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By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…
This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…
We describe fixed points of an infinite dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values on the Cayley tree. This operator is defined by a countable set of parameters…
Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. Spatial facility location models have successfully predicted the outcome of…
The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…
According to Shapley's game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with…
Impartial subtraction games on the nonnegative integers have been studied by many and discussed in detail in for example the remarkable work Winning Ways by Conway, Berlekamp and Guy. We describe how comply variations of these games,…
In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…
This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's…
We introduce and study a new class of nonlinear monotone operators acting in normal cones of real Banach spaces and possessing the property of strong concavity. We establish new constructive principles for the existence of nonzero fixed…
We construct a saddle point in a class of zero-sum games between a stopper and a singular-controller. The underlying dynamics is a one-dimensional, time-homogeneous, singularly controlled diffusion taking values either on $\mathbb{R}$ or on…
We establish the existence of fixed points for set-valued maps defined on metric spaces and satisfying a pointwise or a local version of Banach's contraction property. As an application, we demonstrate the existence of Nash equilibrium in a…
Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…
The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…
In floppy mechanical lattices, robust edge states and bulk Weyl modes are manifestations of underlying topological invariants. To explore the universality of these phenomena independent of microscopic detail, we formulate topological…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some…
In the present paper we establish a fixed point result of Krasnoselskii type for the sum $A+B$, where $A$ and $B$ are continuous maps acting on locally convex spaces. Our results extend previous ones. We apply such results to obtain strong…