1. EC102: Class 9
Christina Ammon

2. Game Theory - Concepts Players Actions Strategies Pay-offs Nodes
What do we assume about the information set?
An equilibrium is described in terms of strategies not in terms of pay-offs

3. Simultaneous Games
In simultaneous games no one can observe the actual strategy played by the other - less information than in a sequential game

4. Question 1 Beta’s dominant strategy is:
If Air Lion produces “high”, then Beta produces “high”, and if Air Lion produces “low”, then Beta produces “low”
Beta produces “low” no matter what Air Lion does
Beta produces “high” no matter what Air Lion does
If Air Lion produces “high”, then Beta produces “low”, and if Air Lion produces “low”, then Beta produces “high”

5. Question 1 What is a dominant strategy?
A dominant strategy is a strategy that is optimal independent of the other player’s actions.
What is a dominant strategy equilibrium ?
A dominant strategy equilibrium is where both players have a dominant strategy.

6. Question 1 Beta’s dominant strategy is:
If Air Lion produces “high”, then Beta produces “high”, and if Air Lion produces “low”, then Beta produces “low”
Beta produces “low” no matter what Air Lion does
Beta produces “high” no matter what Air Lion does
If Air Lion produces “high”, then Beta produces “low”, and if Air Lion produces “low”, then Beta produces “high”

7. Nash equilibrium vs. Perfect Equilibrium
Simultaneous games – just need the Nash condition
Nash condition: Strategies are chosen such that no player has an incentive to deviate given the other player’s strategy
=> A Nash equilibrium is an equilibrium which satisfies the Nash condition
Credibility condition: Strategies are such that no player has an incentive to deviate at any given node.
=>A (Subgame) Perfect Equilibrium is an equilibrium that satisfies both the Nash and the Credibility Condition

8. Question 2
Which of the following pairs of strategies satisfies the Nash condition?
General plays “stay out”; Liege plays “high output” no matter what General does
General plays “enter”; Liege plays “low ouput” if General play “enter” and “high output” if General plays “stay out”
Both of the above pairs of strategies

9. Finding the equilibrium in sequential games
Finding the Perfect Equilibrium: backward induction
I.e. work backwards in time
Start in the last time period and find the optimal strategy at each node
Take as given that in last period will play optimal strategies
Given these optimal strategies, what is optimal in the period before
Work backwards until period 0
Finding (all) Nash Equilibria: usually not required, just know how to check

10. Question 3
Which of the following pairs of strategies satisfies the Credibility condition?
General plays “stay out”; Liege plays “high output” no matter what General does
General plays “enter”; Liege plays “low ouput” if General play “enter” and “high output” if General plays “stay out”
Both of the above pairs of strategies

11. Question 4 Which of the following statements is correct?
Strategic investment effects arise under perfect competition
Strategic investment effects arise under monopolistic competition
Strategic investment effects arise under monopoly with blocked entry
All three previous statements are wrong

12. Question 4 What are strategic investments?
What are the requirements for anyone wanting to undertake these investments?
Non-zero profits
Entry has to be possible (though not free, as otherwise zero profits)
In which market scenario are these satisfied?

13. Question 4 Which of the following statements is correct?
Strategic investment effects arise under perfect competition
Strategic investment effects arise under monopolistic competition
Strategic investment effects arise under monopoly with blocked entry
All three previous statements are wrong

14. Question 5
Consider a penalty shoot-out with three choices for the kicker and the goalie: right, left or middle. An outcome in which each player goes right 40 per cent of the times is:
An equilibrium in pure strategies
An equilibrium in mixed strategies
Not an equilibrium in either strategies

15. Question 5 What is a mixed strategy equilibrium?
Any pure strategy equilibrium is in principle a mixed strategy equilibrium – with probability 1 assigned to one strategy, but we solve for it differently
There always exists an equilibrium in mixed strategies
How do we test if a set of strategies are an equilibrium
Look if someone has an incentive to deviate, or
Check if given the probability chosen by the other player makes the first player indifferent between all actions in expectation
Finding a mixed strategy equilibrium:
Finding the probability for each player that will make the other player indifferent between all actions
This has to be consistent across both players

16. Question 5

17. Question 5
Consider a penalty shoot-out with three choices for the kicker and the goalie: right, left or middle. An outcome in which each player goes right 40 per cent of the times is:
An equilibrium in pure strategies
An equilibrium in mixed strategies
Not an equilibrium in either strategies

18. Question 6
“I recognized that information was, in many respects, like a public good, and it was this insight that made it clear to me that it was unlikely that the private market would provide efficient resource allocations whenever information was endogenous.” (Joseph Stiglitz)

19. Question 6 What is a public good?
Non-rival
Non-excludable
“The defining characteristic of a public good is that consumption of it by one individual does not actually or potentially reduce the amount available to be consumed by another individual” (Gravelle and Rees). 
Why is a public good not efficiently allocated?
In how far is information like a public good?
Is it non-rival?
Is it non-excludable?