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 is a managerial economics presentation on "Game Theory: Prisoners Dilemma" , presented by myself Peerzada Basim. I am a Business student pursuing IMBA degree at University of Kashmir.
I hope this presentation will suffice your need and curiosity of knowing what Game Theory is.
Thank you.
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 is a managerial economics presentation on "Game Theory: Prisoners Dilemma" , presented by myself Peerzada Basim. I am a Business student pursuing IMBA degree at University of Kashmir.
I hope this presentation will suffice your need and curiosity of knowing what Game Theory is.
Thank you.
Prisoner's Dilemma is a paradox in decision analysis in which two individuals acting in their own best interest pursue a course of action that does not result in the ideal outcome. The typical prisoner's dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant. As a result of following a purely logical thought process to help oneself, both participants find themselves in a worse state than if they had cooperated with each other in the decision-making process.
In this session, we will be looking at The Prisoner's Dilemma and how it affects our decision making, group and team dynamics, business decisions. We'll look at real world case studies and nature with a goal of understanding this dilemma better.
The Cramer-Rao Inequality provides us with a lower bound on the variance of an unbiased estimator for a parameter.
The Cramer-Rao Inequality Let X = (X1,X2,. . ., Xn) be a random sample from a distribution with d.f. f(x|θ), where θ is a scalar parameter. Under certain regularity conditions on f(x|θ), for any unbiased estimator φˆ (X) of φ (θ)
Prisoner's Dilemma is a paradox in decision analysis in which two individuals acting in their own best interest pursue a course of action that does not result in the ideal outcome. The typical prisoner's dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant. As a result of following a purely logical thought process to help oneself, both participants find themselves in a worse state than if they had cooperated with each other in the decision-making process.
In this session, we will be looking at The Prisoner's Dilemma and how it affects our decision making, group and team dynamics, business decisions. We'll look at real world case studies and nature with a goal of understanding this dilemma better.
The Cramer-Rao Inequality provides us with a lower bound on the variance of an unbiased estimator for a parameter.
The Cramer-Rao Inequality Let X = (X1,X2,. . ., Xn) be a random sample from a distribution with d.f. f(x|θ), where θ is a scalar parameter. Under certain regularity conditions on f(x|θ), for any unbiased estimator φˆ (X) of φ (θ)
How to Gain Leadership Buy-In for Your Training ProgramBizLibrary
Why is leadership buy-in important? According to Ram Charan, author of Execution: The Discipline of Getting Things Done, seventy percent of strategic failure comes from poor execution – not the actual idea – having well defined processes and leadership buy-in will be the difference between success and failure.”
Leadership support is critical to the success of a training program, but many learning and development professionals are challenged in building that bridge and actually gaining the support that is necessary.
In this session you’ll learn:
• Why leadership buy-in is critical for training and development success
• A five stage leadership buy-in maturity model - what you can expect and how to respond
• A ten step program to gain leadership support in your organization
• How to maintain leadership buy-in
• How to communicate with leadership
• How to manage change
Join Shannon Kluczny*, Vice President of Client Success at BizLibrary, for this one hour webinar. You will walk away with ideas, guides and action plans to implement. This session is perfect for anyone just starting out or struggling to make the leap.
- See more at: http://www.hr.com/en/webcasts_events/webcasts/upcoming_webcasts/how-to-gain-leadership-buy-in-for-your-training-pr_ikehhr72.html#sthash.oz5PFbij.dpuf
This section addresses some of the social dilemmas that currently affect humanity on a global scale. We will see how game theory has provided tools to study them scientifically, and how cooperation theory is looking for a way out of them.
Cooperation theory research and proposals are grouped into three major areas: strategic, institutional and motivational.
We also review some global dilemmas to understand their inner dynamics, what would have to be done to correct them, and what obstacles there are to achieving this.
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.
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
Solutions to Problem Set 2 The following note was very i.docxrafbolet0
Solution
s to Problem Set 2
The following note was very important for the solutions:
In all problems below a rational preference relation is understood as one that satisfies the axioms of
von Neumann and Morgenstern’s utility theory. When solving these problems involving the
expected utility theory use the von Neumann-Morgenstern theorem. In other words, you prove that
a preference relation is rational by showing utility values that satisfy corresponding conditions and
you prove that a preference relation is not rational by showing that no utility values can possibly
satisfy these conditions. SOLUTIONS THAT DON’T USE THIS METHOD WILL NOT BE
ACCEPTED !!!
