Lecture 13
Game Theory and Competitive Strategy
Chapter 1
Topics to be Discussed
Gaming and Strategic Decisions
Dominant Strategies
The Nash Equilibrium
Repeated Games
Chapter 1
Topics to be Discussed
Sequential Games
Threats, Commitments, and Credibility
Entry Deterrence
Bargaining Strategy
Auctions
Chapter 1
Gaming and Strategic Decisions
“If I believe that my competitors are rational and act to maximize their own profits, how should I take their behavior into account when making my own profit-maximizing decisions?”
Chapter 1
Gaming and Strategic Decisions
Noncooperative versus Cooperative Games
Cooperative Game
Players negotiate binding contracts that allow them to plan joint strategies
Example: Buyer and seller negotiating the price of a good or service or a joint venture by two firms (. Microsoft and Apple)
Binding contracts are possible
Chapter 1
Gaming and Strategic Decisions
Noncooperative versus Cooperative Games
Noncooperative Game
Negotiation and enforcement of a binding contract are not possible
Example: Two competing firms assuming the others behavior determine, independently, pricing and advertising strategy to gain market share
Binding contracts are not possible
Chapter 1
Gaming and Strategic Decisions
Noncooperative versus Cooperative Games
“The strategy design is based on understanding your opponent’s point of view, and (assuming your opponent is rational) deducing how he or she is likely to respond to your actions”
Chapter 1
Gaming and Strategic Decisions
An Example: How to buy a dollar bill
1) Auction a dollar bill
2) Highest bidder receives the dollar in return for the amount bid
Chapter 1
Gaming and Strategic Decisions
An Example
3) Second highest bidder must pay the amount he or she bid
4) How much would you bid for a dollar?
Chapter 1
Acquiring a Company
Scenario
Company A: The Acquirer
Company T: The Target
A will offer cash for all of T’s shares
What price to offer?
Chapter 1
Acquiring a Company
Scenario
The value of T depends on the outcome of a current oil exploration project.
Failure: T’s value = $0
Success: T’s value = $100/share
All outcomes are equally likely
Chapter 1
Acquiring a Company
Scenario
T’s value will be 50% greater with A’s management.
A, must submit the proposal before the exploration outcome is known.
T will not choose to accept or reject until after the outcome is known only to T.
How much should A offer?
Chapter 1
Key Ideas
Know your strategic situation, what is the game you are playing?
Do not impose your own wishes and fancies on a game. that has been given to you .
Your competitor is just as smart as you are!
Has same information,rationality, and intelligence.
you cannot “outguess” your opponent.
Think about the response of others to your actions
Game theory and competitive
Game theory
Game theory is the study of strategic behavior in situation of conflict. In a oligopoly, a firm’s output choice depends on its prediction of its rival’s output choices. These strategic choices are complex because other firms are also choosing output based on their predictions of their rival’s outputs. To choose its best output, a firm must determine what the best choices of other firms will be, assuming rational behavior by all other firms and then do the best it can.
Game theory and competitive
Game Theory: Concept
A game is a general concept; it includes almost any situation in which each decision maker’s profits depends on actions of other decision makers. The decision makers are called the players. To describe a game, we need to know the rules of the game, the possible strategies of each player, and the payoffs from each possible combination of actions. Players are assumed to want to maximize their payoffs. The rules include the order of moves by the players and whether binding agreements about actions are possible. If no binding agreements are allowed, then the game is non-cooperative. The Cournot model is example of a non-cooperative game. Each firm independently makes its output choice with no possibility of entering into binding commitments with other firms. In fact, most games studied in economics are non-cooperative games. By contrast, in a cooperative game, firms can make binding commitments that allow them to plan joint strategies. Contract negotiations are an important example of cooperative games.
Chapter 1
Three Factors
1. Players
2. Strategies
3. Payoffs
Chapter 1
Types of the game
With a duopoly example
Cooperative Vs. Non-cooperative
Simultaneous Vs. sequential choice
One-time Vs. repeated games
Game theory and competitive
Prisoners’ Dilemma
Two prisoners have been accused of collaborating in a crime. They are in separate jail cells and cannot communicate with each other. Each has been asked to confess to the crime. If both prisoners confess, each will receive a prison term of five years. If neither confesses, the prosecution’s case will be difficult to make, so the prisoners can expect to plea bargain and receive a term of two years. On the other hand, if one prisoner confesses and other does not, the one who confesses will receive a term of only one year, while the other will go to prison for ten years. If you were one of these prisoners, what would you do --- confess or not confess?
