This presentation about game theory particularly two players zero sum game for under graduate students in engineering program. It is part of operations research subject.
GAME THEORY
Terminology
Example : Game with Saddle point
Dominance Rules: (Theory-Example)
Arithmetic method – Example
Algebraic method - Example
Matrix method - Example
Graphical method - Example
This presentation is an attempt to introduce Game Theory in one session. It's suitable for undergraduates. In practice, it's best used as a taster since only a portion of the material can be covered in an hour - topics can be chosen according to the interests of the class.
The main reference source used was 'Games, Theory and Applications' by L.C.Thomas. Further notes available at: http://bit.ly/nW6ULD
This presentation about game theory particularly two players zero sum game for under graduate students in engineering program. It is part of operations research subject.
GAME THEORY
Terminology
Example : Game with Saddle point
Dominance Rules: (Theory-Example)
Arithmetic method – Example
Algebraic method - Example
Matrix method - Example
Graphical method - Example
This presentation is an attempt to introduce Game Theory in one session. It's suitable for undergraduates. In practice, it's best used as a taster since only a portion of the material can be covered in an hour - topics can be chosen according to the interests of the class.
The main reference source used was 'Games, Theory and Applications' by L.C.Thomas. Further notes available at: http://bit.ly/nW6ULD
Game theory is the study of mathematical models of strategic interaction between rational decision-makers.The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern (1944). For reasons to be discussed later, limitations in their mathematical framework initially made the theory applicable only under special and limited conditions.Increasingly, companies are utilizing the science of Game Theory to help them make high risk/high reward strategic decisions in highly competitive markets and situations. ... Said another way, each decision maker is a player in the game of business.
Game theory is the study of mathematical models of strategic interaction between rational decision-makers.The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern (1944). For reasons to be discussed later, limitations in their mathematical framework initially made the theory applicable only under special and limited conditions.Increasingly, companies are utilizing the science of Game Theory to help them make high risk/high reward strategic decisions in highly competitive markets and situations. ... Said another way, each decision maker is a player in the game of business.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
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• Remote control system for accessing CCR and allied system over serial or TCP.
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Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
2. Definition of game theory
• The branch of mathematics concerned with
the analysis of strategies for dealing with
competitive situations where the outcome of
a participant’s choice of action depends
critically on the actions of other participants.
Game theory has been applied to contexts in
war, business, and biology.
3. Terms Used in Game theory
• Number of Players
• How many players are there?
• If a game involves only two players (competitors), then it
is called a two-person game. However, if the number of
players is more, the game is referred to as n-person game.
• Strategies The strategy for a player is the list of all possible
actions (moves or courses of action) that he will take for every
payoff (outcome) that might arise. It is assumed that the
rules governing the choices are known in advance to the
players.
4. • Payoffs are the consequences for each player
for every possible profile of strategy choices
for all players.
• Zero-sum (or constant-sum) game : one player's
winnings are the others' losses, so the net gain is
zero across all players
• Optimal Strategy The particular strategy by which
a player optimises his gains or losses without
knowing the competitor's strategies.
• Value of game The expected outcome per play
when players follow their optimal strategy.
5. Assumptions of the Game theory
• Each player has available to him a finite
number of possible strategies (courses of
action). The list may not be same for each
player.
• Player A attempts to maximize gains and
player B minimise losses.
• The decision of both players are made
individually prior to the play with no
communication between them.
6. • The decisions are made simultaneously and
also announced simultaneously so that
neither player has an advantage resulting from
direct knowledge of the other player’s
decision.
• Both the players know not only possible
payoffs to themselves but also of each other.
7. Note
• By convention, the payoff table for the player
whose strategies are represented by rows (say
player A) is constructed.
8. Types of Strategies
• Pure Strategy It is the decision rule which is
always used by the player to select the
particular strategy. Thus, each player knows in
advance of all strategies out of which he
always selects only one particular strategy
regardless of the other player’s strategy, and
the objective of the player is to maximize
profit or minimize losses.
9. • Mixed strategy Courses of action that are to
be selected on a particular occasion with
some fixed probability are called mixed
strategies.
10. Pure Strategy
• Maximin – minimax principle
• Maximin Criterion: The player who is
maximizing his outcome or payoff finds out his
minimum gains from each strategy (course of
action) and selects the maximum value out of
these minimum gains.
• Minimax Criterion: In this criterion the
minimizing player determines the maximum
loss from each strategy and then selects with
minimum loss out of the maximum loss list.
