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# Economics of pricing and decision making. (Lecture 1)

## 1. ECONOMICS OF PRICING AND DECISION MAKING

Lecture 1## 2. What makes a business successful?

2What makes a business

successful?

Providing a service that customers like

Building partnerships

Being ahead of competitors

Building brand value

...“Interactions”

with customers, suppliers, competitors, regulators, people within

the firm...

## 3. What is game theory?

3...a collection of tools for predicting outcomes of a group of

interacting agents

... a bag of analytical tools designed to help us understand

the phenomena that we observe when decision makers

interact (Osborne and Rubinstein)

...the study of mathematical models of conflict and

cooperation between intelligent rational decision makers

(Myerson)

## 4. What is game theory?

4Study of interactions between parties (e.g. individuals,

firms)

Helps us understand situations in which decision

makers interact: strategies & likely outcome

Game theory consists of a series of models, often

technical as well as intuitive

The models predict how parties are likely to behave in

certain situations

## 5. The Game: Strategic Environment

5The Game:

Strategic Environment

Players

Actions:

Choices available to the players

Strategies

Everyone who has an effect on your earnings (payoff)

Define a plan of action for every contingency

Payoffs

Numbers associated with each outcome

Reflect the interests of the players

## 6. Strategic Thinking

6Example: Apple vs. Samsung

Apple’s action depends on how Apple predicts

Samsung’s action.

Apple’s action depends on how Apple predicts how

Samsung predicts the Apple’s action.

Apple’s action depends on how Apple predicts how

Samsung predicts how Apple predicts the Samsung’s

action.

etc…

## 7. The Assumptions

7Rationality

Players aim to maximize their payoffs, and are self-interested.

Players are perfect calculators

Players consider the responses/reactions of other players

Common Knowledge

Each player knows the rules of the game

Each player knows that each player knows the rules

Each player knows that each player knows that each player knows the

rules

Each player knows that each player knows that each player knows that each player knows

the rules

Each player knows that each player knows that each player knows that each player knows that each player knows the rules

...

## 8. History of game theory

81928, 1944: John von Neumann

1950: John Nash

1960s: Game theory used to simulate thermonuclear

war between the USA and the USSR

1970s: Oligopoly theory

1980s: Game theory used

Evolutionary biology

Political science

More recent applications: Philosophy, computer science

1994, 2005, 2007, 2012: Economics Nobel prize

## 9. Lectures

91-3: Simultaneous games

4-5: Sequential games

Nash equilibrium

Oligopoly

Mixed strategies

Subgame perfect equilibrium

Bargaining

6: Repeated games

Two firms interacting repeatedly

## 10. Lectures

107: Evolutionary games

8-9: Incomplete information

How do players “learn” to play the Nash equilibrium

Cooperation and coordination with incomplete information

Signaling, and moral hazard.

10: Auctions

Strategies for bidders and sellers

## 11. Assessment

11Assessment consist is a final exam:

100% exam

2-hour

Section A: 5 compulsory questions, at most 3

"mathematical/analytical" questions. (10 marks each)

Section B: choose 1 essay question from a list of 2. (50

marks)

## 12. SIMULTANEOUS GAMES WITH DISCRETE CHOICES Pure strategy Nash Equilibrium

SIMULTANEOUS GAMES WITHDISCRETE CHOICES

## 13. Simultaneous games with discrete choices

13Simultaneous games with

discrete choices

A game is simultaneous when players

choose their actions at the same time

or, choose their actions in isolation, without knowing

what the other players do

Discrete choices: the set of possible actions is finite

e.g. {yes,no}; {a,b,c}.

Opposite of continuous choices: e.g. choose any

number between 0 and 1.

