Supplementary notes on all the game theory content of T2 from EC109 microeconomics. From the uni of Warwick economics course. Achieved >75% in final exams
EC 109: Microeconomics
Topic 4: Game Theory
Decision Theory: decisions are non-strategic, since actions are independent
Game Theory: mathematical technique to analyze interdependent decision problems
Interdependent: one person’s actions affect what the other should do
- To define a game, we need:
Set of players ( N ): parties with decisions to make
Set of actions for every player i ∈ N ( Ai ): different choices available
Payoffs for every player i∈ N ( π i): outcomes for each combination of choices
A1 × A2 ×… × A n → R
Normal form:
- Present payoffs in a matrix format
N={1,2}
A1= { w , x } , A2= { y , z }
π i= A1 × A 2 → R
Action y Action z
Action w π 1 ( w , y ) , π 2 (w , y ) π 1 ( w , z ) , π 2 (w , z)
Action z π 1 ( x , y ) , π 2 (x , y ) π 1 ( x , z ) , π 2 (x , z)
A1 is the row player
A2 is the column player
- Payoffs must encode everything the players care about:
Profit
Long-run consequences of actions
Appetites for risk
Enjoyment they get from ‘hurting’ other players
- We must therefore model players as acting to maximize their payoff
- SO, game theory is not a theory of human behavior
It is a methodology that cannot be disproved by observation
Empirical content only comes in when game theory is applied
- There are three problems for players in a game:
1. Understanding the game
2. Forming expectations about what the other players will do
3. Finding the best response to what they anticipate other players doing
- Modelling task for game theorists is to:
Frame real life situations as games
Develop a solution concept for the situation they want to model
Solution concept: narrows down set of outcomes to reasonable ones
- It has two roles:
, Positive: make better predictions about how people will play (explain real behavior)
Normative: give better advice about how you should play the game
Best Response: an action a i that yields the highest payoff, given opponent’s action profile a−i
Action profile includes actions of all opponents
- Fixing a−i, what is the best a i:
¿
a i =argmax π i (a i , a−i)
ai ∈ Ai
- To form a best response, players must:
Predict what other players might do
Find their best response
Dominance
Prisoner’s Dilemma
Confess Stay Quiet
Confess −5 ,−5 0 ,−10
Stay Quiet −10 , 0 −1 ,−1
- For the row player:
Confess is a best response if they believe the column player will confess
Confess is also the best response if they believe the column player will stay quiet
- For the column player, the same is true
Dominant strategy: an action that is always a best response, no matter your opponent’s choice
Weakly dominant strategy: if all a i ' ≠ ai :
π i ( ai , a−i ) ≥ π i ( a'i ,a−i ) for all a−i
AND:
π i ( ai , a−i ) > π i ( ai ' , a−i) for some a−i
Strongly dominant strategy: if all a i ' ≠ ai :
π i ( ai , a−i ) > π i ( ai ' , a−i) for all a−i
- Not all games have dominant strategies
But if it exists, it gives strong predictive and normative advice
Dominated strategy: an action a i ' that always gives a lower payoff than a i for any a−i
- Optimal decision for individual is not necessarily the same as the optimal communal decision
Beliefs
- How do we model the way players form beliefs about what other players will do?
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller joebloggs123. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.66. You're not tied to anything after your purchase.
