Game theory is the study of strategic decision making where outcomes depend on the choices of multiple players. It originated in the 1920s and was popularized by John von Neumann. Game theory analyzes cooperative and non-cooperative games with various properties like the number of players, information available, and whether choices are simultaneous or sequential. Important concepts in game theory include Nash equilibrium, where no player can benefit by changing strategy alone, and prisoner's dilemma, where defecting dominates but collective cooperation yields higher payoffs. Game theory is now used widely in economics, politics, biology, and other fields involving interdependent actors.
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.
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.
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 - Quantitative Analysis for Decision MakingIshita Bose
WHAT IS GAME THEORY?
HISTORY OF GAME THEORY
APPLICATIONS OF GAME THEORY
KEY ELEMENTS OF A GAME
TYPES OF GAME
NASH EQUILIBRIUM (NE)
PURE STRATEGIES AND MIXED STRATEGIES
2-PLAYERS ZERO-SUM GAMES
PRISONER’S DILEMMA
Applications of game theory on event management Sameer Dhurat
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science and biology.
In this presentation ,discussed regarding Application of game theory on Event Management with the help of Prisoner's Dilemma Game
GAME THEORY
Terminology
Example : Game with Saddle point
Dominance Rules: (Theory-Example)
Arithmetic method – Example
Algebraic method - Example
Matrix method - Example
Graphical method - Example
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 - Quantitative Analysis for Decision MakingIshita Bose
WHAT IS GAME THEORY?
HISTORY OF GAME THEORY
APPLICATIONS OF GAME THEORY
KEY ELEMENTS OF A GAME
TYPES OF GAME
NASH EQUILIBRIUM (NE)
PURE STRATEGIES AND MIXED STRATEGIES
2-PLAYERS ZERO-SUM GAMES
PRISONER’S DILEMMA
Applications of game theory on event management Sameer Dhurat
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science and biology.
In this presentation ,discussed regarding Application of game theory on Event Management with the help of Prisoner's Dilemma Game
GAME THEORY
Terminology
Example : Game with Saddle point
Dominance Rules: (Theory-Example)
Arithmetic method – Example
Algebraic method - Example
Matrix method - Example
Graphical method - Example
Decision making under uncertainty rees presentationaOfer Erez
A partnership of funders invites applications for proposals to support networking of researchers from different disciplines relating to the topic of decision making under uncertainty. The theme of the call builds on some events held by the funding partners and Research Councils UK (RCUK). There is a budget of up to £750,000 to support this activity, and we expect to fund a maximum of two networks, which will include support for feasibility projects, for two years. E-Mail: ofer43211@gmail.com anatbensalmon@gmail cristalanna66@gmail.com
https://www.lucidchart.com/documents/view/396e608b-7121-4983-8774-048364368953
This connects two topics of the last few weeks. The optimal strategies to a matrix game turn out be solutions to linear programming problems. In fact, the strategies are the solutions to the primal and dual versions of the same problem!
Conflict is Human Nature and since society, organizations and associations involves more than one individual, conflict is bound to happen and in most cases subconsciously individuals adjust, tune, and adapt to accommodate other’s point of view to reduce the conflict. This is Conflict Management which is a integral process and takes place without even us knowing about it.
Students should be able to:
Use simple game theory to illustrate the interdependence that exists in oligopolistic markets
Understanding the prisoners’ dilemma and a simple two firm/two outcome model. Students should analyse the advantages/disadvantages of being a first mover
Students will not be expected to have an understanding of the Nash Equilibrium
I provide a (very) brief introduction to game theory. I have developed these notes to
provide quick access to some of the basics of game theory; mainly as an aid for students
in courses in which I assumed familiarity with game theory but did not require it as a
prerequisite
Lecture OverviewSolving the prisoner’s dilemmaInstrumental r.docxSHIVA101531
Lecture Overview
Solving the prisoner’s dilemma
Instrumental rationality
Morality & norms
Repeated games
Three ways to solve the prisoner’s dilemma
Sequential games
Backward induction
Subgame perfect Nash equilibrium
Common knowledge of rationality
Mixed strategies
Game theory: underlying assumptions
Remember:
Homo economicus: instrumental rationality and preferences
Common knowledge of rationality and consistent alignment of believes: given the same information individuals arrive at the same decisions
Individuals know the rules of the game which are exogenously given and independent of individuals’ choices
We will look at these one by one, analysing alternative assumptions.