Prisoner B
Confess
Don’t
Confess
Confess
Don’t
Confess
Prisoner A
-5, -5
-1, -10
-10, -1
-2, -2
Game theory and competitive
Dominant Strategies
Dominant Strategy
I’m doing the best I can no matter what you do.
You’re doing the best you can no matter what I do.
An Example
A & B sell competing products
They are deciding whether to undertake advertising campaigns
Chapter 1
Payoff Matrix for Advertising Game
Firm A
Advertise
Don’t
Advertise
Advertise
Don’t
Advertise
Firm B
10, 5
15, 0
10, 2
6, 8
Chapter 1
Payoff Matrix for Advertising Game
Observations
A: regardless of B, advertising is the best
B: regardless of A, advertising is best
Firm A
Advertise
Don’t
Advertise
Advertise
Don’t
Advertise
Firm B
10, 5
15, 0
10, 2
6, 8
Chapter 1
Payoff Matrix for Advertising Game
Observations
Dominant strategy for A & B is to advertise
Do not worry about the other player
Equilibrium in dominant strategy
Firm A
Advertise
Don’t
Advertise
Advertise
Don’t
Advertise
Firm B
10, 5
15, 0
10, 2
6, 8
Chapter 1
Dominant Strategies
Game Without Dominant Strategy
The optimal decision of a player without a dominant strategy will depend on what the other player does.
Chapter 1
Modified Advertising Game
10, 5
15, 0
20, 2
6, 8
Firm A
Advertise
Don’t
Advertise
Advertise
Don’t
Advertise
Firm B
Chapter 1
Modified Advertising Game
Observations
A: No dominant strategy; depends on B’s actions
B: Advertise
Question
What should A do? (Hint: consider B’s decision
10, 5
15, 0
20, 2
6, 8
Firm A
Advertise
Don’t
Advertise
Advertise
Don’t
Advertise
Firm B
Chapter 1
The Nash Equilibrium
Nash Equilibrium
“I’m doing the best I can given what you are doing”
“You’re doing the best you can given what I am doing.”
Chapter 1
The Nash Equilibrium Revisited
Examples With A Nash Equilibrium
Two cereal companies
Market for one producer of crispy cereal
Market for one producer of sweet cereal
Each firm only has the resources to introduce one cereal
Noncooperative
Product Choice Problem
Chapter 1
Product Choice Problem
Firm 1
Crispy
Sweet
Crispy
Sweet
Firm 2
-5, -5
10, 10
-5, -5
10, 10
Chapter 1
Product Choice Problem
Question
Is there a Nash equilibrium?
If not, why?
If so, how can it be reached
Firm 1
Crispy
Sweet
Crispy
Sweet
Firm 2
-5, -5
10, 10
-5, -5
10, 10
Chapter 1
Beach Location Game
Scenario
Two competitors, Y and C, selling soft drinks
Beach 200 yards long
Sunbathers are spread evenly along the beach
Price Y = Price C
Customer will buy from the closest vendor
Chapter 1
Beach Location Game
Where will the competitors locate (. where is the Nash equilibrium)?
