Related papers: On Decomposition of Solutions for Coalitional Game…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…
The nucleolus is a central solution concept in cooperative game theory. While its computation is NP-hard in general, it can be computed in polynomial time for convex games; however, the only published polynomial-time algorithm relies on the…
The model of incomplete cooperative games incorporates uncertainty into the classical model of cooperative games by considering a partial characteristic function. Thus the values for some of the coalitions are not known. The main focus of…
Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…
A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the \emph{core}--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games…
The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…
The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This…
Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…
We propose in this paper a coinvestment plan between several stakeholders of different types, namely a physical network owner, operating network nodes, e.g. a network operator or a tower company, and a set of service providers willing to…
Cooperative games are an important class of problems in game theory, where the goal is to distribute a value among a set of players who are allowed to cooperate by forming coalitions. An outcome of the game is given by an allocation vector…
This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the…
Lloyd Shapley's cooperative value allocation theory stands as a central concept in game theory, extensively utilized across various domains to distribute resources, evaluate individual contributions, and ensure fairness. The Shapley value…
We explore a broad class of values for cooperative games in characteristic function form, known as \emph{compromise values\/}. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs.…
Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings,…
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the…
We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney…
In this paper, we consider a generalization of cooperative games to the case where a coalition can distribute the earned utility not only among its members but also to other players. In particular, we consider an example where coalitions…
The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…
We study the nucleolus in a class of cooperative games where agents collaborate by sharing demands and production-distribution capacities across multiple markets. These production-distribution games form a structured subclass of linear…
Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential…