Ilya Katsev

Russian Academy of Sciences | RAS · Laboratory of game theory and making decisions

We study ratio overall evaluation criteria (user behavior quality metrics) and, in particular, average values of non-user level metrics, that are widely used in A/B testing as an important part of modern Internet companies» evaluation instruments (e.g., abandonment rate, a user»s absence time after a session). We focus on the problem of sensitivity...

The chapter introduces and analyses the Surplus Distributor-prenucleolus for TU games, a lexicographic value that satisfies core stability, strong aggregate monotonicity and null player out property in the class of balanced games. The solution is characterized in terms of balanced collection of sets and can be easily computed in the class of monoto...

We find that the answer to the open question of whether there is a continuous core solution that satisfies coalitional monotonicity in the class of convex games is yes. We prove that the SD-prenucleolus is a continuous core solution that satisfies coalitional monotonicity for convex games, a class of games widely used to model economic situations.

We introduce and characterize a new solution concept for TU games: The Surplus Distributor Prenucleolus. The new solution is a lexicographic value although it is not a weighted prenucleolus. The SD-prenucleolus satisfies core stability, strong aggregate monotonicity, null player out property in the class of balanced games and coalitional monotonici...

We consider the family of least square values for games with restricted cooperation. We prove several facts about this family and characterize the generalization of the Shapley value with the set-consistency axiom.

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems there is some hierarchical ordering of the players. In this paper we consider a class of games with a permission structure describing situations in which players in a cooperative TU-game are hierarchically order...

The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance...

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature various models of games with restricted cooperation can be found. So, instead...

A cooperative game with a permission structure describes a situation in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. In this paper we consider non-negative additive games with an acyclic permission structure. For su...

The traditional assumption in cooperative game theory is that every coalition is feasible and can form to attain its payoff. However, in many real life situations not every group of players has the opportunity to cooperate and to collect their own payoff. We say that we deal with cooperative games with restricted cooperation when not all coalitions...

A game with a restricted cooperation is a triple consisting of a finite set of players, a collection of feasible coalitions, and a characteristic function. The class of all games with a restricted cooperation with an arbitrary universal set of players is considered. The prenucleolus and the prekernel for games with a restricted cooperation are defi...

A collection of TU games solutions intermediate between the prekernel and the prenucleolus is considered. Each solution from the collection is parametrized by a positive integer k > 1 and is called the k-prekernel for properties extending those verifying by the prekernel such that the 2-prekernel coincides with the prekernel. If the number of playe...

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games wi...

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the nucleolus. A cooperative game with a permission structure d...

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the nucleolus. A cooperative game with a permission structure d...