Related papers: Game Representations and Extensions of the Shapley…
Can we predict how well a team of individuals will perform together? How should individuals be rewarded for their contributions to the team performance? Cooperative game theory gives us a powerful set of tools for answering these questions:…
The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…
The Shapley value is a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that…
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…
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by…
Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of…
Several extensions of the equal division value and the equal surplus division value to the family of games with a priori unions are proposed in Alonso-Meijide et al. (2020) ``On egalitarian values for cooperative games with a priori…
Cooperative game theory has diverse applications in contemporary artificial intelligence, including domains like interpretable machine learning, resource allocation, and collaborative decision-making. However, specifying a cooperative game…
We study the efficient computation of Shapley values for \emph{product games} -- cooperative games in which the coalition value factorizes as a product of per-player terms. Such games arise in machine learning explainability whenever the…
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.…
We consider two player quadratic games in a cooperative framework known as social value orientation, motivated by the need to account for complex interactions between humans and autonomous agents in dynamical systems. Social value…
In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a…
In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…
Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…
Measuring individual productivity (or equivalently distributing the overall productivity) in a network structure of workers displaying peer effects has been a subject of ongoing interest in many areas ranging from academia to industry. In…
The Shapley value is widely used for data valuation in data markets. However, explaining the Shapley value of an owner in a data coalition is an unexplored and challenging task. To tackle this, we formulate the problem of finding the…
We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and…