Ocean
0
B
Beach
A
200 yards
C
Chapter 1
Beach Location Game
2) Examples of this decision problem include:
Locating a gas station
Presidential elections
Ocean
0
B
Beach
A
200 yards
C
Chapter 1
The Nash Equilibrium
Maximin Strategies
Scenario
Two firms compete selling file-encryption software
They both use the same encryption standard (files encrypted by one software can be read by the other - advantage to consumers)
Chapter 1
The Nash Equilibrium
Maximin Strategies
Scenario
Firm 1 has a much larger market share than Firm 2
Both are considering investing in a new encryption standard
Chapter 1
Maximin Strategy
Firm 1
Don’t invest
Invest
Firm 2
0, 0
-10, 10
20, 10
-100, 0
Don’t invest
Invest
Chapter 1
Maximin Strategy
Observations
Dominant strategy Firm 2: Invest
Nash equilibrium
Firm 1: invest
Firm 2: Invest
Firm 1
Don’t invest
Invest
Firm 2
0, 0
-10, 10
20, 10
-100, 0
Don’t invest
Invest
Chapter 1
Maximin Strategy
Observations
If Firm 2 does not invest, Firm 1 incurs significant losses
Firm 1 might play don’t invest
Minimize losses to 10 --maximin strategy
Firm 1
Don’t invest
Invest
Firm 2
0, 0
-10, 10
20, 10
-100, 0
Don’t invest
Invest
Chapter 1
The Nash Equilibrium
If both are rational and informed
Both firms invest
Nash equilibrium
Maximin Strategy
Chapter 1
The Nash Equilibrium
Consider
If Player 2 is not rational or completely informed
Firm 1’s maximin strategy is to not invest
Firm 2’s maximin strategy is to invest.
If 1 knows 2 is using a maximin strategy, 1 would invest
Maximin Strategy
Chapter 1
Prisoners’ Dilemma
Prisoner A
Confess
Don’t Confess
Confess
Don’t
Confess
Prisoner B
-5, -5
-1, -10
-2, -2
-10, -1
Chapter 1
Prisoners’ Dilemma
What is the:
Dominant strategy
Nash equilibrium
Maximin solution
Prisoner A
Confess
Don’t Confess
Confess
Don’t
Confess
Prisoner B
-5, -5
-1, -10
-2, -2
-10, -1
Chapter 1
Example
Two companies want to open business in a new area . They can choose Hotel or supermarket. Resulting profit are given by the payoff matrix
What outcomes , if any , are Nash equilibrium?
If the manager of each firms conservative and each follows a maximin strategy,
what be the outcome?
What is the cooperative
outcome?
Which benefits most from
the cooperative? How much
need to offer the other to persuade it to collude?
-50, -80
900, 500
200,800
60, 80
Firm 2
Hotel
Supermarket
Hotel
Supermarket
Firm 1
Game theory and competitive
The Nash Equilibrium
Pure Strategy
Player makes a specific choice
Mixed Strategy
Player makes a random choice among two or more possible actions based on a set of chosen probabilities
Mixed Strategy
Chapter 1
Matching Pennies
Player A
Heads
Tails
Heads
Tails
Player B
1, -1
-1, 1
1, -1
-1, 1
Chapter 1
Matching Pennies
Observations
Pure strategy: No Nash equilibrium
Mixed strategy: Random choice is a Nash equilibrium
Would a firm set price based on random choice assumption?
Player A
Heads
Tails
Heads
Tails
Player B
1, -1
-1, 1
1, -1
-1, 1
Chapter 1
The Battle of the Sexes
Jim
Wrestling
Opera
Wrestling
Opera
Joan
2,1
0,0
1,2
0,0
Chapter 1
The Battle of the Sexes
Pure Strategy
Both watch wrestling
Both watch opera
Mixed Strategy
Jim chooses wrestling
Joan chooses wrestling
Jim
Wrestling
Opera
Wrestling
Opera
Joan
2,1
0,0
1,2
0,0
Chapter 1
Example
What is the Nash equilibrium of the right table? If there is no Nash equilibrium involving pure strategies, check that players are indifferent among the actions used in their mixed strategies in equilibrium. Calculate the expected payoffs.
A
1
2
1
2
B
30,40
70,50
80,80
20,100
Chapter 1
博弈模型与竞争策略
警卫与窃贼的博弈
警卫睡觉,小偷去偷,小偷得益B,警卫被处分-D。
警卫不睡，小偷去偷，小偷被抓受惩处-P, 警卫不失不得。
警卫睡觉，小偷不偷，小偷不失不得，警卫得到休闲R.