Problem 1 (3p) Suppose you have asked your friend Peter if he prefers a sure payment of
$20 or a lottery in which he gets $15 with probability 0.5 and $10 with probability 0.5. Is it
rational for Peter to prefer the sure payment over the lottery? Is it rational to prefer the
lottery over the sure payment? Is it rational to be indifferent between the lottery and the sure
payment? Would your answer be any different had I asked you the same question but with
A substituted for $20, B for $15 and C for $10? What is the general lesson to learn from
this exercise?
SOLUTION: You can assign numbers to u($20), u($15) and u($10) in such a way that
u($20) will be larger than, or equal to, or smaller than 0.5u($15)+0.5u($10). This shows that
all three preferences are rational. If instead of $20, $15 and $10 you write A, B and C the
solution to this problem, which does not depend in any way on the specifics of the three
alternatives, should be obvious. A few general lessons here: (1) Expected utility theory,
just like preference theory, does not “impose any values” on your preferences. (2) Be
careful never to use assumptions that are not clearly stated. (3) If you are given a single
piece of information about decision maker’s preferences then no matter what this
information is it cannot be possibly irrational. Rationality is, in essence, a requirement of
consistency of preferences. If there is only one condition, what would it be possibly
inconsistent with?
Problem 2 (3p) George tells you that he prefers more money over less. George also tells
you about his preference between a lottery in which he gets $30 with probability 0.9 and 0
with probability 0.1 and a sure payment of $20. Assume that George is rational. Is it
possible for him to prefer the lottery over the sure payment? Is it possible to prefer the sure
payment over the lottery? Is it possible for him to be indifferent between the sure payment
and the lottery? What is the general lesson to learn from this exercise?
SOLUTION: Suppose you have assigned numbers to u($30), u($20) and u($0) in such a
way that u($30)>u($20)>u($0):
Can such numbers satisfy u($20) < 0.9u($30)+0.1u($0)? Yes, they can. For instance,
u($30)=1, u($20)=0.5 and u($0)=0. .
This is the first of an 8 lecture series that I presented at University of Strathclyde in 2011/2012 as part of the final year AI course.
This lecture introduces the concept of a game, and the branch of mathematics known as Game Theory.
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.
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.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
2. Concepts to Know
• Social Dilemma
• Prisoners’ Dilemma
• Public Goods Dilemma
• Commons Dilemma (‘Tragedy of the Commons’)
• Free-Riders
• Assurance/Coordination Games
• Game of Chicken
• Dominant Strategy
• Nash Equilibrium
• Matrix and Decision-Trees (how to read)
3. Social Dilemmas
(individual vs. group)
• Social dilemmas= are situations in which
individual rationality leads to collective
irrationality
4. Social Dilemmas
(individual vs. group)
• Social dilemmas
1. In other words, individually reasonable behavior
leads to a situation in which everyone is worse
off than they might have been otherwise.
2. All social dilemmas have at least one deficient
equilibrium
5. Social Dilemmas
(individual vs. group)
• Deficient Equilibrium?
– Equilibrium (plural = equilibria):
situation in which no individual
has an incentive to change their
behavior
• (Equilibrium just means balance)
– Deficient = means that there is at
least one other outcome in which
everyone is better off (examples
below)
6. Social Dilemmas
• Social Dilemmas are everywhere!
– Cleaning dorm rooms: best thing for you is other
guy to tidy up; but worst outcome is to tidy up
for other person. What do you do?
– Nuclear arms race (Prisoner’s Dilemma)
– Pollution, over-fishing, deforestation (Tragedy
of the Commons)
– Paying taxes, Pot Lucks, Charities (Public Goods
Dilemmas)
7. Types of Social Dilemmas
Social
dilemmas
Two-person
(dyadic)
Prisoner’s
Dilemma
Assurance
Game,
Coordination
Chicken
Game
N-persons
Public Goods
Dilemma
Commons
Dilemma
9. What are ‘Games?’
• Game Theory = the study of
interactive, strategic
decision making among
rational individuals.
– A ‘GAME’ in this sense is any
form of strategic interaction!
– The Key idea is that players
make decisions that affect
one another.
10. What are ‘Games?’
• Ingredients of a game:
1. The Players
2. Options (i.e. their options or
possible ‘moves’)
3. ‘Payoffs’ – the reward or
loss a player experiences
11. Describing Games
• We can describe ‘games’ in
three ways:
1. Verbally
2. Using a matrix (= table)
3. Using a Tree diagram
12. Describing Games
1. A MATRIX (table) most easily
describes a simultaneous
game (where players move at the same time,
like the game ‘rock, paper, scissors’)
– Note, however, that a matrix can
also describe a sequential game; it’s
just a little more complicated.
