A biased roulette
A characterization of evolutionarily stable strategies.
A game of composing binary relations
A gradient-type algorithm for the numerical solution of two-player zero-sum differential game problems
A probabilistic approach to automaton-environment systems
An extended view of the Chu-construction.
An infinite solitaire game with a random strategy
Boolean games – Classifying strategies and omitting cardinality assumptions
Calcul des probabilités et modélisation.
Conway's Games and Some of their Basic Properties
We formulate a few basic concepts of J. H. Conway's theory of games based on his book [6]. This is a first step towards formalizing Conway's theory of numbers into Mizar, which is an approach to proving the existence of a FIELD (i.e., a proper class that satisfies the axioms of a real-closed field) that includes the reals and ordinals, thus providing a uniform, independent and simple approach to these two constructions that does not go via the rational numbers and hence does for example not need...
Détermination des jeux boréliens et problèmes logiques associés
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.
Exercices de mathématiques générales
Hercules and Hydra
Hercules and Hydra, a game on rooted finite trees
Hercules versus Hidden Hydra Helper
L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a “short” strategy (he wins in a primitively recursive number of moves) and also a “long” strategy (the finiteness of the game cannot be proved in Peano Arithmetic). We investigate the conflict of the “short” and “long” intentions (a problem suggested by J. Nešetřil). After each move of Hercules (trying to kill Hydra fast)...
Infinite games and singular sets
Information and the Bayesian-Nash equilibrium in a game with incomplete information.
Linear time-optimal control problem with incomplete information about state. Optimization of guaranteed result