Search results for "Nash equilibrium"
showing 10 items of 58 documents
Cooperative Inventory control
2005
In multi-retailer inventory control the possibility of sharing setup costs motivates communication and coordination among the retailers. We solve the problem of finding suboptimal distributed reordering policies that minimize setup, ordering, storage, and shortage costs incurred by the retailers over a finite horizon. Neuro-dynamic programming (NDP) reduces the computational complexity of the solution algorithm from exponential to polynomial on the number of retailers.
Solving Two-Person Zero-Sum Stochastic Games With Incomplete Information Using Learning Automata With Artificial Barriers
2021
Learning automata (LA) with artificially absorbing barriers was a completely new horizon of research in the 1980s (Oommen, 1986). These new machines yielded properties that were previously unknown. More recently, absorbing barriers have been introduced in continuous estimator algorithms so that the proofs could follow a martingale property, as opposed to monotonicity (Zhang et al., 2014), (Zhang et al., 2015). However, the applications of LA with artificial barriers are almost nonexistent. In that regard, this article is pioneering in that it provides effective and accurate solutions to an extremely complex application domain, namely that of solving two-person zero-sum stochastic games that…
Scheduling Domestic Shiftable Loads in Smart Grids: A Learning Automata-Based Scheme
2017
In this paper, we consider the problem of scheduling shiftable loads, over multiple users, in smart grids. We approach the problem, which is becoming increasingly pertinent in our present energy-thirsty society, using a novel distributed game-theoretic framework. From a modeling perspective, the distributed scheduling problem is formulated as a game, and in particular, a so-called “Potential” game. This game has at least one pure strategy Nash Equilibrium (NE), and we demonstrate that the NE point is a global optimal point. The solution that we propose, which is the pioneering solution that incorporates the theory of Learning Automata (LA), permits the total supplied loads to approach the p…
Quasi-nash equilibria for non-convex distributed power allocation games in cognitive radios
2013
In this paper, we consider a sensing-based spectrum sharing scenario in cognitive radio networks where the overall objective is to maximize the sum-rate of each cognitive radio user by optimizing jointly both the detection operation based on sensing and the power allocation, taking into account the influence of the sensing accuracy and the interference limitation to the primary users. The resulting optimization problem for each cognitive user is non-convex, thus leading to a non-convex game, which presents a new challenge when analyzing the equilibria of this game where each cognitive user represents a player. In order to deal with the non-convexity of the game, we use a new relaxed equilib…
Multicell power allocation method based on game theory for inter-cell interference coordination
2009
As a new technology, coordinated multipoint (CoMP) transmission is included in LTE-Advanced study item. Moreover, the network architecture in LTE-Advanced system is modified to take into account coordinated transmission. Under this background, a novel power allocation game model is established to mitigate inter-cell interference with cellular coordination. In the light of cellular cooperation relationship and centralized control in eNodeB, the power allocation in each served antenna unit aims to make signal to interference plus noise ratio (SINR) balanced among inter-cells. Through the proposed power allocation game algorithm, the users' SINR can reach the Nash equilibrium, making it feasib…
A New Distributed Optimization Approach for Solving CFD Design Problems Using Nash Game Coalition and Evolutionary Algorithms
2013
For decades, domain decomposition methods (DDM) have provided a way of solving large-scale problems by distributing the calculation over a number of processing units. In the case of shape optimization, this has been done for each new design introduced by the optimization algorithm. This sequential process introduces a bottleneck.
A Study of Nash-Evolutionary Algorithms for Reconstruction Inverse Problems in Structural Engineering
2014
In this paper we deal with solving inverse problems in structural engineering (both the reconstruction inverse problem and the fully stressed design problem are considered). We apply a game-theory based Nash-evolutionary algorithm and compare it with the standard panmictic evolutionary algorithm. The procedure performance is analyzed on a ten bar sized test case of discrete real cross-section types structural frame, where a significant increase of performance is achieved using the Nash approach, even achieving super-linear speed-up.
Nash Equilibrium in a Road Network with Many Groups of Users
2019
In this chapter concentrates on the relationships between individual and group behaviour of drivers in a road network. Such relationships are established by comparing the optimal routing of drivers (system optimum of Wardrop), the competitive drivers’ groups routing (Nash equilibrium), and the selfish drivers routing (user equilibrium of Wardrop). Thus, the boundary conditions for traffic assignment in a road network were recently obtained for the first time. Wide analytical discussion on the topic as well as a survey of relevant references are presented. Moreover, a new behavioural model of traffic assignment in case of simultaneous selfish and group behaviour of drivers in a road network …
A Domain Decomposition/Nash Equilibrium Methodology for the Solution of Direct and Inverse Problems in Fluid Dynamics with Evolutionary Algorithms
2008
The uniqueness of the subscription equilibrium with endogenous labor supply
1993
Abstract This paper presents a proof of the uniqueness of the Nash equilibrium if public goods are financed through private donations and distortionary income taxation.