Sequential games. (Lecture 4)

Содержание

Слайд 2

Introduction Lecture 1-3: Simultaneous games: Prisoner’s dilemma (Ad, No Ad): Unique

Introduction

Lecture 1-3: Simultaneous games:
Prisoner’s dilemma (Ad, No Ad):
Unique PSNE, both

players defect.
Games without PSNE (shirk/monitor):
MSNE is the intuitive outcome.
Coordination games:
2 PSNE & 1 MSNE. Players may try to coordinate.
Слайд 3

Introduction Lecture 4-5: Sequential games. Games where players move one after

Introduction
Lecture 4-5: Sequential games.
Games where players move one after another. Sequential

games are asymmetric.
Games we play: chess
Games businesses play: entry, pricing…
L4: Subgame perfect equilibrium.
L5: Experimental evidence, and an application to bargaining.
Слайд 4

Sequential games Looking forward: Players, when make moves, have to consider

Sequential games

Looking forward: Players, when make moves, have to consider how

other players will react.
Reasoning backward: Given other players’ reaction, what is my optimal strategy?
Asymmetry in order of play causes asymmetry in payoffs. It matters who plays first and who plays second.
Слайд 5

Entry game Two restaurant chains must choose whether to open or

Entry game

Two restaurant chains must choose whether to open or no

to open a restaurant in a new shopping area.
If the game is simultaneous: 2 PSNE, 1 MSNE.

Firm 1

Firm 2

Слайд 6

Entry game What if Firm 1 is first mover, and Firm

Entry game

What if Firm 1 is first mover, and Firm 2

the follower?
Game Trees: all possible moves, and all possible outcome and payoffs.

Firm 1

Firm 2

Firm 2

E

E

E

D

D

D

-1, -1

3,0

0,3

0,0

Branches

Nodes

Payoffs

Root

Слайд 7

Solving the Game Tree Method use to solve game tree: Backward

Solving the Game Tree

Method use to solve game tree:
Backward Induction, or

rollback
Start from the end, and rollback until the root
Difference with simultaneous game
Drop the concept of joint best response
There is a hierarchy of actions, of players
Слайд 8

Solving the Game Tree Subgame: any node with all subsequent nodes:

Solving the Game Tree

Subgame: any node with all subsequent nodes:
Subgame perfect

equilibrium (SPE):
The SPE is the equilibrium in sequential games.
The SPE is such that players' strategies constitute a Nash equilibrium in every subgame of the original game
Start with terminal nodes and eliminate dominated actions from the game

E

D

-1,-1

3,0

Firm 2

Слайд 9

Looking Forward… And Reasoning Back Firm 1 makes the first move,

Looking Forward… And Reasoning Back

Firm 1 makes the first move, and

must take into account how the response of Firm 2:

Firm 1

Firm 2

Firm 2

E

E

E

D

D

D

-1, -1

3,0

0,3

0,0

The SPE is (E,D)

Слайд 10

Discussion Compared to the simultaneous version of the game, Firm 1

Discussion

Compared to the simultaneous version of the game,
Firm 1 can obtain

the outcome that yields the highest payoff (3), whereas Firm 2 obtains a low payoff (0)
First-mover advantage:
Ability to commit oneself to an advantageous position
Firm 1 benefits from taking an irreversible action
Note: not all games have a first-mover advantage
e.g. some bargaining games may have a second-mover advantage (see lecture 5).
Слайд 11

Sequential games and oligopoly Cournot model of oligopoly: Simultaneous game. Producers

Sequential games and oligopoly

Cournot model of oligopoly:
Simultaneous game.
Producers have market power

(profits>0), but less than the monopolist.
Producers would be better off if they could cooperate (e.g. OPEC oil cartel), however cooperation is not a stable outcome.
Decisions of how much to produce can also be sequential ? Stackelberg model of oligopoly
Слайд 12

Firm 1 Firm 2 Cournot NE BR1 BR2 240 240 Sequential

Firm 1

Firm 2

Cournot NE

BR1

BR2

240

240

Sequential games and oligopoly

What is the equilibrium if


firms play sequentially?
Слайд 13

The Stackelberg model A Cournot game with sequential actions Two producers,

The Stackelberg model A Cournot game with sequential actions

Two producers, Firm 1

and Firm 2.
Produce the same goods, and sell on the same market.
Слайд 14

The Stackelberg model Rather than assuming that producers choose quantity simultaneously,

The Stackelberg model

Rather than assuming that producers choose quantity simultaneously, the

Stackelberg model identifies a leader (who chooses quantity first), and a follower.
The follower will observe the leader’s quantity level before choosing his own quantity.
Слайд 15

