coalition ◽

Transferable Utility ◽

Price Model ◽

Coalition Structures ◽

Novel Approach ◽

Stable Coalition ◽

Core Solution ◽

Player Game ◽

Stability Concept

We study a three-player cooperative game with transferable utility where the players may form different coalition structures. A new concept of stability of a coalition is introduced, and the existence of a stable coalition is proven. Based on this stability concept, a novel approach is given to determine sensible allocations in a grand coalition of three players. We also compare our result with classical core solution and implement our theory on a specific price model.

Download Full-text

Coalition Formation Based Staffing Strategy Development

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2012.p0430 ◽

2012 ◽

Vol 16 (3) ◽

pp. 430-435

Author(s):

Mayuko Miyata ◽

◽

Shao-Chin Sung

Keyword(s):

Staff Development ◽

Coalition Formation ◽

Sufficient Conditions ◽

Balance Of Power ◽

Theoretical Models ◽

Strategy Development ◽

Coalition Structures ◽

Staffing Strategy ◽

Hedonic Coalition Formation ◽

Stability Concepts

In this paper, we propose game theoretical models for developing staffing strategies, i.e., strategies which support managers’ decision making on hiring, head hunting, staff reassignment, and implementation of staff development policy in enterprises. Our staffing models are hedonic coalition formation games with newly proposed stability concepts calledinvitation based stabilities, in which players’ activities of changing their coalitions are motivated based on invitation from other coalitions. These stabilities capture behaviors of managers, employees, and contractors depending on the balance of power in business situations. We analyze the existence of stable coalition structures under invitation based stabilities, and provide several sufficient conditions with natural interpretations as staffing strategies.

Download Full-text

Cooperative Games with Overlapping Coalitions

Journal of Artificial Intelligence Research ◽

10.1613/jair.3075 ◽

2010 ◽

Vol 39 ◽

pp. 179-216 ◽

Cited By ~ 59

Author(s):

G. Chalkiadakis ◽

E. Elkind ◽

E. Markakis ◽

M. Polukarov ◽

N. R. Jennings

Keyword(s):

Coalition Formation ◽

Cooperative Games ◽

Cooperative Game Theory ◽

Coalition Structure ◽

Coalitional Games ◽

The Core ◽

Coalition Structures ◽

Coalition Formation Process ◽

The Social ◽

Overlapping Coalitions

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 coalitionsor 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.

Download Full-text

Testing stability properties in graphical hedonic games

Autonomous Agents and Multi-Agent Systems ◽

10.1007/s10458-021-09505-x ◽

2021 ◽

Vol 35 (2) ◽

Author(s):

Hendrik Fichtenberger ◽

Anja Rey

Keyword(s):

Time Complexity ◽

Coalition Structure ◽

Property Testing ◽

Core Stability ◽

Bounded Degree ◽

Coalition Structures ◽

Input Size ◽

Stable Coalition ◽

Hedonic Games ◽

The Stability

AbstractIn hedonic games, players form coalitions based on individual preferences over the group of players they could belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed in the literature. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stability in a model of hedonic games represented by graphs with bounded degree. In graph property testing, one shall decide whether a given input has a property (e.g., a game admits a stable coalition structure) or is far from it, i.e., one has to modify at least an $$\epsilon$$ ϵ -fraction of the input (e.g., the game’s preferences) to make it have the property. In particular, we consider verification of perfection, individual rationality, Nash stability, (contractual) individual stability, and core stability. While there is always a Nash-stable coalition structure (which also implies individually stable coalitions), we show that the existence of a perfect coalition structure is not tautological but can be tested. All our testers have one-sided error and time complexity that is independent of the input size.

Download Full-text

Common Pool Resource Management: Assessing Water Resources Planning for Hydrologically Connected Surface and Groundwater Systems

Hydrology ◽

10.3390/hydrology8010051 ◽

2021 ◽

Vol 8 (1) ◽

pp. 51

Author(s):

Francisco Muñoz-Arriola ◽

Tarik Abdel-Monem ◽

Alessandro Amaranto

Keyword(s):

Water Resources ◽

Collective Action ◽

Large Scale ◽

Integrated Management ◽

Design Principles ◽

Water Levels ◽

High Plains ◽

Common Pool Resource ◽

Common Pool ◽

Connected Surface

Common pool resource (CPR) management has the potential to overcome the collective action dilemma, defined as the tendency for individual users to exploit natural resources and contribute to a tragedy of the commons. Design principles associated with effective CPR management help to ensure that arrangements work to the mutual benefit of water users. This study contributes to current research on CPR management by examining the process of implementing integrated management planning through the lens of CPR design principles. Integrated management plans facilitate the management of a complex common pool resource, ground and surface water resources having a hydrological connection. Water governance structures were evaluated through the use of participatory methods and observed records of interannual changes in rainfall, evapotranspiration, and ground water levels across the Northern High Plains. The findings, documented in statutes, field interviews and observed hydrologic variables, point to the potential for addressing large-scale collective action dilemmas, while building on the strengths of local control and participation. The feasibility of a “bottom up” system to foster groundwater resilience was evidenced by reductions in groundwater depths of 2 m in less than a decade.

Download Full-text