相关论文: Conditional Expectation of Banach Valued Correspon…

We prove some regularity properties (convexity, closedness, compactness and preservation of upper hemicontinuity) for distribution and regular conditional distribution of correspondences under the nowhere equivalence condition. We show the…

We characterize the properties of convexity, compactness and preservation of upper hemicontinuity for conditional expectations of correspondences. These results are then applied to obtain a necessary and sufficient condition for the…

We show that each of the regularity properties of regular conditional distributions of correspondences (convexity, closedness, compactness, and preservation of closed graphs) is equivalent to the condition of nowhere equivalence. This…

This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of…

We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and…

In this paper, I prove the existence of a pure-strategy Nash equilibrium for a large class of games with nonconvex strategy spaces. Specifically, if each player's strategies form a compact, connected Euclidean neighborhood retract and if…

Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…

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…

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and…

We study the existence and computation of Nash equilibria in concave games where the players' admissible strategies are subject to shared coupling constraints. Under playerwise concavity of constraints, we prove existence of Nash…

A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…

We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant…

Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…

The notion of fault tolerant Nash equilibria has been introduced as a way of studying the robustness of Nash equilibria. Under this notion, a fixed number of players are allowed to exhibit faulty behavior in which they may deviate…

We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

We provide an in-depth study of Nash equilibria in multi-objective normal form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a utility-based approach, we assume that each player's utility can be modelled with a…

In this article we study the convergence of the Nash Equilibria in a N-player differential game towards the optimal strategies in the Mean Field Games, when the dynamic of the generic player includes a reflection process which guarantees…

Game contingent claims (GCCs) generalize American contingent claims by allowing the writer to recall the option as long as it is not exercised, at the price of paying some penalty. In incomplete markets, an appealing approach is to analyze…

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…