The Stackelberg model The leader can predict the follower’s choice, and

The Stackelberg model

The leader can predict the follower’s choice, and will

take it into account when making its decision.
Слайд 16

The Stackelberg model Backward induction In a sequential game, Firm 2’s

The Stackelberg model Backward induction

In a sequential game, Firm 2’s output will

be its best response to Firm 1’s output decision. Best response of Firm 2:
Substitute into Firm 1’s profit function:
Слайд 17

The Stackelberg model Derive the optimal output for Firm 1: For

The Stackelberg model

Derive the optimal output for Firm 1:
For Firm 2,

substitute q1 in the best response function:
Слайд 18

360 720 Firm 1 Firm 2 EQUILIBRIUM BR1 BR2 240 240 360 180 The Stackelberg model

360

720

Firm 1

Firm 2

EQUILIBRIUM

BR1

BR2

240

240

360

180

The Stackelberg model

Слайд 19

The Stackelberg model Note that the equilibrium is not on Firm

The Stackelberg model

Note that the equilibrium is not on Firm 1’s

Cournot best response function.
By playing first, Firm 1 can select the point on Firm 2’s best response function that maximizes its own payoff
First-mover advantage: By committing to a high quantity, Firm 1 can force Firm 2 to produce a low quantity.
The first-mover has the advantage because his action is irreversible. The Stackelberg leader is the player that makes an irreversible decision first.
Слайд 20

Stackelberg vs. Cournot Stackelberg yields a higher total quantity than Cournot.

Stackelberg vs. Cournot

Stackelberg yields a higher total quantity than Cournot.

To exploit

the first-mover advantage, the leader should produce more output than in Cournot. This results into higher total output, and a lower price.
Слайд 21

Stackelberg in the pharmaceutical industry Patents for new drugs last up

Stackelberg in the pharmaceutical industry

Patents for new drugs last up to

20-30 years. During the patent period, the firm that invented the drug has a monopoly and can sell the drug at a high price.
Once the patent expires, anyone is allowed to produce generic version of drug and sell at a low price.
Just before the patent expires, brand name pharmaceutical companies enter into the generic drug competition by marketing their brand name drug with a pseudo-generic label before the generic drug manufacturers can enter the generic market.
This allows the pseudo-generic drug to attain most of the market share and establish itself as the market leader.
Слайд 22

Price MC 0.28 720 Demand: P=1-0.001Q 1 Welfare and perfect competition

Price

MC

0.28

720

Demand: P=1-0.001Q

1

Welfare and perfect competition

Consumer
surplus

Consumer surplus is the area
between the demand

curve and P.

0

Слайд 23

360 Price MC 0.28 0.64 Demand (Q) 1 Welfare and monopoly

360

Price

MC

0.28

0.64

Demand (Q)

1

Welfare and monopoly

Consumers
surplus

Dead weight loss

Producers surplus

Total surplus is consumer surplus


+ producers surplus

0

720

Слайд 24

360 Price MC 0.28 0.64 720 Demand (Q) 1 Welfare and

360

Price

MC

0.28

0.64

720

Demand (Q)

1

Welfare and Cournot

480

Cournot deadweight loss

0

Слайд 25

360 Price MC 0.28 0.64 720 Demand (Q) 1 Welfare and

360

Price

MC

0.28

0.64

720

Demand (Q)

1

Welfare and Stackelberg

540

Stackelberg deadweight loss

0

Слайд 26

Entry game with incumbent Suppose that Pepsi (the incumbent) is already

Entry game with incumbent

Suppose that Pepsi (the incumbent) is already in

the local market, and Coca-Cola is deciding whether to Enter or stay Out. 
Pepsi: adopt a Tough defensive response or Acquiesce.
Tough: increase production, fight on prices, advertising campaign etc.
Acquiesce: no aggressive commercial war with Coca-Cola
Слайд 27

Entry game with incumbent Pepsi will choose to acquiesce. Since Coca-Cola

Entry game with incumbent

Pepsi will choose to acquiesce. 
Since Coca-Cola knows

that Pepsi will Acquiesce, its best course of action is to Enter. 
? First mover advantage
Слайд 28

Entry game with incumbent Sequential games may have more than two

Entry game with incumbent

Sequential games may have more than two rounds.

