Some observations and solutions to short and long global Nim.
Some remarks about Mycielski ideals
Some remarks on equilibria in semi-Markov games
This paper is a first study of correlated equilibria in nonzero-sum semi-Markov stochastic games. We consider the expected average payoff criterion under a strong ergodicity assumption on the transition structure of the games. The main result is an extension of the correlated equilibrium theorem proven for discounted (discrete-time) Markov games in our joint paper with Raghavan. We also provide an existence result for stationary Nash equilibria in the limiting average payoff semi-Markov games with...
Some values for constant-sum and bilateral cooperative games
We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of constant-sum...
Some weak covering properties and infinite games
We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz...
Spaces defined by topological games
Spaces defined by topological games, II
Spaces related to gamma-sets
Spatial evolutionary games of interaction among generic cancer cells.
Special Issue Dedicated to Milan Bareš
Split of an Optimization Variable in Game Theory
In the present paper, a general multiobjective optimization problem is stated as a Nash game. In the nonrestrictive case of two objectives, we address the problem of the splitting of the design variable between the two players. The so-called territory splitting problem is solved by means of an allocative approach. We propose two algorithms in order to find fair allocation tables
Spreading mechanisms of cooperation for the evolutionary Prisoner's Dilemma games
We survey several mechanisms supporting the maintenance of cooperation for evolutionary Prisoner's Dilemma games. In these models players are located on the sites of a lattice or graph and they can follow one of the pure strategies: cooperation (C) or defection (D). Their total income comes from Prisoner's Dilemma games with their neighbors. We discuss the consequences of different evolutionary rules determining the time-dependence of the strategy distribution and compare the results of spreading...
Stability, bifurcation, and chaos in -firm nonlinear Cournot games.
Stability of coalition structures and imputations in coalition-games
Stability of Nash equilibria in locational games
Stackelberg solution concept for general multistage games
Stationary and convergent strategies in Choquet games
If Nonempty has a winning strategy against Empty in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows Nonempty to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits Nonempty to consider the previous move by Empty. We show that Nonempty has a stationary winning strategy for every second-countable T₁ Choquet space. More generally, Nonempty has a stationary winning strategy for...
Stationary Strategies in Topological Games
Statistische Interferenz und strategisches Spiel.
Stochastic control optimal in the Kullback sense
The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector on a sample space of dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of given are known for . Our objective is to determine the remaining conditional probability distributions of given such...