Microeconomics C Amine Ouazad Who am I Assistant prof at INSEAD since 2008 Teaching Prices and Markets in the MBA program Econometrics A B Microeconometrics in the PhD program Research ID: 567049
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Slide1
Bayesian Games
Microeconomics C
Amine OuazadSlide2
Who am I
Assistant prof. at INSEAD since 2008.
Teaching
Prices and Markets in the MBA
program, Econometrics A, B, Microeconometrics, in the PhD program.
Research:
Applied empirical work on Urban Economics.
Economics of Discrimination.
Banking/Competition.
Econometric Forecasts.
I tend to cold call.Slide3
Goals of my Micro C classes
Economics and psychology have a large number of common interests, but use different toolboxes.
Subjective perceptions, gender, culture.
Economics and individual rationality.
Formation of perceptions using Bayes’ framework.
Economics and strategy use very similar tools and have a large number of common interests:
Strategic interactions.
Strategic interactions with imperfect information.Slide4
Two maths
/econ tools for today
Bayes’ formula(s):
P(A)= P(A|B) P(B) + P(
A|not
B)P(not B)
E(A)= E(A|B) P(B) + E(
A|not
B) P(not B)
Risk neutrality, risk aversion:
Do you prefer : 0 with 50% chance, 10 euros with 50% chance
or
5 euros with certainty?
Risk neutral: indifferent between the two choices. What matters for your choice is the expected payoff.
Assumption throughout: players are risk neutral.Slide5
Outline
Recap on games, strategies,
and Nash
equilibria
.
Guess a number
Prisoners’ Dilemma
Perfect information
Uncertainty
Entry Game.
Basic Entry Game
With Uncertainty
Multiple
Periods
Multiple Periods with Uncertainty
Recommended Books and Papers.
Remember: “Economists do it with models”Slide6
1
. Recap on games, strategies, and Nash
Equilibria
Key concepts: Players, Strategies, Payoffs.
Simultaneous-move and sequential games.
Sequential games: Nash Equilibrium by backward induction.
Simultaneous move game: 1. Nash Equilibrium by finding mutual best responses. 2. Nash equilibrium by finding strategies where no player has an incentive to deviate unilaterally.
Typical games:
The prisoner’s dilemma.
The battle of the sexes.Slide7
2. Guess a number
Each person gives me a number between 0 and 100.
The person who is closest to 2/3 of the average gets a bottle of champagne.
Number?
What’s the reasoning?
Typical outcomes?Slide8
2. Guess a number
The Bayesian Approach
Assumption of perfect rationality is not consistent with the empirical observations…
Assume that players are of one of two types: either rational or random.
The random players choose a number between 0 and 100 randomly.
What should be the choice of the rational players?
Note first that all rational players will choose the same number.
Call this number x.
Then we use Bayes’ formula.
E(numbers) = E(
numbers|rational
players). P(rational players) + E(
numbers|random
players).P(random player).
Solution? Slide9
2. Guess a number
Another approach to the problem.
“Iterated Elimination of Dominated Strategies”
Anyone playing a number between 67 and 100?
Anyone playing a number between 44 and 100?
Etc…
What is the number left?
But is everybody thinking so deeply?
(Nagel, 2002)
Can we explain our empirical results in the MBA classroom? What is students’ depth of thinking?Slide10
3. Prisoners’ Dilemma
Example #1: Prisoners.
Example #2: Price Competition.Slide11
Example #1: Prisoners.
Roadmap
Players, Strategies, and Payoffs.
Write the payoff matrix.
Are there dominant strategies?
What is the Nash equilibrium?
Where is the uncertainty?
Write the payoff matrix(
ces
) with uncertainty.
What is one Bayesian Nash equilibrium?
2. Prisoners’ DilemmaSlide12
Prisoners
Confess/Not Confess
Simultaneous or sequential move game?
Dominant strategy? Weakly dominant strategy?
Nash equilibrium?
Jim/John
Not
Confess
Confess
Not Confess
-2,-2
-8,0
Confess
0,-8
-5,-5Slide13
Prisoners
The psychology of the game is essential.
How does that affect the game?
Players’
types?
Players’ beliefs?
The psychological cost of confessing. If both players have a cost of confessing:
Jim/John
Not
Confess
Confess
Not Confess
-2,-2
-8,0
Confess
0,-8
-5,-5
Jim/John
Not
Confess
Confess
Not Confess
-2,-2
-8,0
-c
Confess
0
-c
,-8
-5
-c
,-5
-cSlide14
Golden BallsSlide15
Bayesian game:
Types,
Beliefs
,
Strategies
,
Payoffs
.
