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10 NASH EQUILIBRIUM
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Contents
Index
3
Examples of Models
Subsections
10
NASH EQUILIBRIUM
1
Optimization Problems in Market Models
2
Nash Model
1
Customers of Different Taste
3
Search for Nash Equilibrium
1
Existence of Nash Equilibrium
4
Stable Coalition, Core of Games
1
Example of Server Coalition
11
WALRAS EQUILIBRIUM
1
Walras Model
2
Search for Nash Equilibrium
3
"Nash-Look-Ahead" (NLA) Equilibrium
1
First Version: NLA(p)
1
Search for NLA(p) Equilibrium
2
Second Version: NLA(p,y)
1
Search for NLA(p,y) Equilibrium
4
"Greedy-Look-Ahead" (GLA) Equilibrium
1
Search for GLA(p,y) Equilibrium
5
Monte-Carlo Simulation
1
Search for Equilibrium
2
Modeling Customers of Different Taste
3
Testing Equilibrium Conditions
4
Wiener Filter
6
Software Example
12
DIFFERENTIAL GAME
1
Introduction
2
Convex Version
3
Mixed Strategies
4
Search for Equilibrium
1
Bimatrix Game Algorithm
2
Matrix Game Algorithm
5
One-dimensional Example
6
Economic Duel. Nash Model
1
Simplified Nash Model. Static Case
2
Dynamic Nash Model
1
Search for Nash Equilibrium
7
Software Example
1
Operating Duel
2
Future Developments
13
INSPECTION MODEL
1
Bimatrix Game (BG)
1
Quadratic Bimatrix Game (QBG)
2
Poaching Game
3
Security Game
2
Search for Equilibrium
1
Direct Search Algorithm (DS)
2
Necessary and Sufficient Conditions of BG
3
Irrelevant Fraud Algorithm (IF)
1
Example-1 ( explicit solution of poaching game)
4
Quadratic Strategy Elimination Algorithm (QSE)
1
QSE and Equilibrium conditions
2
Example-2 (numerical solution of poaching game)
3
Example-3 (numerical solution of security game)
5
Preventing Corruption
1
Example-4 (corrupt inspector)
3
Matrix Game
4
Software Example
5
Future Developments
14
INVESTMENT PROBLEM
1
Introduction
2
Expected Utility
1
Investment in CD
2
Investment in CD and Stocks
3
Optimal Portfolio, Special Cases
4
Optimal Insurance
5
Utility Functions
6
Software Example
1
Running the Program
2
A Set of Utility Functions
3
Predicting Investment Results
4
Data
5
Results
6
Future Developments
7
Minimization of Road Accident Damages
1
Distribution Between Groups
2
Geographical Distribution
3
Definition of Optimal Investment
4
Dynamic Programming
1
Bellman's Equations
15
EXCHANGE RATE PREDICTION
1
Introduction
2
Auto Regressive Moving-Average Models (ARMA)
1
Definitions
2
Definition of Residuals
3
Minimization of Residuals of ARMA Models
1
Optimization of AR Parameters
2
Optimization of MA Parameters
3
Predicting "Next-Day" Rate
4
Evaluation of ARMA Prediction Errors
4
External Factors
1
Missing Data
5
Applying ARMA to External Factors
6
Auto Regressive Models (AR-ABS)
1
Definitions
2
Definition of Residuals
3
Minimization of Residuals of AR-ABS Models
4
Applying AR-ABS to External Factors
5
Applying AR models to Linear Regression (LR)
6
Simplest Illustration of AR and AR-ABS Models
7
Artificial Neural Networks Models (ANN)
1
Involving Auto Regression (AR) into ANN
8
Bilinear Models (BL)
9
Auto Regressive Fractionally Integrated
Moving Average Models (ARFIMA)
1
Definitions
2
Minimization of Residuals
3
Discussions
10
Multi-Step Predictions
11
Structural Stabilization
1
Stabilization of Structures of Time Series
2
Simple Example
3
Examples of Structural Optimization with
External Factors
12
Examples of Squared Residuals Minimization
1
Multi-Modality Examples
2
Optimization Results
13
Software Examples
1
C Version of ARMA Software (ARMAC)
1
Illustrative Example of ARMA Software: Stock Rate Prediction
2
Illustrative Example of ARMA Software: Simple Test File
2
Java version of ARMA Software (ARMAJ)
1
Users Guide
2
Illustrations
3
AR-ABS Model
4
ANN Software
14
Stock Exchange Game Model
1
Monte Carlo Algorithm
2
Nash Model
3
Prediction of Simulated Stock Rates by ARMA Model
4
Software Example
16
CALL CENTERS
1
Introduction
1
Outline
2
Assumptions, Notations, and Objectives
2
Calculation of Stationary Probabilities
3
Asymptotic Expressions
4
"Surrogate" Services
5
Call Rate Estimate
6
Optimization of Number of Servers
7
Monte Carlo Simulation (MCS)
1
Event Generation
2
Monte Carlo Errors
3
Stopping Monte Carlo
8
Common Waiting
1
Analytical Approximation: Reservation Model
2
Statistical Approximation: Monte Carlo Model
3
Call Rate Estimate
4
Testing Analytical Approximation
9
Time-Dependant Cases
1
Simple Example
10
Call Rate Predictions
1
Introduction
2
Call Rate Prediction by Scale Models
3
Expert Model, Event Scale Version
1
Definition of Special Events
2
Procedures
3
Scalar Prediction
4
Method of Least Squares
5
Vector Prediction, Event Scale Version
6
Method of Least Squares
4
Time Scale Version, Vector Prediction
1
Procedures
2
Daily Vector Prediction
3
Method of Least Squares
4
Remarks
5
Time Series Model (ARMA)
1
Scalar Prediction
2
Vector Prediction
6
Application Examples
11
Call Center Scheduling
12
Software Example
1
ARMA Model
2
Scales Model
17
OPTIMAL SCHEDULING
1
Introduction
2
Flow-Shop Problem
1
Permutation Schedule
2
Heuristics
3
Results
3
Traditional School Scheduling
1
Constraints
2
Data Structure
3
Permutation and Evaluation Algorithm
4
Running Software
4
Profiled Schools
1
Introduction
2
Schedule Representation
3
Objective Function
4
Normative Constraints
5
Convenience Constraints
6
Penalty Function
1
Normative Penalties
2
Penalties of Inconvenience
7
Defining the Initial Schedule
8
Optimization by Permutations
9
Software Example
1
Applet version
2
User Data
3
Initial Schedule
4
Optimization by Permutations
5
Servlet versions
10
Conclusions
18
SEQUENTIAL DECISIONS
1
Introduction
2
Average Utility
3
Single-Marriage Case
1
Bellman's Equations
2
Discrete Approximation
3
Including the Waiting Cost
4
Non-Linear Case
4
Multi-Marriage Case
1
" Buy-a-PC" Example
2
Bellman's Equations
1
One-Step-Ahead Approximation
5
Optimal Ordering of Supplies
1
Uncertain Demand
2
Uncertain Wholesale Price
3
Market Elasticity
6
Software Examples
1
Single "Marriage"
1
"Buy-a-Car" Version
2
Many "Marriages"
jonas mockus 2004-03-20
