On the logic of coalitional games (original) (raw)

2007

We define formalisms to reason about Coalitional Games (CGs), in which one can express what coalitions of agents can achieve. We start with Quantified CGs (QCGs), in which each agent has some goals he wants to satisfy, which may change over time. Then we focus on CGs themselves. Although CGs can be well analysed in a formalism close to Pauly's

Logics for Qualitative Coalitional Games

Logic Journal of IGPL, 2009

Reasoning about coalitional games

Artificial Intelligence, 2009

We develop, investigate, and compare two logic-based knowledge representation formalisms for reasoning about coalitional games. The main constructs of Coalitional Game Logic (cgl) are expressions for representing the ability of coalitions, which may be combined with expressions for representing the preferences that agents have over outcomes. Modal Coalitional Game Logic (mcgl) is a normal modal logic, in which the main construct is a modality for expressing the preferences of groups of agents. For both frameworks, we give complete axiomatisations, and show how they can be used to characterise solution concepts for coalitional games. We show that, while cgl is more expressive than mcgl, the former can only be used to reason about coalitional games with finitely many outcomes, while mcgl can be used to reason also about games with infinitely many outcomes, and is in addition more succinct. We characterise the computational complexity of satisfiability for cgl, and give a tableaux-based decision procedure.

Coalition games and alternating temporal logics

2001

We draw parallels between coalition game logics developed in , [Pauly, 2000c], and on one hand, and alternating-time temporal logics of computations introduced in [Alur et al, 97] on the other. In particular, we show equivalence of their semantics, embedding of coalition game logics into alternating-time temporal logic, and propose axiomatic systems for these logics.

A logical characterisation of qualitative coalitional games

Journal of Applied Non-Classical Logics, 2007

Qualitative coalitional games (QCGs) were introduced as abstract formal models of goal-oriented cooperative systems. A QCG is a game in which each agent is assumed to have some goal to achieve, and in which agents must typically cooperate with others in order to satisfy their goals. In this paper, we show how it is possible to reason about QCGs using Coalition Logic (CL), a formalism intended to facilitate reasoning about coalitional powers in game-like multiagent systems. We introduce a correspondence relation between QCGs and interpretations for CL, which defines the circumstances under which a CL interpretation correctly characterises a QCG. The complexity of deciding correspondence between QCGs and interpretations for CL is shown to vary from being tractable up to Π p 2 -complete, depending on the representation chosen for the QCG and interpretation. We then show how various properties and solution concepts of QCGs can be characterised as CL formula schemes. The ideas are illustrated via a detailed worked example, in which we demonstrate how a model checker can be deployed to investigate whether a particular system has the properties in question.

On a logic for coalitional games with priced-resource agents

Electronic Notes in Theoretical Computer Science, 2011

Alternating-time Temporal Logic (ATL) and Coalition Logic (CL) are well-established logical formalisms particularly suitable to model games between dynamic coalitions of agents (like e.g. the system and the environment). Recently, the ATL formalism has been extended in order to take into account boundedness of the resources needed for a task to be performed. The resulting logic, called Resource-Bounded ATL (RB-ATL), has been presented in quite a variety of scenarios. Even if the model checking problem for extensions of ATL dealing with resource bounds is usually undecidable, a model checking procedure for RB-ATL has been proposed. In this paper, we introduce a new formalism, called PRB-ATL, based on a different notion of resource bounds and we show that its model checking problem remains in EXPTIME and has a PSPACE lower bound. Then, we tackle the problem of coalition formation. How and why agents should aggregate is not a new issue and has been deeply investigated, in past and recent years, in various frameworks, as for example in algorithmic game theory, argumentation settings, and logic-based knowledge representation. We face this problem in the setting of priced resource-bounded agents with the goal specified by an ATL formula. In particular we solve the problem of determining the minimal cost coalitions of agents acting in accordance to rules expressed by a priced game arena and satisfying a given formula. We show that such problem is computationally not harder than verifying the satisfaction of the same formula with fixed coalitions.

A Logic for Coalitions with Bounded Resources

2009

Recent work on Alternating-Time Temporal Logic and Coalition Logic has allowed the expression of many interesting properties of coalitions and strategies. However there is no natural way of expressing resource requirements in these logics. This paper presents a Resource-Bounded Coalition Logic (RBCL) which has explicit representation of resource bounds in the language, and gives a complete and sound axiomatisation of RBCL.

Quantified coalition logic

Synthese, 2008

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express properties as "there exists a coalition C satisfying property P such that C can achieve ϕ". We give an axiomatization of QCL, and show that while it is no more expressive than Coalition Logic, it is exponentially more succinct. The time complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents.

Axiomatising Nash-Consistent Coalition Logic

Lecture Notes in Computer Science, 2002

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Logic for coalitions with bounded resources

Journal of Logic and Computation, 2010

On the logic of coalitional games (original) (raw)

Related papers