警卫不睡，小偷不偷，都不得不失。
警卫
睡觉
不睡觉
偷
不偷
窃贼
B, -D
-P, 0
0, R
0, 0
Chapter 1
博弈模型与竞争策略
混合博弈的两个原则
不能让对方知道或猜到自己的选择，因此必须在决策时采取随机决策；
二 选择每种策略的概率要恰好使对方无机可乘，对方无法通过有针对性的倾向于某种策略而得益
Chapter 1
博弈模型与竞争策略
警卫是不是睡觉决定于小偷偷不偷的概率，而小偷偷不偷的概率在于小偷猜警卫睡不睡觉
小偷一定来偷，警卫一定不睡觉；
小偷一定不来偷，警卫一定睡觉。
警卫的得益
与小偷偷不偷的概率有关
Chapter 1
博弈模型与竞争策略
若小偷来偷的概率为 偷 警卫的得益为： R ( 1- 偷) + (-D) 偷 小偷认为警卫不会愿意得益为负，最多为零。 即R/D= 偷/ ( 1- 偷) 小偷偷不偷的概率等于R与D的比率
0
1
小偷偷
的概率
警卫睡觉的期望得益
R
D
P偷
Chapter 1
博弈模型与竞争策略
同样的道理警卫偷懒的概率
（睡觉） 睡 决定了小偷的得益为： (-P) ( 1- 睡) + (B) 睡 警卫也认为小偷不会愿意得益为负，最多为零。 即B / P = ( 1- 睡)/ 睡 警卫偷不偷懒的概率取决于 B与P的比率 有趣的激励悖论
管理经济学考什么？
0
1
警卫偷懒
的概率
小偷的期望得益
P睡
P
B
Chapter 1
Repeated Games
Oligopolistic firms play a repeated game.
With each repetition of the Prisoners’ Dilemma, firms can develop reputations about their behavior and study the behavior of their competitors.
Chapter 1
Pricing Problem
Firm 1
Low Price
High Price
Low Price
High Price
Firm 2
10, 10
100, -50
50, 50
-50, 100
Chapter 1
Pricing Problem
Non-repeated game
Strategy is Low1, Low2
Repeated game
Tit-for-tat strategy is the most profitable
Firm 1
Low Price
High Price
Low Price
High Price
Firm 2
10, 10
100, -50
50, 50
-50, 100
Chapter 1
Repeated Games
Conclusion:
With repeated game
The Prisoners’ Dilemma can have a cooperative outcome with tit-for-tat strategy
Chapter 1
Repeated Games
Conclusion:
This is most likely to occur in a market with:
Few firms
Stable demand
Stable cost
Chapter 1
Repeated Games
Conclusion
Cooperation is difficult at best since these factors may change in the long-run.
Chapter 1
Oligopolistic Cooperation
in the Water Meter Industry
Characteristics of the Market
Four Producers
Rockwell International (35%), Badger Meter, Neptune Water Meter Company, and Hersey Products (Badger, Neptune, and Hersey combined have about a 50 to 55% share)
Chapter 1
Oligopolistic Cooperation
in the Water Meter Industry
Characteristics of the Market
Very inelastic demand
Not a significant part of the budget
Chapter 1
Oligopolistic Cooperation
in the Water Meter Industry
Characteristics of the Market
Stable demand
Long standing relationship between consumer and producer
Barrier
Economies of scale
Barrier
Chapter 1
Oligopolistic Cooperation
in the Water Meter Industry
Characteristics of the Market
This is a Prisoners’ Dilemma
Lower price to a competitive level
Cooperate
Repeated Game
Question
Why has cooperation prevailed?
Chapter 1
Competition and Collusion
in the Airline Industry
What Do You Think?
Is there cooperation & collusion in the airline industry?
Chapter 1
Example
Right table shows a Prisoner’s Dilemma game in which the players are the two networks ABC and NBC. Their strategies are advertise or not advertise their new fall lineup. If they don’t advertise, they will split the market and they will have saved on advertising expenditure. If they both advertising, ratings are high, but so are costs, so profits fall. If one advertises and the other doesn’t, there is a clear gain to be made. Profits are indicated in the payoff matrix in millions of dollars per year.
ABC
Advertise
Don’t Advertise
Advertise
Don’t advertise
NBC
100, 100
300, 0
200, 200
0,300
Chapter 1
Example (Cont.)
What is the Nash equilibrium if this game is played only once?
Now consider a repeated game based on above table. Suppose ABC refuses to advertise in the first period and continues not to advertise as long as NBC doesn’t advertise. But if NBC fails even once to cooperate, ABC will revert forever to the safe policy of advertising. Although this is supposed to be an infinitely repeated game, consider just a ten-period game make the algebra easier. Calculate the sum of NBC’s profits over time if it adopts a parallel strategy. Then calculate the sum of NBC’s profits over time if it takes advantage of ABC’s willingness to corporate by choosing to advertise in the first period. Comparing these two income streams, what will NBC do?
