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This paper studies how to attain fairness in communication for omniscience, where a set of users exchange their observations of a discrete multiple random source to attain omniscience---the state that all users recover the entire source.…
The Shapley value, a solution concept from cooperative game theory, has recently been considered for both unrooted and rooted phylogenetic trees. Here, we focus on the Shapley value of unrooted trees and first revisit the so-called split…
Many environments assign several Elo ratings to the same agent: a chess player has classical, rapid, and blitz ratings; an online platform may rate by time control, mode, or format; an evaluator may rate performance across tasks or roles.…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
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…
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the…
We study strong equilibria in symmetric capacitated cost-sharing games. In these games, a graph with designated source $s$ and sink $t$ is given, and each edge is associated with some cost. Each agent chooses strategically an $s$-$t$ path,…
Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility…
We show that computing approximate stationary Markov coarse correlated equilibria (CCE) in general-sum stochastic games is computationally intractable, even when there are two players, the game is turn-based, the discount factor is an…
We introduce a two-player game involving two tokens located at points of a fixed set. The players take turns to move a token to an unoccupied point in such a way that the distance between the two tokens is decreased. Optimal strategies for…
We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…
"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…
We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The game differs from other ones in the literature on dynamic,…
This paper investigates applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for characterisation of systems with transitive competition when mutations deviate from Gibbs…
Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to…
The presence of artificial intelligence (AI) in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images,…
A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional…
We consider a multi-organizational system in which each organization contributes processors to the global pool but also jobs to be processed on the common resources. The fairness of the scheduling algorithm is essential for the stability…
Purpose: We propose a model to present a possible mechanism for obtaining sizeable behavioural structures by simulating an agent based on the evolutionary public good game with available social learning. Methods: The model considered a…
The Shapley value, originating from cooperative game theory, has been employed to define responsibility measures that quantify the contributions of database facts to obtaining a given query answer. For non-numeric queries, this is done by…