## 14. Strategic Interaction

14Players:

Payoffs:

Strategies:

Strategic Landscape:

Reynolds and Philip Morris

Companies’ profits

Advertise or Not Advertise

Each firm initially earns $50 million from its existing

customers

Advertising costs a firm $20 million

Advertising captures $30 million from competitor

Simultaneous game with discrete choices

## 15. Representing a Game (strategic form / normal form)

Representing a Game15

(strategic form / normal form)

Philip Morris

No Ad

Ad

Reynolds

No Ad

50 , 50

20 , 60

Ad

60 , 20

30 , 30

50-20+3050-30

50-20+30-30

What is the likely outcome?

We want a “stable”, “rational” outcome.

## 16. Solving the game: Nash equilibrium

16The Nash equilibrium, is a set of strategies, one for each

player, such that no player has incentive to unilaterally

change his action

The NE describes a stable situation.

Nash equilibrium: likely outcome of the game when

players are rational

Each player is playing his/her best strategy given the

strategy choices of all other players

No player has an incentive to change his or her action

unilaterally

## 17. Solving the Game

17Reynolds

60 , 20

30 , 30

No, 60>50

Can (No Ad,Ad) be a Nash equilibrium?

Ad

Can (No Ad,No Ad) be a Nash equilibrium?

No Ad

Philip Morris

No Ad

Ad

50 , 50

20 , 60

No: 30>20

Can (Ad,No Ad) be a Nash equilibrium?

No: 30>20

## 18. Solving the Game

18Reynolds

No Ad

Ad

Philip Morris

No Ad

Ad

50 , 50

20 , 60

60 , 20

Can (Ad,Ad) be a Nash equilibrium?

30 , 30

Equilibrium

YES: 30>20

If Philip Morris “believes” that Reynolds will choose Ad, it will also choose

Ad.

If Reynolds “believes” that Philip Morris will choose Ad, it will also choose

Ad.

(Ad, Ad) is a “stable” outcome, neither player will want to change action

unilaterally.

## 19. Equilibrium vs. optimal outcome

19“Optimal”

No Ad

No Ad

50 , 50

Ad

20 , 60

Ad

60 , 20

30 , 30

Equilibrium

The optimal outcome is the one that maximizes the sum of all

players’ payoffs. (No Ad, No Ad)

The NE does not necessarily maximize total payoff. (Ad,Ad). The

NE is individually rational, but not always collectively rational.

## 20. Game of cooperation (prisoner’s dilemma)

20Game of cooperation

(prisoner’s dilemma)

Player 1

Player 2

Cooperate

Defect

20 , 60

Cooperate 50 , 50

Defect

60 , 20

30 , 30

Players can choose between cooperate and defect. The NE is

that both players defect. But the optimal outcome is that both

cooperate.

In this example: Cooperate = No Ad ; Defect = Ad

## 21. Nash equilibrium existence

21Q: Does a NE always exist?

A: Yes (in almost every cases). [If there is no

equilibrium with pure strategies, there will be one with

mixed strategies.]

Theorem (Nash, 1950)

“There exists at least one Nash equilibrium in any

finite games in which the numbers of players and

strategies are both finite.”

## 22. Nash equilibrium A formal definition

Any social problem can be formalized as a “game,”consisting of three elements:

Players: i=1,2,…,N

i’s Strategy: si S i

i’s Payoff: i ( s1 ,..., s N )

22

## 23. Nash equilibrium A formal definition

Nash equilibrium23

A formal definition

Definition: A Nash Equilibrium is a profile of strategies

such that each player’s strategy is an optimal

( si* , s *i )

response to the other players strategies:

i ( s , s ) i ( si , s )

*

i

*

i

*

i

If all players play according to the NE, no player has any

incentive to change his action unilaterally.

Why is the NE the most likely outcome:

Any other outcome is not “stable”.

In the long term, players learn how to play and always select the

NE

## 24. How to find the Nash equilibrium?

24How to find the Nash

equilibrium?

There are two techniques to find the NE

1.

2.