Chapter 1
Sequential Games
Players move in turn
Players must think through the possible actions and rational reactions of each player
Chapter 1
Sequential Games
Examples
Responding to a competitor’s ad campaign
Entry decisions
Responding to regulatory policy
Chapter 1
Sequential Games
Scenario
Two new (sweet, crispy) cereals
Successful only if each firm produces one cereal
Sweet will sell better
Both still profitable with only one producer
The Extensive Form of a Game
Chapter 1
Modified Product Choice Problem
Firm 1
Crispy
Sweet
Crispy
Sweet
Firm 2
-5, -5
10, 20
-5, -5
20, 10
Chapter 1
Modified Product Choice Problem
Question
What is the likely outcome if both make their decisions independently, simultaneously, and without knowledge of the other’s intentions?
Firm 1
Crispy
Sweet
Crispy
Sweet
Firm 2
-5, -5
10, 20
-5, -5
20, 10
Chapter 1
Modified Product Choice Problem
Assume that Firm 1 will introduce its new cereal first (a sequential game).
Question
What will be the outcome of this game?
The Extensive Form of a Game
Chapter 1
Sequential Games
The Extensive Form of a Game
Using a decision tree
Work backward from the best outcome for Firm 1
The Extensive Form of a Game
Chapter 1
Product Choice Game in Extensive Form
Crispy
Sweet
Crispy
Sweet
-5, -5
10, 20
20, 10
-5, -5
Firm 1
Crispy
Sweet
Firm 2
Firm 2
Chapter 1
Sequential Games
The Advantage of Moving First
In this product-choice game, there is a clear advantage to moving first.
Chapter 1
Sequential Games
Assume: Duopoly
The Advantage of Moving First
Chapter 1
Sequential Games
Duopoly
The Advantage of Moving First
Chapter 1
Choosing Output
Firm 1
Firm 2
,
,
0, 0
,
125,
50, 75
, 125
75, 50
100, 100
10
15
10
15
Chapter 1
Choosing Output
This payoff matrix illustrates various outcomes
Move together, both produce 10
Question
What if Firm 1 moves first?
Firm 1
Firm 2
,
,
0, 0
,
125,
50, 75
, 125
75, 50
100, 100
10
15
10
15
Chapter 1
Threats, Commitments, and Credibility
Strategic Moves
What actions can a firm take to gain advantage in the marketplace?
Deter entry
Induce competitors to reduce output, leave, raise price
Implicit agreements that benefit one firm
Chapter 1
Threats, Commitments, and Credibility
How To Make the First Move
Demonstrate Commitment
Firm 1 must constrain his behavior to the extent Firm 2 is convinced that he is committed
Chapter 1
Threats, Commitments, and Credibility
Empty Threats
If a firm will be worse off if it charges a low price, the threat of a low price is not credible in the eyes of the competitors.
Chapter 1
Pricing of Computers
and Word Processors
Firm 1
High Price
Low Price
High Price
Low Price
Firm 2
100, 80
80, 100
10, 20
20, 0
Chapter 1
Pricing of Computers
and Word Processors
Question
Can Firm 1 force Firm 2 to charge a high price by threatening to lower its price?
Firm 1
High Price
Low Price
High Price
Low Price
Firm 2
100, 80
80, 100
10, 20
20, 0
Chapter 1
Threats, Commitments, and Credibility
Scenario
Race Car Motors, Inc. (RCM) produces cars
Far Out Engines (FOE) produces specialty car engines and sells most of them to RCM
Sequential game with RCM as the leader
FOE has no power to threaten to build big since RCM controls output.
Chapter 1
Production Choice Problem
Far Out Engines
Small cars
Big cars
Small engines
Big engines
Race Car Motors
3, 6
3, 0
8, 3
1, 1
Chapter 1
Threats, Commitments, and Credibility
Question
How could FOE force RCM to shift to big cars?