Type is either {
high cost c,low cost c
}.
Beliefs
about the other player’s type are represented by the subjective probability of being of a high cost c of deviation/low cost.
Simultaneous move game.
Strategy:
one action for each type.
Payoffs:
the payoff matrix for each pair of types of players.Slide16
Bayesian Nash equilibrium
is a strategy for each player, for each type, such that:
each player’s strategy is a best response to the other player’s strategy
given
(a) his beliefs about the other player’s type and
(b) given the other player’s strategy for each type.Slide17
We check that the following is a Bayesian Nash equilibrium:
The high cost of deviation player does not confess.
The low cost of deviation player confesses.
Checking this is an equilibrium:
What is Jim’s best response?
when he is of a high cost of confessing?
w
hen he is of a low cost of confessing?
… and when he believes that John is of a high cost with probability p.
… and when he assumes the above strategy (blue box) for John.
Same question for John.
What fraction of games see both players cooperating?
Bayesian Nash equilibriumSlide18
Key concepts for this session (1/2)
Simultaneous move games with imperfect information.
Players, Strategies, Payoffs.
Beliefs, Types.
Bayesian Nash Equilibrium.Slide19
Example #2: Price competition.
Airline pricing.
Capacity Constraints?
Players, Strategies, Payoffs.
Write the Payoff Matrix.
Are there dominant strategies?
What is the Nash equilibrium?
Where could be the uncertainty?
3
. Prisoners’ DilemmaSlide20
Price competition:
Tiger vs. Singapore Airlines
Singapore
Airlines/Tiger
High price
Low
price
High price
$3600,$3600
0,$5200
Low price
$5200,0
$2600,$2600
Flight at 10am on January 23
rd
At 4pm the previous day… what should the Tiger and Singapore Airlines pricing people display
o
n the website? Two pricing points: $200 or $150.
Demand for seats: 40.
Marginal cost: $20 per seat.
Airline with the lowest price sells 40 seats.
If equal prices: customers indifferent between the two airlines.Slide21
What if… Tiger does not have 40 empty seats?
If Tiger only has 10 seats unbooked…
When both set the same price, Singapore sells 30 seats, Tiger sells 10 seats. (Total demand is 40).
Singapore
Airlines
/Tiger
High price
Low
price
High price
$5400,$1800
$5400,$1300
Low price
$5200,$0
$3900,$1300Slide22
Singapore Airlines does not know for sure Tiger’s remaining capacity
Tiger can be of one of two types. Either Unconstrained, or Constrained
Prior p=P(Constrained).
Singapore’s capacity is common knowledge.
Check whether the following is a Bayesian Nash equilibrium:
The unconstrained Tiger Airways deviates, the constrained Tiger Airways does not deviate; Singapore Airlines does not deviate.
“deviate”=“sets a low price.”
Under what constraint on p is this a Bayesian Nash equilibrium?Slide23
4. Entry Game
Example #1: The
f
latmate
.
Example #2: Apple
vs
Samsung.
Roadmap for this section
Write the
s
equential game.
What is the subgame perfect Nash equilibrium?
Where is the uncertainty?
Consider the game with no uncertainty, repeated multiple times. What is the subgame perfect Nash equilibrium?
What about uncertainty with multiple periods?
Takeaways?Slide24
Apple vs
Samsung
Rivals: Handsets are (imperfect) substitutes in the eyes of consumers.
Entrant and incumbent?
Fighting against the entrant?
Cost of fighting?
Benefit of fighting?Slide25
“A little less Samsung in Apple sourcing.”
Beyondbrics
, Financial Times, Sep 10, 2012.
“Trade Judge backs Apple in Samsung fight.”
Oct 24, Financial Times.
“Tension on Display: Samsung may end Dwindling LCD Panel Deal with Apple.” Wall Street Journal, Oct 22, 2012.
“Samsung, Apple, amass 4G Patents for Battle,” Wall Street Journal, Sep 12, 2012.
"I'm willing to go thermonuclear war on
this“
-- Steve Jobs Slide26
Entry deterrence
Predatory pricing.
Walmart
.
But
Increases in output (commodity markets, close substitutes).
Lawsuits.
Apple
vs
Samsung.Slide27
Entry Game, “Soft” Incumbent
Discuss the payoffs. Give at least 2 examples of market competition to which this sequential game may apply.
