Related papers: Complementary cooperation, minimal winning coaliti…

Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…

Concurrent stochastic games (CSGs) are an ideal formalism for modelling probabilistic systems that feature multiple players or components with distinct objectives making concurrent, rational decisions. Examples include communication or…

LP-duality theory has played a central role in the study of cores of games, right from the early days of this notion to the present time. The classic paper of Shapley and Shubik \cite{Shapley1971assignment} introduced the "right" way of…

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…

The Shapley value is the solution concept in cooperative game theory that is most used in both theoretical as practical settings. Unfortunately, computing the Shapley value is computationally intractable in general. This paper focuses on…

This article uses data from two experimental studies of two-person Prisoner's Dilemma games [1, 2] and compares the data with the theoretic predictions calculated with the use of a quantum game theoretical method. The experimental findings…

Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…

We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is…

We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some…

In this paper the extended model of Minority game (MG), incorporating variable number of agents and therefore called Grand Canonical, is used for prediction. We proved that the best MG-based predictor is constituted by a tremendously…

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…

We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of…

A quantitative assessment of the global importance of an agent in a team is as valuable as gold for strategists, decision-makers, and sports coaches. Yet, retrieving this information is not trivial since in a cooperative task it is hard to…

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed…

We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

We study the complexity of the following problem: Given two weighted voting games G' and G'' that each contain a player p, in which of these games is p's power index value higher? We study this problem with respect to both the…

Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of…

We consider manipulations in the context of coalitional games, where a coalition aims to increase the total payoff of its members. An allocation rule is immune to coalitional manipulation if no coalition can benefit from internal…