Related papers: On exact capacities
We study Lindstrom quantifiers that satisfy certain closure properties which are motivated by the study of polymorphisms in the context of constraint satisfaction problems (CSP). When the algebra of polymorphisms of a finite structure B…
A strong mode of a probability measure on a normed space $X$ can be defined as a point $u$ such that the mass of the ball centred at $u$ uniformly dominates the mass of all other balls in the small-radius limit. Helin and Burger weakened…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
We consider isomorphism between the idempotent measure monad based on the maximum and the addition operations and the idempotent measure monad based on the maximum and the multiplication operations. A one of the consequences of this result…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…
The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion…
Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of…
We introduce games with probabilistic uncertainty, a natural model for controller synthesis in which the controller observes the state of the system through imprecise sensors that provide correct information about the current state with a…
Characterisations of metrizable topological spaces or metrizable uniform spaces are well known. A natural counterpart to being metrizable for topological spaces can be expressed in terms of probabilistic metrizability for approach spaces.…
We study binary coordination games with random utility played in networks. A typical equilibrium is fuzzy -- it has positive fractions of agents playing each action. The set of average behaviors that may arise in an equilibrium typically…
This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…
We introduce a new class of totally balanced cooperative TU games, namely p -additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo, 2002) and contains the class…
We show that there is an effectively closed maximal eventually different family of functions in spaces of the form $\prod_n F(n)$ for $F\colon \mathbb{N} \to \mathbb{N}\cup\{\mathbb{N}\}$ and give an exact criterion for when there exists an…
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…
The property of a normal functor to be open-multicommutative proposed by Kozhan and Zarichnyi (2004) is investigated. A number of normal functors related to the functor of probability measures and equipped with convex structure are…
We show that for a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) on a non-empty compact metrizable space $\Omega$, the existence of a affine space dense in the set of continuous functions on $\Omega$ constituted by elements…
In this paper we introduce a fuzzy version of symport/antiport membrane systems. Our fuzzy membrane systems handle possibly inexact copies of reactives and their rules are endowed with threshold functions that determine whether a rule can…