Summary
ECO2007 - Game Theory Full Summary
- Course
- Economics
- Institution
- University Of Cape Town (UCT)
These notes contain in-detail and in-depth comprehensive notes of the entire Game Theory course.
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ECO2007SGAME THEORY ( Module 2.1)
Applications:
- Decisions about companies
- Methods to avoid mutually destructive price-wars
- Pricing decisions
- Politics
Examples:
1. GETTING THE GRADES
Course mark determined by a curve
(40% get an A, 40% get a B)
You work hard relative to how hard others work
The class colludes to not work hard
You then secretly work hard to do well, but everyone also does so your mark stays the same
PRISONERS DILLEMMA
B
CONFESS REMAIN SILENT
A CONFESS 5 Years 5 Years 0 Years 20 Years
REMAIN SILENT 20 Years 0 Years 1 Year 1 Year
- If you confess first, you get a good deal ( Less Years )
2. FLAT TYRE
Two students don’t study for an exam and ask for a rewrite because they got a “flat tyre”
Lecturer separates them for the rewrite and asks, “which tyre?”
Students should have foreseen this and planned ahead
The students answers must match : A CONVERGANCE OF EXPECTATIONS needed
Focal point: Common expected strategy where players can successfully coordinate
3. ROOMMATE TROUBLE:
2 Friends in a room need to do a supply run but neither are willing
Each friend can:
, Housemate
Shop Stay Home
You Shop Waste Your worst
Stay Home Your best Chaos
Each player waits the other out: War of Attrition
Which is why this strategy is called Brinkmanship: a game of escalating mutual risk
4. GAMES OF INFORMATION
Manipulation of information
E.g., The Dating Game
Where you show off your best attributes which is done simultaneously by each player
You must determine which is real or fake
Screening devices: are strategies that induce others to act in a way that credibly reveals their private
information
Signals: are strategies that convey good information about you
STRATEGIC GAMES
Game:
- Board games, card games, etc
Strategy:
- Is not about luck or chance
- Is the mental skill or calculation needed to do well in a game
- E.g., Tennis, where skill is needed
GAME THEORY IS STRATEGIC THINKING
You can think strategically about your interactions with others
• But the other players in the interaction are doing the same thinking at the same time as you ∴You
must consider their thinking, just as they are considering your thinking
• So, we can say that Game Theory is…
the analysis or science of interactive decision-making
the science of rational strategic game
,in interactive situations
What is a strategic game?
- For strategic game to be present, there must be a mutual awareness of the cross effect of
the actions
- (What one player does must affect the outcome for the other player)
CLASSIFYING GAMES
1. Sequential vs Simultaneous Moves
2. Conflict or Cooperation
Most known games have a winner or loser
This is called a Zero-Sum game
When players interests are in conflict
If its not zero, there could be a positive amount that players are in conflict
over – Constant-sum game
3. One shot vs Repeated
One shot:
Have no repercussions on other games
Have no repercussions with other players who could learn about your strengths or
weaknesses
This also means that it tends to be ruthless as you won’t see them again
Secrecy and surprise
, Repeated games:
In repeated games with ongoing relationships, there is opportunity to build reputations and
learn about each other
You get to know your opponent
Over time, you can both mutually exploit each other
TYPES OF INFORMATION
External uncertainty: Uncertainty about external circumstances (weather or unanticipated shock)
Strategic uncertainty: Uncertainty about what kind of moves your opponent has made in the past or
is currently making
If the game does not have external or strategic uncertainty, the game is one of perfect information.
Otherwise, the game has imperfect information
There are also instances where a player knows more than another player does, which is called
incomplete or asymmetric information
With information, you need to be selective about releasing it
Sometimes, it can benefit you to release good information earlier. Will he believe you?
You have an incentive to exaggerate or lie and your opponent knows this
The more informed player will send out signals, which are actions that sever as credible
proof of your information
The less informed player will need to do some screening using screening devices to get you
to credibly reveal your information
COOPERATIVE NON-COOPERATIVE
Games in which joint-action agreements are Games in which enforcement is not possible,
enforceable and individual participants are allowed to act in
their own interests
Since many strategic interactions include a cooperative component, there’s an incentive for
players to get together and reach an agreement.
But with this comes an incentive to cheat
Does one player get a better outcome if he/she goes against the agreement?
And if both players know this, why stick to the agreement at all?
E
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