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Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…
This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and…
A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…
Fictitious Play (FP) is a simple and natural dynamic for repeated play with many applications in game theory and multi-agent reinforcement learning. It was introduced by Brown (1949,1951) and its convergence properties for two-player…
In 1964 Shapley devised a family of games for which fictitious play fails to converge to Nash equilibrium. The games are two-player non-zero-sum with 3 pure strategies per player. Shapley assumed that each player played a specific pure…
In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-Fran\c{c}ois Mertens and…
The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation…
We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…
In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of…
The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and…
Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work…
In this research, we discuss a problem of calculating the Shapley value in bankruptcy games. We show that the decision problem of computing the Shapley value in bankruptcy games is NP-complete. We also investigate the relationship between…
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class…
We study some ergodicity property of zero-sum stochastic games with a finite state space and possibly unbounded payoffs. We formulate this property in operator-theoretical terms, involving the solvability of an optimality equation for the…
Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the…
Shapley values, which were originally designed to assign attributions to individual players in coalition games, have become a commonly used approach in explainable machine learning to provide attributions to input features for black-box…
As the use of complex machine learning models continues to grow, so does the need for reliable explainability methods. One of the most popular methods for model explainability is based on Shapley values. There are two most commonly used…
We consider a weighted Shapley network design game, where selfish players choose paths in a network to minimize their cost. The cost function of each edge in the network is affine linear with respect to the sum of weights of the players who…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning…