EC102: CLASS 9
Christina Ammon
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
Simultaneous Games
 In simultaneous games no one can observe the actual
strategy played by the other - less information than in a
sequential game
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”

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.
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”

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
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
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
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
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
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?
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
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
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
a. Look if someone has an incentive to deviate, or
b. 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
Question 5
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
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)
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?