We will use the prisoner’s dilemma as example.
Why?
Coordination game with conflict
Arguably it describes many social situations, e.g. the free rider problem:
Voting
Trade union affiliation
Wage cuts to increase profit
Domestic work
Prisoner’s dilemma
The homo economicus maximises his/her utility.
In a prisoner’s dilemma the dominant strategy is to confess (defect).
Fallacy of compositions: what is individually rational is neither Pareto optimal not socially rational.
But do people really defect?
Kant’s categorical imperative: not the outcome but the act is crucial (morality)
Altruism: blood donation
Social norms: forest people hunting in the Congo (Turnbull 1963)
Instrumental rationality
Gauthier: it is instrumentally rational to cooperate rather than to defect
Assume there are two sorts of maximisers in the economy: straight maximisers (SM) and constrained maximisers (CM); SMs defect, CMs cooperate with other CMs:
E(return from CM) = p*(-1)+(1-p)*(-3)
E(return from SM) = -3
For any p>0 the CM
strategy is better than
the SM one.
Instrumental rationality
Tit-for-tat
Unsurprisingly (maybe), in a repeated Prisoner’s dilemma the best strategy is not to defect but to adopt a tit-for-tat strategy.
In the 1980s, Robert Axelrod invited professional game theorists to enter strategies into a tournament of a repeated game (200 times).
The winning strategy was tit-for-tat entered by Anatol Rapaport:
Start off with cooperation
If opponent defects punish him/her by defecting
If opponent comes back to cooperation ‘forgive’ them and go back to cooperation
Overall, forgiving and cooperative strategies did better.
Repeated games & reputation
A tit-for-tat strategy can only be played in repeated games.
The folk theorem states that in an infinitely repeated game (or given uncertainty to the end of the game) any strategy with a feasible payoff can be an equilibrium.
This is important for social interaction: the prisoner’s dilemma can be overcome without (!) external authority.
Players enforce compliance (cooperate rather than defect) through punishment.
The loss of future returns deters players from defecting.
The surprising thing about Axelrod’s tournament was that the tit-for-tat strategy won in a finite (and defined) repeated game ...
2013.05 Games We Play: Payoffs & Chaos MonkeysAllison Miller
Expansion on application of game theory & behavioral analytics to information security and risk management. New concepts include some ideas from coalitional game theory, i.e. not just individual actors but teams.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
2. Game Theory - Introduction
The decision-making process in situations where
outcomes depend upon choices made by one or
more players.
The word "game" describes any situation
involving positive or negative outcomes
determined by the players' choices and, in some
cases, chance.
3. Game Theory - Evolution
1921 - Emile Borel, a French mathematician, published
several papers on the theory of games using poker as an
example.
1928 - John Von Neumann published his first paper on
game theory in 1928, is made it popular.
1944 – Theory of games and Economic Behavior by John
von Neumann and Oskar Morgenstern is published.
1950 – Prisoner‟s Dilemma is introduced, introducing the
dominant strategy theory.
1953 – Solution to non-cooperative games was provided
with the evolution of the Nash Equilibrium.
1970 – Extensively applied in the field of biology with the
development of „evolutionary game theory‟.
2007 – Used in almost all the fields for decision making
purposes, including the software to track down the
terrorists.
4. Game Theory - Assumptions
Each player is rational, acting in his self-interest;
The players' choices determine the outcome of
the game, but each player has only partial control
of the outcome;
Each decision maker has perfect knowledge of
the game and of his opposition;
5. Game Theory - Classification
Single Player v Multi Player Games
Co-operative v Non-Cooperative Games
Symmetric v Asymmetric Games
Zero-sum v Non-Zero-sum Games
Simultaneous v Sequential Games
Perfect Information v Imperfect Information
6. Single Player Game – Games
against Nature
The outcome and the player‟s payoff depends on both
his chosen strategy and the “choice” made by a totally
disinterested nature.