11. Example 1
Player
A
Player B
B1 B2 B3
A1
A2
-1 2 -2
6 4 -6
For the game with payoff matrix:
Determine the best strategies for
players A and B. Also determine the
value of game. Is this game (i) fair?
(ii) strictly determinable?
12. Example 1
Player A Player B
B1 B2 B3
Row Minimum
A1
A2
-1 2 -2
6 4 -6
-2
-6
Column Maximum 6 4 -2
Maximin
Minimax
Player A adopts A1 strategy.
Player B adopts B3 strategy.
Value of game V = -2
Not fair but strictly determinable.
13. Saddle Point or Equilibrium Point
• In a payoff matrix the value, which is the
smallest in its row and the largest in the
column, is called the saddle point.
14. Example 2
• A company management and the labour union
are negotiating a new three year settlement.
Each of these has 4 strategies:
(i) Hard and aggressive bargaining
(ii) Reasoning and negotiating approach
(iii)Legalistic strategy
(iv)Conciliatory approach
15. • The cost to the company are given for every
pair of strategy choice
Union Strategies
Company Strategies
I II III IV
I
II
III
IV
20 15 12 35
25 14 8 10
40 2 10 5
-5 4 11 0
What strategy will the two
sides adopt? Also determine
the value of the game.
16. Union Strategies
Company Strategies
I II III IV
I
II
III
IV
20 15 12 35
25 14 8 10
40 2 10 5
-5 4 11 0
Union Strategies
Company Strategies
I II III IV
I
II
III
IV
20 15 12 35
25 14 8 10
40 2 10 5
-5 4 11 0
The company will adopt strategy III
And union will always adopt strategy I.
Value of game V = 12
17. Mixed Strategies
• A method of playing a matrix game in which
the player attaches a probability weight to
each of the possible options, the probability
weights being nonnegative numbers whose
sum is unity, and then operates a chance
device that chooses among the options with
probabilities equal to the corresponding
weights.
18. 1. Odds Method (2X2 matrix)
• If payoff matrix for player A is given by
The following formulae are used to find the
value of game and optimal strategies:
Player A
Player B
B1 B2
A1
A2
a11 a12
a21 a22
20. Example 2
• Two players A and B are involved in a game of
matching coins. When there are both heads,
player A wins 100 points and wins 0 when
there are two tails. When there is one head
and one tail, B wins 50 points. Determine the
payoff matrix, the best strategy for both
players A and B. Find the value of game to A.
21. Player A
Player B
H T
Odds
H
T
100 -50
-50 0
50
150
Odds 50 150
Value V = {100 (50) + (-50)(150)} / {(-50) + (150)}
= -12.5
Prob. of A selecting strategy H = 50/200 = 1/4
Prob. of A selecting strategy T = 150/200 = 3/4
Prob. of B selecting strategy H = 50/200 = 1/4
Prob. of B selecting strategy T = 150/200 = 3/4
22. Dominance Method
• Rule 1. If all the elements in a row (say ith
row) of a payoff matrix are less than or equal
to the corresponding elements of the other
row (say jth row) then the player A will never
choose the ith strategy or in other words the
ith strategy is dominated by the jth strategy.
23. • Rule 2. If all the elements in a column (say rth
column) of a payoff matrix are greater than or
equal to the corresponding elements of the
other column (say sth column) then the player
B will never choose the rth strategy or in other
words the rth strategy is dominated by the sth
strategy.
• Rule 3. A pure strategy may be dominated if it
is inferior to average of two or more other
pure stategies.
24. Example 3
• Reduce the following game by dominance
method and find the game value:
Player B
Player A
I II III IV
I 3 2 4 0
II 3 4 2 4
III 4 2 4 0
IV 0 4 0 8
25. Example 4
• Using the dominance probability, obtain the
optimal strategies for both the players and
determine the value of the game. The payoff
matrix for player A is given
Player B
Player A
I II III IV V
I 2 4 3 8 4
II 5 6 3 7 8
III 6 7 9 8 7
IV 4 2 8 4 3
26. Graphic Method (mX2 or 2Xn)
Example 5. Solve the game with payoff matrix
Player A
Player B
B1 B2 B3
A1
A2
1 2 0
0 -2 2
28. Example 6
Solve the following game graphically.
A
B
1 2 3 4 5
1
2
-5 5 0 -1 8
8 -4 -1 6 -5
29. Example 7
• Solve the game graphically where payoff
matrix for player A has been prepared:
Player B
Player A
A1 A2 A3 A4 A5
B1
B2
1 5 -7 4 2
2 4 9 -3 1