Successive elimination of dominated strategies

Best response analysis

## 25. Elimination of dominated strategies (1st method)

25Elimination of dominated

strategies (1st method)

Procedure: eliminate, one by one, the strategies that are

strictly dominated by at least one other strategy.

Consider two strategies, A and B. Strategy A strictly

dominates Strategy B if the payoff of Strategy A is strictly

higher than the payoff of Strategy B no matter what

opposing players do.

For Philip Morris, Ad dominates No Ad: π(Ad,any)> π(No

Ad,any). For Reynolds Ad also dominates No Ad.

Strictly dominated strategies can be eliminated, they would

not be chosen by rational players.

No Ad can be eliminated for both players.

## 26. Elimination of dominated strategies

26Elimination of dominated

strategies

Reynolds

No Ad

Ad

Philip Morris

No Ad

Ad

50 , 50

20 , 60

60 , 20

30 , 30

## 27. Elimination of dominated strategies

27Elimination of dominated

strategies

The order in which strategies are eliminated does not

matter. Select any player, any strategy, and check

whether it is strictly dominated by any other strategy. If it

is strictly dominated, eliminate it.

When several strategies are strictly dominated, it does not

matter which one you eliminate first.

## 28. Elimination of dominated strategies

LeftMiddle

Right

Up

5, 2

2, 3

3, 4

Medium

4, 1

3, 2

4, 0

Down

3, 3

1, 2

2, 2

## 29. Elimination of dominated strategies

LeftMiddle

Right

Up

5, 2

2, 3

3, 4

Medium

4, 1

3, 2

4, 0

Down

3, 3

1, 2

2, 2

Up dominates (>)Down.

Now that Down is out, Middle>Left.

Now that Left is out, Medium>Up.

Middle>Right

The NE is {Medium,Middle}

## 30. Weak dominance

Strategy A weakly dominates strategy B if its strategy A’s payoffis in some cases higher (>) and in some cases equal ( ) to

strategy B’s payoff.

Alternative scenario:

50 , 50

30 , 60

60 , 30

30 , 30

One strategy weakly dominates the other

60>50

30=30

## 31. Weak dominance

Weakly dominated strategies cannot be eliminated.In some cases, when strategies are only weakly

dominated, successive elimination can get eliminate

some Nash equilibria.

## 32. Best response analysis (2nd method)

32Best response analysis (2nd

method)

Reynolds

No Ad

Ad

Philip Morris

No Ad

Ad

50 , 50

20 , 60

60 , 20

30 , 30

Procedure: For each possible strategy, draw a circle around

the best response of the other player.

The NE is where there is a joint best response.

## 33. Best response analysis

LeftMiddle

Right

Up

5, 2

2, 3

3, 4

Medium

4, 1

3, 2

4, 0

Down

3, 3

1, 2

2, 2

33

## 34. Exercise

ColumnLeft

Middle

Right

Top

3, 1

2, 3

10, 2

High

4, 5

3, 0

6, 4

Low

2, 2

5, 4

12, 3

Bottom

5, 6

4, 5

9, 7

Row

34

## 35. Comparing the two methods

35The two methods for finding the NE are NOT equivalent.

The best response analysis is fully reliable, and always

finds the NE.

Sometimes, the elimination of dominated strategies will

fail to find the NE. This may happen when that are more

than one NE.

## 36. Comparing the two methods

36Example of an entry game:

Two businesses must choose which market to enter.

Market Market

A

B

Market

A

0,0

2,2

Market

B

2,2

0,0

This is a game of coordination (not cooperation!): class

of games with multiple NE (two in this case).

## 37. Comparing the two methods

1st method: The game is not dominance solvable, there areno dominated strategies.

2nd method: With best response analysis, both equilibria

are found.

When best-response analysis of a discrete strategy game

does not find a Nash equilibrium, then the game has no

equilibrium in pure strategies.

37

## 38. Summary

What is game theoryGame representation

Nash equilibrium as the likely outcome of the game

Finding the NE: dominance vs. best response

38