24 citations · 30 across the 11 of their papers we have counts for
11 papers
Paradoxical decompositions and finitary colouring rules
Robert Samuel Simon, Grzegorz Tomkowicz
We define "paradoxical colouring rule", show its relation to measure theoretic paradoxes, and demonstrate that proper vertex colouring can be a paradoxical colouring rule.
A Continuous Paradoxical Colouring Rule Using Group Action
Tugkan Batu, Robert Samuel Simon, Grzegorz Tomkowicz
Given a probability space , measure preserving transformations of , and a colour set , a colouring rule is a way to colour the space with…
Myopic equilibria, the spanning property, and subgame bundles
Robert Simon, Stanislaw Spiez, Henryk Torunczyk
For a set-valued function on a compact subset of a manifold, spanning is a topological property that implies that for interior points of . A myopic equi…
Paradoxical decompositions and finitary rules
Robert Samuel Simon, Grzegorz Tomkowicz
We colour every point x of a probability space X according to the colours of a finite list x_1, ...., x_k of points such that each of the x_i, as a function of x, is a measure pres…
A Bayesian Game without epsilon equilibria
Robert Samuel Simon, Grzegorz Tomkowicz
We present a three player Bayesian game for which there is no epsilon equilibria in Borel measurable strategies for small enough epsilon, however there are non-measurable equilibri…
A zero-sum game between a singular stochastic controller and a discretionary stopper
Daniel Hernandez-Hernandez, Robert S. Simon, Mihail Zervos
We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines…
Locally Finite Knowledge Structures
Robert Samuel Simon
In a game of incomplete information, an infinite state space can create problems. When the space is uncountably large, the strategy spaces of the players may be unwieldly, resultin…
The Common Knowledge of Formula Exclusion
Robert Samuel Simon
For every set of primitive propositions and agents there is a canonical Kripke structure and a canonical map from any Kripke structure (defined with the same primitive propositions…
A Proof of the Vieille Result Using a Kind of Discount Factor
Robert Samuel Simon
We give an alternative proof that every two-person non-zero-sum absorbing positive recursive stochastic game with finitely many states has approximate equilibria, a result proven b…
How many times can a function be iterated?
Massimo Gobbino, Robert Samuel Simon
Let C be a closed subset of a topological space X, and let f : C --> X. Let us assume that f is continuous and f(x) lies in C for every x in the boundary of C. How many times can o…
A parametrized version of the Borsuk Ulam theorem
Thomas Schick, Robert Simon, Stanislav Spiez +1
The main result of this note is a parametrized version of the Borsuk-Ulam theorem. We show that for a continuous family of Borsuk-Ulam situations, parameterized by points of a comp…