2. A DECISION-TREE is used to
describe a sequential game
(where players take turns).
13. Matrix Descriptions
Rock, Paper, Scissors
STEP 1: Write down the options
for both players in a table.
– Player 1 = row chooser
– Player 2 = column chooser
ROCK PAPER SCISSORS
ROCK
PAPER
SCISSORS
14. Matrix Descriptions
Rock, Paper, Scissors
STEP 2: Write down the ‘payoffs’ (i.e.
preferences) for each possible joint outcome.
– Note that there are two different payoffs!
ROCK PAPER SCISSORS
ROCK tie, tie lose, win win, lose
PAPER Win, lose tie, tie lose, win
SCISSORS lose, win win, lose tie, tie
PLAYER 1
PLAYER 2
15. Decision-trees
• Decision-trees (aka tree diagrams) are useful
depictions of situations involving sequential
turn-taking rather than simultaneous moves.
• Asking Boss for a Raise?
Employee
0,0
Boss
2, -2
-1, 0
16. Prisoners’ Dilemma
(verbal description)
• Imagine you are one of two guilty prisoners. You and your partner
in crime are being interrogated by the police, separately. You cannot
communicate with your partner. Each of you faces a choice: you can
either CONFESS (defect) or NOT CONFESS (cooperate).
• If neither of you confess, there will be insufficient evidence against
you, and you will both receive only 1 year in prison. If both of you
confess, you will each receive 5 years in prison. If you confess and
your partner does not confess, however, you do not go to prison,
but your partner goes to prison for 10 years. If, on the other hand,
you don't cooperate and confess, but your partner confesses ('rats
you out'), then your partner does not go to prison, and you go to
prison for 10 years.
• QUESTION: DO YOU CONFESS (defect) OR NOT (cooperate)? WHY,
WHY NOT? (Note: “Cooperate” here means ‘cooperate with your
partner!)
17. Prisoners’ Dilemma
(matrix form)
CONFESS
(defect)
NOT CONFESS
(cooperate)
CONFESS
(defect)
5 YRS, 5 YRS 0 YRS, 10 YRS
NOT
CONFESS
(cooperate)
10 YRS, 0 YR 1 YR, 1 YR
18. Prisoners’ Dilemma
• Another prisoner’s dilemma:
– Two students are asked to take $1 out of their wallets.
Each, in secret, decides whether to place the money in
an envelope (cooperate) or to keep the money in
one’s pocket (defect).
– Each envelope is then given to the other person, and I
double whatever money has been given, with possible
amounts given below:
cooperate defect
cooperate $2, $2 $0, $3
defect $3, $0 $1, $1
19. PRISONER’S DILEMMA
• ALL SITUATIONS WITH THE FOLLOWING
PAYOFFS ARE CALLED ‘PRISONER’S
DILEMMAS’
– DC > CC > DD > CD
COOPERATE DEFECT
COOPERATE SECOND, SECOND WORST, BEST
DEFECT BEST, WORST THIRD, THIRD
Payoffs written in RED are payoffs for player 1 (row-chooser)
Payoffs written in BLACK are payoffs for player 2 (column-chooser)
20. Assurance Games and Coordination
• ASSURANCE GAME= any situation in which mutual
cooperation leads to a better outcome than
unilateral defection.
• ‘Assurance Games’ have the following payoff order:
– CC > DC > DD > CD
COOPERATE DEFECT
COOPERATE BEST, BEST WORST, SECOND
DEFECT SECOND, WORST THIRD, THIRD
Payoffs written in RED are payoffs for player 1 (row-chooser)
Payoffs written in BLACK are payoffs for player 2 (column-chooser)
21. Assurance Games and Coordination
• EXAMPLE:
– The $100 button game (if played between two
people) would be an assurance game.
– These situations are called assurance games
because the best outcomes depend on mutual
TRUST.
22. Game: $100 Button
Pushing this button has two effects:
1. When you push your button, every other player
loses $2.
2. If you lose money because other players push
their buttons, pushing your button will cut those
losses in half.
23. Assurance Games and Coordination
• Coordination games (closely related to assurance games)
refer to situations in which the best choice to
make is the choice the other player makes.
– The potential problem is figuring out what the other
player will choose.
• Example: Which side of the road to drive on?
Left Right
Left 10, 10 0, 0
Right 0, 0 10, 10
24. Assurance Games and Coordination
• Example: Shake hands or Bow?
Shake Bow
Shake Best,
Second
Worst,
Worst
Bow Worst,
Worst
Second,
Best
25. ‘CHICKEN’
• GAME of Chicken = any situation in which mutual
defection yields worse outcome than unilateral
cooperation.
