A refinement of the concept of equilibrium in multiple objective continous games.
A repeated imitation model with dependence between stages: Decision strategies and rewards
Adversarial decision making is aimed at determining strategies to anticipate the behavior of an opponent trying to learn from our actions. One defense is to make decisions intended to confuse the opponent, although our rewards can be diminished. This idea has already been captured in an adversarial model introduced in a previous work, in which two agents separately issue responses to an unknown sequence of external inputs. Each agent's reward depends on the current input and the responses of both...
A silent duel under arbitrary moving
A silent versus partially noisy one-bullet duel under arbitrary motion
A silent-noisy versus silent duel
A silent-silent duel with randomly detected opponents
A simple proof of the minimax-theorem
A simple proof that determinacy implies Lebesgue measurability.
A solution of two-person single-suit whist.
A survey on topological games and their applications in analysis.
In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.
A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending...
A tandem version of the cops and robber game played on products of graphs
In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.
A two armed bandit type problem revisited
In Benaïm and Ben Arous (2003) is solved a multi-armed bandit problem arising in the theory of learning in games. We propose a short and elementary proof of this result based on a variant of the Kronecker lemma.
A two armed bandit type problem revisited
In Benaïm and Ben Arous (2003) is solved a multi-armed bandit problem arising in the theory of learning in games. We propose a short and elementary proof of this result based on a variant of the Kronecker lemma.
A value based on marginal contributions for multi–alternative games with restricted coalitions
This paper deals with cooperative games with players and alternatives which are called multi-alternative games. In the conventional multi-alternative games initiated by Bolger, each player can choose any alternative with equal possibilities. In actual social life, there exist situations in which players have some restrictions on their choice of alternatives. Considering such situations, we study restricted multi-alternative games. A value for a given game is proposed.
A von Neumann model with an arbitrary number of steps
A winner's mean earnings in lottery and inverse moments of the binomial distribution.
Additivities in fuzzy coalition games with side-payments
The fuzzy coalition game theory brings a more realistic tools for the mathematical modelling of the negotiation process and its results. In this paper we limit our attention to the fuzzy extension of the simple model of coalition games with side-payments, and in the frame of this model we study one of the elementary concepts of the coalition game theory, namely its “additivities”, i. e., superadditivity, subadditivity and additivity in the strict sense. In the deterministic game theory these additivites...
Additivity in general coalition-games
Algorithms for dynamic negotiation.