Notice the order of the payoffs. The first mover comes first.
What is the subgame perfect Nash equilibrium?
Entrant
Incumbent
(0,10)
(-5,4)
Stay out
Enter
Accommodate
Fight
(5,5)Slide28
Entry Game, “Tough” Incumbent
What is the subgame perfect Nash equilibrium? Such an equilibrium justifies talking about a “tough” incumbent.
Entrant
Incumbent
(0,10)
(-5,6)
Stay out
Enter
Accommodate
Fight
(5,5)Slide29
What if we don’t know the incumbent’s type?
Prior about the incumbent.
We represent this prior with a probability p: The entrant believes that the incumbent is tough with probability p.\
Fill in the payoffs below.
When does the entrant choose to enter? When does he choose to stay out?
Entrant
Incumbent
( , )
( , )
Stay out
Enter
Accommodate
Fight
( , )Slide30
Playing the entry game twice…
knowing that the incumbent is soft.
Would the incumbent fight?
Entrant
Incumbent
Stay out
Enter
Accommodate
Fight
Entrant
Incumbent
Stay out
Enter
Accommodate
Fight
Round 1
Round 2
(0,10)
(-5,4)
(5,5)
(0,10)
(-5,4)
(5,5)Slide31
Playing the entry game twice…
knowing that the incumbent is tough.
Would the incumbent fight?
Entrant
Incumbent
Stay out
Enter
Accommodate
Fight
Entrant
Incumbent
Stay out
Enter
Accommodate
Fight
Round 1
Round 2
(0,10)
(-5,6)
(5,5)
(0,10)
(-5,6)
(5,5)Slide32
Playing the entry game twice…
not knowing the incumbent’s type.
Would the incumbent fight?
What information does the fight (or not fighting) give?
Entrant 1
Incumbent
Stay out
Enter
Accommodate
Fight
Entrant 2
Incumbent
Stay out
Enter
Accommodate
Fight
Round 1
Round 2
( , )
( , )
( , )
( , )
( , )
( , )Slide33
Reputation management
Fighting tells potential entrants that you are either tough or a soft guy trying to build his reputation.
Accommodating tells potential entrants that you are
soft with certainty.
➭One discordant piece of information is enough to destroy one’s reputation.
“it takes a lifetime to build a reputation and one second to destroy it.” Warren Buffett and many other “wise” guys.Slide34
The tough incumbent fights in every period.
The soft incumbent fights if…
The cost of fighting is smaller than the benefits of building a reputation.
What is this cost of fighting?
What is the benefit of having a reputation?
With a discount factor?
What is the meaning of the discount factor?
Playing the entry game twice…
not knowing the incumbent’s type.Slide35
Perfect Bayesian Nash Equilibrium
Pooling equilibrium:
Tough and soft incumbents fight in the first period.
Soft incumbents find it rational to fight in the first period.
Separating equilibrium:
Tough incumbents fight.
Soft incumbents accommodate.
Soft incumbents do not find it rational to fight in the first period.
All types play the same strategy.
Observing the actions does not bring information on the types.
Different types play different strategies.
Observing the actions gives information about types.Slide36
Playing the Entry game n times… not knowing the incumbent’s type.
When there are k periods (think years, quarters), the reputational benefits are multiplied by k (if discount factor is 1), so the earlier the entry, the larger the reputational benefits of fighting.
Confident of being present in the market for a large number of years/quarters?
The longer the time horizon, the more important
r
eputation is.
Solve this with 3 periods.Slide37
Key concepts for this session (2/2)
Sequential games with imperfect information.
Players, Strategies, Payoffs.
Beliefs, Types.
Perfect Bayesian equilibrium.
In a Perfect Bayesian equilibrium, players “update” their beliefs according to Bayes rule.Slide38
5
. Recommended Books and Chapters
Strategic Thinking
Dixit and
Nalebuff’s
“The Art of Strategy”
and “Thinking Strategically.”
David
Besanko’s
“Economics of Strategy.”
More than Strategic Thinking
“The Armchair Economist.”
“The Undercover Economist.” Slide39
Key concepts for this session (1/2)
Simultaneous move games with imperfect information.
Players, Strategies, Payoffs.
Beliefs, Types.
Bayesian Nash Equilibrium.
Make sure you know the meaning of these concepts.Slide40
Key concepts for this session (2/2)
Sequential games with imperfect information.
Players, Strategies, Payoffs.
Beliefs, Types.
Perfect Bayesian equilibrium.
Make sure you know the meaning of these concepts.