After observing Pepsi's stance, Coca-Cola can itself choose to be Tough, Acquiesce, or go Out of the market.   
Слайд 29

Entry game with incumbent Coca-Cola looks at Pepsi's Tough play and

Entry game with incumbent

Coca-Cola looks at Pepsi's Tough play and should

choose to go Out of the market since it then only loses -$1. If Coca-Cola sees Pepsi Acquiesce then it should itself Acquiesce and earn $1. 
Pepsi knows that when it plays Tough Coca-Cola will exit. Its best choice is to act Tough to force Coca-Cola to go Out.
Coca-Cola reasons backwards:  if it enters, then Pepsi will play Tough and the best response is to go Out. Hence, Coca-Cola’s best play is to Stay Out since it loses 0 instead of -1.
Слайд 30

Strategic moves Players are rational and know how the game will

Strategic moves

Players are rational and know how the game will be

played and the subsequent payoff. What can player do to alter the predicted outcome?
Strategic moves: Commitment/threat/promise
Commitment: Commit to take a particular decision unconditionally on the other player’s action.
Having fewer choices is typically worse than having many choices. In sequential games, however, having fewer choices can actually increase your payoff.
Слайд 31

Strategic moves Threat: A response rule that leads to a bad

Strategic moves

Threat: A response rule that leads to a bad outcome

for the other player if he acts contrary to your interests.
Promise: A response rule by which you offer to create a good outcome for the other player if he acts in a way that promotes your interests.
Слайд 32

Threat and entry Equilibrium without strategic moves: (Enter,Acquiesce) What could Pepsi

Threat and entry

Equilibrium without strategic moves: (Enter,Acquiesce)
What could Pepsi do? Threaten

to be tough if Coca-Cola enters:
Rollback: Coca-Cola stays out!
Слайд 33

Threat and entry: Credibility problem If Coca-Cola enters, it is in

Threat and entry: Credibility problem

If Coca-Cola enters, it is in Pepsi’s

best interest to acquiesce.
Pepsi’s threat to be tough if Coca-Cola enters is not credible.
Coca-Cola, knowing that, will enter.
“Talk is cheap”
Слайд 34

Credible strategic move How to make a credible strategic move? Binding

Credible strategic move How to make a credible strategic move?

Binding contract between

Pepsi and retailers.
We will sell you Pepsi at a lower price than Coca-Cola does.
“Tough” becomes credible.
Decide to expand capacity, in order to reduce the marginal costs of increasing quantity.
Keep innovating, in order to commit to improve quality and deter entry.
Слайд 35

Credible strategic move How to make a credible strategic move? Pepsi

Credible strategic move How to make a credible strategic move?

Pepsi can also

make threat credible by acquiring a reputation for toughness. By being tough towards potential entrants today, it may deter other firms from entering.
Being tough is not subgame perfect, however the entrant may think the incumbent will be tough if he has such a reputation.
If a threat is credible, other firms won’t enter, and the threat to be tough is never materialized.
Слайд 36

Credible strategic move How to make a credible strategic move? Polaroid

Credible strategic move How to make a credible strategic move?

Polaroid instant photography
Refused

to diversify out of its core business. With all its chips in instant photography, it was committed to fight against any intruder in the market.
In 1976, after 28 years of a Polaroid monopoly on the instant photography market, Kodak entered the fray.
Edwin Land, Polaroid founder:
“This is our very soul we are involved with. This is our whole life…We will stay in our lot and protect that lot.”
- Предыдущая
Sequential games. Empirical evidence and bargaining. (Lecture 5)
Следующая -
Mixed strategy Nash equilibrium. (Lecture 3)

Похожие презентации

Задания для тех, кто не боится трудностей
Сравнение десятичных дробей
Многогранники. Все формулы. Геометрия (10-11 класс)
Элементы высшей математики. Обратная матрица
Аттестационная работа. Элективный курс "Тайны математических приёмов и решений". (9 класс)
Итоговый тест по математике. 2 класс. УМК «Гармония»
Обучающая самостоятельная работа «Взаимно обратные числа» математика - 6 Выполнила учитель математики МБ ОУ Газопроводская СО
Детерминационный, факторный, кластерный анализ
Основные понятия криптографии
Свойства медиан треугольника
Презентация по математике "Древний Египет" - скачать
Розв’язування задач за допомогою рівнянь
Свертка
Дія ділення.(2 клас)
Призма как многогранник
Решение задач с помощью дробных рациональных уравнений
Конические сечения
Уңай һәм тискәре саннар
Процентные вычисления в жизненных ситуациях
Реляционная алгебра. Решение задач
Закрепление изученного. Решение задач (2 класс)
Особенности оценивания задания С3 по математике
Тренажер по геометрии. Задачи на готовых чертежах
Квадратные уравнения. Урок-путешествие
Многогранники. Вершины, ребра, грани многогранника. Теорема Эйлера
Вынесение общего множителя за скобки
Сложение и вычитание десятичных дробей
Компьютерные технологии принятия решений в формализованных и неформализованных задачах
Вы можете прислать нам Вашу презентацию и мы опубликуем ее на сайте.
Обратная связь
Для правообладателей
Email: Нажмите что бы посмотреть