• ‘Games of Chicken’ have the following payoff order:
– DC > CC > CD > DD
COOPERATE DEFECT
COOPERATE SECOND, SECOND THIRD, BEST
DEFECT BEST, THIRD WORST, WORST
Payoffs written in RED are payoffs for player 1 (row-chooser)
Payoffs written in BLACK are payoffs for player 2 (column-chooser)
28. Public Goods Dilemma
• Public Good: any resource
which benefit everybody
regardless of whether they
have helped provide the
resource.
– Everyone has a temptation to
free-ride, i.e. to enjoy the
good without actually
contributing to it.
29. Public Goods Dilemma
• Public goods are both:
– ‘non-excludable’- it is difficult to exclude those
who don’t contribute from using it.
– ‘non-rival’- one person using it doesn’t
diminish its availability for someone else.
Example: I can enjoy a city park without paying taxes to support it.
30. Public Goods Game
• An experimental
game in which people
secretly decide to
contribute or not to a
public pot.
• The tokens in the pot
are then multiplied by
some amount, and
divided evenly to all
participants, whether
or not they
contributed.
31. Commons Dilemmas
• Tragedy of the Commons: individuals, acting
independently and rationally according to
each one's self-interest, behave contrary to
the whole group's long-term best interests by
depleting some common resource.
32. Commons Dilemma vs
Public Goods Dilemma
• Public Goods Dilemma involve the production of
a resource; Commons Dilemma involves joint use
of a resource.
• Public goods are non-rivalrous
• Common goods are rivalrous- using it diminishes
its availability for others (‘uses it up’)
34. Dominant Strategy
• In Game Theory, a player’s dominant strategy is a
choice that always leads to a higher payoff,
regardless of what the other player(s) choose.
– In the game prisoner’s dilemma, both players have a
dominant strategy. Can you determine which choice
dominates the others? (defect, or confess)
– Not all games have a dominant strategy, and games
may exist in which one player has a dominant strategy
but not the other.
35. Dominant Strategy
(PLAYER 1)
1. Assume Player 2 Cooperates (look only at first column)-
Is cooperate or defect better?
• Defect beats cooperate: BEST is better than SECOND
best.
COOPERATE DEFECT
COOPERATE SECOND WORST
DEFECT BEST THIRD
vs
2. Assume Player 2 Defects (look only at second column)-
Is cooperate or defect better?
• Defect still beats cooperate! THIRD is better than WORST!
COOPERATE DEFECT
COOPERATE SECOND WORST
DEFECT BEST THIRD
vs
IN BOTH CASES, ‘DEFECT’ IS THE BEST CHOICE AND THEREFORE A DOMINANT STRATEGY.
36. Dominant Strategy
(PLAYER 2)
1. Assume Player 1 Cooperates (look only at first row)-
Is cooperate or defect better?
• Defect beats cooperate: BEST is better than SECOND
best.
COOPERATE DEFECT
COOPERATE SECOND BEST
DEFECT WORST THIRD
2. Assume Player 2 Defects (look only at second row)-
Is cooperate or defect better?
• Defect still beats cooperate! THIRD is better than WORST!
COOPERATE DEFECT
COOPERATE SECOND BEST
DEFECT WORST THIRD
IN BOTH CASES, ‘DEFECT’ IS THE BEST CHOICE AND THEREFORE A DOMINANT STRATEGY.
37. Nash Equilibrium
• Nash Equilibrium: an outcome is a Nash
Equilibrium if no player has anything to gain by
changing only their own choice.
– In other words, a Nash Equilibrium is a situation in
which neither player can improve his position given
what the other player has chosen.
38. Nash Equilibrium
Procedure:
• Pretend you are one player (row chooser or column chooser)
• Suppose that you believe your opponent is playing Veer. Find
your best response to "Veer". In this example, your best response is
to play "Drive", because 5 > 0.
• Do the same for each of your opponent's actions
• Now pretend you are the other player. Repeat steps 2 and 3.
• For a Nash equilibrium, you need each player to be "best-responding"
to what the other player is doing. My action is my best
response to what you're doing, and your action is your best response
to what I am doing.
GAME OF CHICKEN
DRIVE VEER
(turn away)
DRIVE -200, -200 5, -2
VEER
(turn away)
-2, 5 0, 0
Editor's Notes
Public goods are ‘non-excludable’ and ‘non-rival’- one person using it doesn’t diminish its availability for someone else.
Public goods are ‘non-excludable’ and ‘non-rival’- one person using it doesn’t diminish its availability for someone else.