Grekos’ S function has a linear growth

• Each player has a utility function up: S → R.

We start by giving a few precise definitions. Definition 1. A n-player finite game 〈[n], (Sp)p∈[n], (up)p∈[n]〉 is formally defined as follows. • We have a set of n players [n] = {1, 2, . . . , n}. • Each player p ∈ [n] has a finite set of strategies or actions Sp. • The set S = ∏ p∈[n] Sp is the set of strategy profiles. • Each player can choose a distribution of strategies x ̃p ∈ ∆p = {xp ∈ Rp ...

The growth function of S-recognizable sets

A set X ⊆ N is S-recognizable for an abstract numeration system S if the set repS(X) of its representations is accepted by a finite automaton. We show that the growth function of an S-recognizable set is always either Θ((log(n))n ) where c, d ∈ N and f ≥ 1, or Θ(nrθΘ(nq)), where r, q ∈ Q with q ≤ 1. If the number of words of length n in the numeration language is bounded by a polynomial, then t...

THE DUALITY OF THE L?-REPRESENTATION ALGEBRA ?(S ) OF A FOUNDATION SEMIGROUP S AND FUNCTION ALGEBRAS

In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.

Bilevel Linear Programming with Thefollower ' S Ambiguous Objective Function

The Transfer Function of Generic Linear Quantum Stochastic Systems Has a Pure Cascade Realization

This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum stochastic systems. In particular, a cascade realization therefore exists for generic active linear quantum stochastic systems that require an external source o...