Class notes
ECO2007S notes (Competition & Cooperation/ Game theory)
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- University Of Cape Town (UCT)
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Co-operation & CompetitionGAME THEORY
ECO2007S
Module 1:
History of game theory:
- Invented in 1944 by John von Neumann and Oskar Morgenstern
- Initially, it could only be applied to pure conflict situations where one agent’s gain is
exactly another’s loss (zero-sum game)
- Thanks to work by two generations of pioneers (Nash, Selten, Aumann, Harsanyi,
Maynard Smith), by the late 1980s game theory had been developed to the point
where it became the main mathematical technology in several branches of
economics, particularly branches concerned with politics and business strategy
Chapter 1: basic ideas & examples
GAME
- Board games, card games, arcade and computer games, sports, outdoor games,
word games
- We interpret events and interactions as instances of games
STRATEGY
- It’s the mental skill /calculation needed to do well in a game
- not about luck /chance
- E.g. tennis: physical skill is developed by practicing whilst mental skill might be
knowing where to place your next shot
Game theory= the analysis/ science of interactive decision-making AND/OR the science of
rational behaviour in interactive situations. It is strategic thinking.
Examples of strategic games:
1. Prisoners Dilemma (getting the grades):
Suppose your grade in this course is
determined by a curve (40% of
students will get an A & 40% will get
a B).You have to work hard relative
to how hard everyone else works.
The class then gets together and
agrees not to work too hard. Over
time you start to change your mind
about this agreement, so you start to
study more. It turns out, so has
everyone else. So your grade is no
better than it would have been, had
everyone abided by the agreement
, 2. Flat tyre:
The weekend before their final ECO2007S exam, two students go to a party at
Stellenbosch, but they could not prepare for their Monday exam. They go to their
lecturer with the story that they got a flat tyre. The lecturer says they can write a make-
up exam on the Tuesday. On Tuesday they write the make-up exam in two separate
venues. There is only 1 question on the exam worth 100 marks: Which tyre?
The students should have looked ahead and foreseen this action by the lecturer, and
should have been prepared to answer the question
This involves looking ahead to future moves and reasoning backward to identify the
best action now
It’s not always possible to see every future move
You may resort to logically providing the tyre that it is most likely to be
But it’s important that the friends’ answers match
Therefore a convergence of expectations is needed
Focal point= a commonly-expected strategy on which players can successfully
coordinate
3. Tough lecturers:
- Students might be in need of an extension but find the lecturer to be tough in
response (despite valid reasons)
- Problem for the lecturer: determining valid excuses from questionable ones
- If the lecturer becomes known for being lenient, students may procrastinate and
hand in late
- Therefore the lecturer may choose not to accept any excuses by making a
commitment to avoid the temptation to give in
How?
- By making the commitment firm and credible
4. Game of chicken (roommate trouble)
game of chicken= 2 people drives their cars toward each other and the 1st to swerve (to
avoid the collision) is the chicken
Example:
- Suppose you and 4 friends share a house, with an agreement that you share
expenses equally
- Supplies are running out and each of you is playing the waiting game
- Usually, the most impatient housemate gives in first
This game of strategy can be viewed in two ways:
1. Each housemate has a binary choice: to go shopping or not
, B. Each housemate waits out the others
- aka War of Attrition
- Each person waits out the other (patience & tolerance)
- How close to the brink of disaster will the housemates let the situation get?
- This strategy is called Brinkmanship.
Brinkmanship=a game of escalating mutual risk.
5. Games of information:
- Manipulation of information
- E.g. the dating game:
Involves showing off your best attributes 1st
This is simultaneously being done by the other player too
One needs to identify which of their qualities are real and which are not,
while making credible signals of your own true qualities.
Signals =strategies that convey good information about you
Screening devices= strategies that induce others to act in a way that credibly reveals their
private information
Chapter 2: How to think about strategic games
Strategic game:
- there needs to be a mutual awareness of the cross-effect of the actions
- what 1 player does must affect the outcome for the other player
- If you know this (1) you can react / take actions to prevent experiencing any bad
outcomes or (2) you could take steps to alter your opponent’s future action to
ensure that you receive a good outcome
- But if you know this then so does your opponent and they will be taking similar such
actions, therefore there’s strategic interaction between players
Players in a large pool:
- E.g. A farmer’s crop production as a proportion of South Africa’s total crop
production is quite insignificant. The decision of one KZN farmer to reduce his output
would not affect the decision of a Limpopo farmer to increase his output because it’s
impersonal (there are too many participants)
- This type of interaction can become a strategic interaction with just 2+ participants
because of (1) Mutual commitments and/or (2) Private information
, A participant can be significant in the interaction if:
1. Each player is large to start with
2. Commitments / Private Info make players more important within the relationship
Mutual commitments:
- think of an impersonal scenario
- once you have chosen an individual from a larger pool of individuals, and the
agreement is clear & known by both parties, you have created a mutual commitment
- the 2 parties become tied to each other, and the relationship becomes bilateral
- Strategy comes in when you may need to influence the actions of the other player
E.g. a contract that anticipates defaulting by either participant and thus specifies a clear
future-looking plan
Private information:
- consider the market for a loan (large & impersonal market)
- since there is info available on the individual loan applicants, the risk of default is
personalized
- the borrower-lender relationship can be seen as a separate game
- The bank will seek out info on the borrower & similarly the borrower will seek to
show off their creditworthiness to the bank
Classifying games:
1. Sequential vs Simultaneous
sequential= your current action is governed by your expectation of its future consequences.
(e.g. Chess)
simultaneous= figuring out what your opponent is going to do right now; what you think
they are going to do. (e.g. rock, paper, scissors or a silent auction)
2. Conflict or cooperation
Zero Sum Game= there is a winner and a loser, one player gains, other loses out.
Non-Zero Sum= Multiple winners and losers, sum of payoff is not constant.
But it need not be zero: there could be some positive amount that players are in conflict
over, called a constant-sum game=
3. One-shot vs repeated:
Once-shot= no concern over reputation, & players do not know much about the other’s
strengths & weaknesses. Secrecy and surprise is important. Usually ruthless.
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