scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (4) ◽  
pp. 1165-1172 ◽  
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (04) ◽  
pp. 1165-1172
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

scholarly journals An Investigation of the Optimistic Solution to the Linear Trilevel Programming Problem

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 179
Author(s):  
Maryam Esmaeili ◽  
Habibe Sadeghi
Keyword(s):  
Programming Problem ◽  
Mathematical Formulation ◽  
Optimal Solution ◽  
Feasible Region ◽  
Optimal Solutions ◽  
General Version ◽  
Numerical Example ◽  
Optimistic Solution ◽  
Different Types ◽  
The Given

In this paper, we consider a general version of a linear trilevel programming problem. Three different types of optimistic optimal solutions for a special trilevel programming problem have formerly been suggested. This paper presents the mathematical formulation of all of the three types of optimistic optimal solutions for the given linear trilevel programming problem. Moreover, some properties of the inducible region (the feasible region for the trilevel programming problem) corresponding to each optimistic optimal solution are investigated. Finally, a numerical example is presented to compare the different types of optimistic optimal solutions.

scholarly journals An Abstraction-Refinement Methodology for Reasoning about Network Games

2017 ◽  
Author(s):  
Guy Avni ◽  
Shibashis Guha ◽  
Orna Kupferman
Keyword(s):  
Nash Equilibrium ◽  
State Space ◽  
Directed Graphs ◽  
Optimal Solution ◽  
Global Optimum ◽  
Network Games ◽  
Abstraction Refinement ◽  
State Spaces ◽  
Infinite State ◽  
Special Strategy

Network games (NGs) are played on directed graphs and are extensively used in network design and analysis. Search problems for NGs include finding special strategy profiles such as a Nash equilibrium and a globally optimal solution. The networks modeled by NGs may be huge. In formal verification, abstraction has proven to be an extremely effective technique for reasoning about systems with big and even infinite state spaces. We describe an abstraction-refinement methodology for reasoning about NGs. Our methodology is based on an abstraction function that maps the state space of an NG to a much smaller state space. We search for a global optimum and a Nash equilibrium by reasoning on an under- and an over-approximation defined on top of this smaller state space. When the approximations are too coarse to find such profiles, we refine the abstraction function. Our experimental results demonstrate the efficiency of the methodology.

scholarly journals Economic Analysis of Accident Law: A New Liability Rule that Induces Socially Optimal Behaviour in Case of Limited Information

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Astha Srivastava ◽  
Ankur Srivastava
Keyword(s):  
Nash Equilibrium ◽  
Economic Analysis ◽  
Standard Of Care ◽  
Limited Information ◽  
Liability Rule ◽  
Rule Based ◽  
Liability Rules ◽  
Levels Of Care ◽  
Unique Nash Equilibrium ◽  
Optimal Behaviour

AbstractIn accident law, we seek a liability rule that will induce both the parties to adopt socially optimal levels of precaution. Economic analysis, however, shows that none of the commonly used liability rules induce both parties to adopt optimal levels, if courts have access only to ‘Limited Information’ on. In such a case, it has also been established (K. (2006). Efficiency of liability rules: a reconsideration. J. Int. Trade Econ. Dev. 15: 359–373) that no liability rule based on cost justified untaken precaution as a standard of care can be efficient. In this paper, we describe a two-step liability rule: the rule of negligence with the defence of relative negligence. We prove that this rule has a unique Nash equilibrium at socially optimal levels of care for the non-cooperative game, and therefore induces both parties to adopt socially optimal behaviour even in case of limited information.

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

Lower limb exoskeleton robots’ dynamics parameters identification based on improved beetle swarm optimization algorithm

Robotica ◽  
2022 ◽  
pp. 1-16
Author(s):  
Peng Zhang ◽  
Junxia Zhang
Keyword(s):  
Optimization Algorithm ◽  
Robot Control ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Global Optimum ◽  
Identification Accuracy ◽  
Dynamic Parameters ◽  
Dynamics Modeling ◽  
Swarm Optimization ◽  
Exoskeleton Robot

Abstract Efficient and high-precision identification of dynamic parameters is the basis of model-based robot control. Firstly, this paper designed the structure and control system of the developed lower extremity exoskeleton robot. The dynamics modeling of the exoskeleton robot is performed. The minimum parameter set of the identified parameters is determined. The dynamic model is linearized based on the parallel axis theory. Based on the beetle antennae search algorithm (BAS) and particle swarm optimization (PSO), the beetle swarm optimization algorithm (BSO) was designed and applied to the identification of dynamic parameters. The update rule of each particle originates from BAS, and there is an individual’s judgment on the environment space in each iteration. This method does not rely on the historical best solution in the PSO and the current global optimal solution of the individual particle, thereby reducing the number of iterations and improving the search speed and accuracy. Four groups of test functions with different characteristics were used to verify the performance of the proposed algorithm. Experimental results show that the BSO algorithm has a good balance between exploration and exploitation capabilities to promote the beetle to move to the global optimum. Besides, the test was carried out on the exoskeleton dynamics model. This method can obtain independent dynamic parameters and achieve ideal identification accuracy. The prediction result of torque based on the identification method is in good agreement with the ideal torque of the robot control.

scholarly journals Neutrosophic Number Optimization Models and Their Application in the Practical Production Process

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Angyan Tu ◽  
Jun Ye ◽  
Bing Wang
Keyword(s):  
Production Process ◽  
Optimal Solution ◽  
Optimization Models ◽  
Optimal Solutions ◽  
Practical Applications ◽  
Linear And Nonlinear Programming ◽  
Constrained Conditions ◽  
Minimum Objective Function ◽  
Maximum Minimum ◽  
Neutrosophic Number

In order to simplify the complex calculation and solve the difficult solution problems of neutrosophic number optimization models (NNOMs) in the practical production process, this paper presents two methods to solve NNOMs, where Matlab built-in function “fmincon()” and neutrosophic number operations (NNOs) are used in indeterminate environments. Next, the two methods are applied to linear and nonlinear programming problems with neutrosophic number information to obtain the optimal solution of the maximum/minimum objective function under the constrained conditions of practical productions by neutrosophic number optimization programming (NNOP) examples. Finally, under indeterminate environments, the fit optimal solutions of the examples can also be achieved by using some specified indeterminate scales to fulfill some specified actual requirements. The NNOP methods can obtain the feasible and flexible optimal solutions and indicate the advantage of simple calculations in practical applications.

scholarly journals Efficiency and Equilibrium in Network Games: An Experiment

2021 ◽  
pp. 1-44
Author(s):  
Edoardo Gallo ◽  
Chang Yan
Keyword(s):  
Nash Equilibrium ◽  
Network Structure ◽  
Economic Systems ◽  
Central Feature ◽  
Network Games ◽  
Trade Off ◽  
Network Game ◽  
Asymmetric Networks ◽  
Unique Nash Equilibrium

Abstract The tension between efficiency and equilibrium is a central feature of economic systems. We examine this trade-off in a network game with a unique Nash equilibrium in which agents can achieve a higher payoff by following a “collaborative norm”. Subjects establish and maintain a collaborative norm in the circle, but the norm weakens with the introduction of one hub connected to everyone in the wheel. In complex and asymmetric networks of 15 and 21 nodes, the norm disappears and subjects’ play converges to Nash. We provide evidence that subjects base their decisions on their degree, rather than the overall network structure.

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