A Game Against Nature part of what is generally
called decision theory (rather than game theory)
because there is only one player who makes a
rational choice and is interested in the outcome.
7. Multi Player Games - Examples
Prisinor‟s Dilemma
Travellers‟ Dilemma
Battle of the Sexes
Diners‟ Dilemma
Rock, Paper, Scissors!!!
8. Prisoners‟ Dilemma
Both the prisoners are more likely to defect
irrespective of what the other prisoner does, even
though it gets them a sub-optimal output.
If they were allowed to communicate and reach a
consensus, then they could have reached the optimal
output.
Prisoner B stays silent Prisoner B confesses
(cooperates) (defects)
Prisoner A stays silent Prisoner A: 1 year
Each serves 1 month
(cooperates) Prisoner B: goes free
Prisoner A confesses Prisoner A: goes free
Each serves 3 months
(defects) Prisoner B: 1 year
9. Battle of the Sexes
A couple had agreed to meet in the evening but
had not agreed on the venue and cannot
communicate now.
They can either go to the opera or the football
match.
Their pay-off matrix can be Football by –
Oper given
a
Opera 3,2 1,1
Football 0,0 2,3
10. Diners‟ dilemma
It is a n-person‟s prisoners‟ dilemma.
A group of individuals go out to dine together.
They agree that they will split the cheque equally
between them.
Each individual must now decide whether to order
the cheaper dish or the expensive one.
It is presumed that the exensive dish is better
than the cheaper ones but the price differential is
not justified.
11. Diners‟ dilemma - Consequences
Each individual reasons that the expense which
they add to their bill while ordering the more
expensive item is very low.
Hence, they justify the cost to experience the
improved dining experience.
However, each individual reasons similarly, and
thus they all end up paying for a more expensive
dish.
By assumption, this is worse than each of them
ordering and paying for the cheaper dish.
12. Rock, Paper, Scissors!!!
It is a two-player zero-sum game.
No matter what a person decides, the
mathematical probability of his winning, drawing,
or losing is exactly the same.
The dominant strategy to this game seems to
exists, which is why the same person end up in
the merit roll of the championships held around
the world every year.
Child 2
rock paper Scissors
rock 0,0 -1,1 1,-1
Child 1 paper 1,-1 0,0 -1,1
scissors -1,1 1,-1 0,0
13. Travellers‟ Dilemma
Case designed by Dr. Kaushik Basu in 1994.
Each traveller can value there belongings for
anything between $2 and $100.
They will be reimbursed the lower value of the
two claims.
The lower claimant will be rewarded with
additional $2 while the higher claimant will be
charged $2.
14. Travellers‟ Dilemma - Paradox
The rational strategy for the travellers would be to
claim the lower value, i.e. $2.
In reality, people chose $100, which resulted
them in being better-off financially.
This experiment rewards people for deflecting
from the Nash Equilibrium and act non-rationally.
This has led people to question the practicality of
the game theory.
Subsequently, the idea of „super-rationality‟ was
developed under this, which stated that under
pure strategies $100 is the optimal solutioin for
the problem.
15. Strategies
Dominant Strategy – a strategy which dominates
irrespective of what the other player does.
Maximax Strategy – The player looks to maximize the
maximum pay-off that he may stand to gain from the
game.
Minimax Strategy – The player looks to maximize the
minimum payoff that he receives.
Collusion – When both players decide to co-operate to
maximise their total output.
Tit for tat – A player reacts to the opponents actions by
following it, i.e deflection followed by deflection.
Backward Induction – The player derives his strategies by
working the most likely strategy of his opponent and then
working backwards.
Markov Strategy – A strategy through which a player
decides his actions based only on his present
state, ignoring the past states.
16. Nash Equilibrium
It is a solution concept of a game involving two or
more players, in which each player is assumed to
know the equilibrium strategies of the other
players, and no player has anything to gain by
changing only his own strategy unilaterally.
If each player has chosen a strategy and no
player can benefit by changing his or her strategy
while the other players keep theirs
unchanged, then the current set of strategy
choices and the corresponding payoffs constitute
a Nash equilibrium.
It does not necessarily mean the best pay-off for
all the players involved although it might be
achieved as is the case with cartels.