Related papers: On convexity and solution concepts in cooperative …
We study the geometric structure of the set of cooperative transferable utility games having a nonempty core, characterized by Bondareva and Shapley as balanced games. We show that this set is a nonpointed polyhedral cone, and we find the…
The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e.,…
In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by…
Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…
Cooperative games can be distinguished as non-cooperative games in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When the payoffs…
We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of…
Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…
Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by…
The core of a game $v$ on $N$, which is the set of additive games $\phi$ dominating $v$ such that $\phi(N)=v(N)$, is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular…
In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation…
Cooperation and defection may be considered as two extreme responses to a social dilemma. Yet the reality is much less clear-cut. Between the two extremes lies an interval of ambivalent choices, which may be captured theoretically by means…
Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…
The concept of forming harmonious coalitions is introduced to both classical and quantum symmetric cooperative game. In both cases, players are motivated to form coalitions. Also, the main feature of the cooperative game is conserved.
Motivated by the fact that the worth of a coalition may depend on the order in which agents arrive, Nowak and Radzik (1994) (NR) introduced cooperative games with generalized characteristic functions. We study such temporal cooperative…
We study the notion of efficiency for cooperative games on simplicial complexes. In such games, the grand coalition $[n]$ may be forbidden, and, thus, it is a non-trivial problem to study the total number of payoff $v_{\Delta}$ of a…
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…
The range of a payoff function for an $n$-player finite strategic game is investigated using a novel approach, the notion of extreme points of a non-convex set. The shape of a noncooperative payoff region can be estimated using extreme…
Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…
We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…