Chapter 1
Modified Production Choice Problem
0, 6
0, 0
8, 3
1, 1
Far Out Engines
Small cars
Big cars
Small engines
Big engines
Race Car Motors
Chapter 1
Modified Production Choice Problem
Questions
1) What is the risk of this strategy?
2) How could irrational behavior give FOE some power to control output?
Chapter 1
Wal-Mart Stores’
Preemptive Investment Strategy
Question
How did Wal-Mart become the largest retailer in the . when many established retail chains were closing their doors?
Hint
How did Wal-Mart gain monopoly power?
Preemptive game with Nash equilibrium
Chapter 1
The Discount Store Preemption Game
Wal-Mart
Enter
Don’t enter
Enter
Don’t enter
Company X
-10, -10
20, 0
0, 0
0, 20
Chapter 1
The Discount Store Preemption Game
Two Nash equilibrium
Low left
Upper right
Must be preemptive to win
Wal-Mart
Enter
Don’t enter
Enter
Don’t enter
Company X
-10, -10
20, 0
0, 0
0, 20
Chapter 1
Entry Deterrence
To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable.
Chapter 1
Entry Possibilities
Incumbent
Enter
Stay out
High price
(accommodation)
Low Price
(warfare)
Potential Entrant
100, 20
200, 0
130, 0
70, -10
Chapter 1
Entry Deterrence
Scenario
Incumbent monopolist (I) and prospective entrant (X)
X single cost = $80 million to build plant
Chapter 1
Entry Deterrence
Scenario
If X does not enter I makes a profit of $200 million.
If X enters and charges a high price I earns a profit of $100 million and X earns $20 million.
If X enters and charges a low price I earns a profit of $70 million and X earns $-10 million.
Chapter 1
Entry Deterrence
Question
How could I keep X out?
Is the threat credible?
Chapter 1
Entry Deterrence
How could I keep X out?
1) Make an investment before entry (irrevocable commitment)
2) Irrational behavior
Chapter 1
Entry Deterrence
Incumbent
Enter
Stay out
High price
(accommodation)
Low Price
(warfare)
Potential Entrant
50, 20
150, 0
130, 0
70, -10
After $50 million Early Investment
Chapter 1
Entry Deterrence
Warfare likely
X will stay out
Incumbent
Enter
Stay out
High price
(accommodation)
Low Price
(warfare)
Potential Entrant
50, 20
150, 0
130, 0
70, -10
After $50 million Early Investment
Chapter 1
Entry Deterrence
Airbus vs. Boeing
Without Airbus being subsidized, the payoff matrix for the two firms would differ significantly from one showing subsidization.
Chapter 1
Development of a New Aircraft
Boeing
Produce
Don’t produce
Airbus
-10, -10
100, 0
0, 0
0, 120
Produce
Don’t produce
Chapter 1
Development of a New Aircraft
Boeing will produce
Airbus will not produce
Boeing
Produce
Don’t produce
Airbus
-10, -10
100, 0
0, 0
0, 120
Produce
Don’t produce
Chapter 1
Development of a Aircraft
After European Subsidy
Boeing
Produce
Don’t produce
Airbus
-10, 10
100, 0
0, 0
0, 120
Produce
Don’t produce
Chapter 1
Development of a Aircraft
After European Subsidy
Airbus will produce
Boeing will not produce
Boeing
Produce
Don’t produce
Airbus
-10, 10
100, 0
0, 0
0, 120
Produce
Don’t produce
Chapter 1
Diaper Wars
Even though there are only two major firms, competition is intense.
The competition occurs mostly in the form of cost-reducing innovation.
Chapter 1
Competing Through R & D
P&G
R&D
No R&D
R&D
No R&D
Kimberly-Clark
40, 20
80, -20
60, 40
-20, 60
Chapter 1
Competing Through R & D
Both spend on R&D
Question
Why not cooperate
P&G
R&D
No R&D
R&D
No R&D
Kimberly-Clark
40, 20
80, -20
60, 40
-20, 60
Chapter 1
Bargaining Strategy
Alternative outcomes are possible if firms or individuals can make promises that can be enforced.
Chapter 1
Bargaining Strategy
Consider:
Two firms introducing one of two complementary goods.
