Search results for "Stochastic Game"
showing 10 items of 43 documents
Distributed Consensus in Noncooperative Inventory Games
2009
This paper deals with repeated nonsymmetric congestion games in which the players cannot observe their payoffs at each stage. Examples of applications come from sharing facilities by multiple users. We show that these games present a unique Pareto optimal Nash equilibrium that dominates all other Nash equilibria and consequently it is also the social optimum among all equilibria, as it minimizes the sum of all the players’ costs. We assume that the players adopt a best response strategy. At each stage, they construct their belief concerning others probable behavior, and then, simultaneously make a decision by optimizing their payoff based on their beliefs. Within this context, we provide a …
Consensus in inventory games
2008
This paper studies design, convergence, stability and optimality of a distributed consensus protocol for n-player repeated non cooperative games under incomplete information. Information available to each player concerning the other players' strategies evolves in time. At each stage (time period), the players select myopically their best binary strategy on the basis of a payoff, defined on a single stage, monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in reordering or not from a common warehouse. As information evolves in time, the number of active players changes t…
Existence and Optimality of Nash Equilibria in Inventory Games
2005
Abstract This paper studies the stability and optimality of a distributed consensus protocol for n -player repeated non cooperative games under incomplete information. At each stage, the players choose binary strategies and incur in a payoff monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in whether reordering or not from a common warehouse. The authors focus on Pareto optimality as a measure of coordination of reordering strategies, proving that there exists a unique Pareto optimal Nash equilibrium that verifies certain stability conditions.
Noncooperative dynamic games for inventory applications: A consensus approach
2008
We focus on a finite horizon noncooperative dynamic game where the stage cost of a single player associated to a decision is a monotonically nonincreasing function of the total number of players making the same decision. For the single-stage version of the game, we characterize Nash equilibria and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multi-stage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately not necessarily Pareto optimal. The algorithm returns a seque…
Allocation des ressources dans l’informatique en brouillard le calcul du brouillard véhiculaire pour une utilisation optimale des véhicules électriqu…
2019
Abstract: Technological advancements made it possible for Electric vehicles (EVs) to have onboard computation, communication, storage, and sensing capabilities. Nevertheless, most of the time these EVs spend their time in parking lots, which makes onboard devices cruelly underutilized. Thus, a better management and pooling these underutilized resources together would be strongly recommended. The new aggregated resources would be useful for traffic safety applications, comfort related applications or can be used as a distributed data center. Moreover, parked vehicles might also be used as a service delivery platform to serve users. Therefore, the use of aggregated abundant resources for the …
On the qualitative analysis of the solutions of a mathematical model of social dynamics
2006
Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.
Large Networks of Dynamic Agents: Consensus under Adversarial Disturbances
2012
This paper studies interactions among homogeneous social groups within the framework of large population games. Each group is represented by a network and the behavior described by a two-player repeated game. The contribution is three-fold. Beyond the idea of providing a novel two-level model with repeated games at a lower level and population games at a higher level, we also establish a mean field equilibrium and study state feedback best-response strategies as well as worst-case adversarial disturbances in that context.
Asymptotic Hölder regularity for the ellipsoid process
2020
We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.
Commitment and choice of partner in a negotiation with a deadline
2002
This paper analyses the effects of partially revocable endogenous commitments of a seller in a negotiation with a deadline. In particular, we examine when commitment is a source of strength, a source of inefficiency and when it does not affect the bargaining outcome at all. We show that when commitment possesses a minimum amount of irrevocability this crucially determines the bargaining outcome. In the bilateral bargaining case, commitment becomes a source of inefficiency since it causes a deadline effect. In the choice of partner framework, however, the deadline effect disappears and there is an immediate agreement and, moreover, commitment becomes a source of strength since it increases t…
On the local and global regularity of tug-of-war games
2018
This thesis studies local and global regularity properties of a stochastic two-player zero-sum game called tug-of-war. In particular, we study value functions of the game locally as well as globally, that is, close to the boundaries of the game domains. Furthermore, we formulate a continuous time stochastic differential game and discuss, among other things, the equicontinuity of the families of value functions. The main motivation is to understand the properties of the games on their own right. As applications, we obtain an existence and a regularity result for a nonlinear elliptic p-Laplace type partial differential equation and a characterization of the solution to a parabolic p-Laplace typ…