Chapter 1
Bargaining Strategy
Firm 1
Produce A
Produce B
Produce A
Produce B
Firm 2
40, 5
50, 50
5, 45
60, 40
Chapter 1
Bargaining Strategy
With collusion:
Produce A1B2
Without collusion:
Produce A1B2
Nash equilibrium
Firm 1
Produce A
Produce B
Produce A
Produce B
Firm 2
40, 5
50, 50
5, 45
60, 40
Chapter 1
Bargaining Strategy
Suppose
Each firm is also bargaining on the decision to join in a research consortium with a third firm.
Chapter 1
Bargaining Strategy
Firm 1
Work alone
Enter consortium
Work alone
Enter
consortium
Firm 2
10, 10
10, 20
40, 40
20, 10
Chapter 1
Bargaining Strategy
Dominant strategy
Both enter
Firm 1
Work alone
Enter consortium
Work alone
Enter
consortium
Firm 2
10, 10
10, 20
40, 40
20, 10
Chapter 1
Bargaining Strategy
Linking the Bargain Problem
Firm 1 announces it will join the consortium only if Firm 2 agrees to produce A and Firm 1 will produce B.
Firm 1’s profit increases from 50 to 60
Chapter 1
Bargaining Strategy
Strengthening Bargaining Power
Credibility
Reducing flexibility
Chapter 1
Negotiating Game: An Example
You play the following bargaining game. Player A moves first, and makes Player B an offer for the division of RMB100 with offer in units of RMB1. (For example, Player A could suggest that she takes RMB60 and Player B takes RMB40). Player B can accept or reject the offer. If he rejects, the amount of money available drops to RMB90, and he then makes an offer for the division of this amount. If Player A rejects this offer, the amount of money drops to RMB80, and Player A makes an offer for its division. Both player are rational, fully informed, and want to maximize their payoffs. Questions: (1) If you are Player A, and want the negotiation 2 rounds end, what is your offer in the first round? (2) How about 3 rounds end? (3) How about 10 rounds end?
Chapter 1
Answer
The best way is to jump to the last round and find the optimal strategy, than back to the beginning
Game theory and competitive(continued)
Auctions
Auction Formats
Traditional English (oral)
Dutch auction
Sealed-bid
First price
Second price
Chapter 1
Auctions
How to choose an auction format
Private-value auction: bidders uncertain about the other bidders reservation price
Common-value auction: bidders uncertain what the value is
Valuation and Information
Chapter 1
Auctions
Second-price sealed auction: bid your reservation price
English auction: Bid in small increments until you reach your reservation price
Private Value Auction
Chapter 1
Auctions
The winning bids in both auctions is the reservation price of the second highest bidder
Private Value Auction
Chapter 1
Auctions
Sealed-bid auction
First-price auction: lowers the bid
Second-price auction: bid just above the second highest reservation price
Both yield the same revenue
Private Value Auction
Chapter 1
Auctions
Winner’s Curse
The winner is worse off than those who did not win
Common Value Auction
Chapter 1
Auctions
Examples
Bidding on a construction job
Bidding on offshore oil reserves
Common Value Auction
Chapter 1
Auctions
Question
How can you avoid the winner’s curse?
Common Value Auction
Chapter 1
Auctions
Private-value Auction
Have as many bidders as possible
Common-value Auction
Use open-bid format
Release information about value
Maximizing Auction Revenue
Chapter 1
Internet Auctions
A Few Caveats
Now quality control function
Poor seller feedback
Bid manipulation may occur
Chapter 1
Summary
A game is cooperative if the players can communicate and arrange binding contracts; otherwise it is noncooperative.
A Nash equilibrium is a set of strategies such that all players are doing their best, given the strategies of the other players.
Chapter 1
Summary
Some games have no Nash equilibrium in pure strategies, but have one or more equilibria in mixed strategies.
Strategies that are not optimal for a one-shot game may be optimal for a repeated game.
In a sequential game, the players move in turn.
Chapter 1
Summary
An empty threat is a threat that one would have no incentive to carry out.
To deter entry, an incumbent firm must convince any potential competitor that entry will be unprofitable.
Bargaining situations are examples of cooperative games.
Chapter 1
Summary
Auctions can be conducted in a number of formats which influence the revenue raised and the price paid by the buyer.
Chapter 1
End of Lecture 13
Game Theory and Competitive Strategy
Chapter 1
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