- 87 Views
- Updated On :

Game Theory. Mike Shor Lecture 3. “Loretta’s driving because I’m drinking and I’m drinking because she’s driving.”. - The Lockhorns. Review. Understanding the game Noting if the rules are flexible Anticipating our opponents’ reactions Thinking one step ahead

Related searches for Game Theory

Download Presentation
## PowerPoint Slideshow about 'Game Theory' - nanette

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Game Theory

Cigarette companies fear lawsuits Companies strike agreement

Mike ShorLecture 3

“Loretta’s driving because I’m drinking and I’m drinking because she’s driving.”

- The Lockhorns

Review

- Understanding the game
- Noting if the rules are flexible
- Anticipating our opponents’ reactions
- Thinking one step ahead
- Where does this lead us?
- We’ve defined the “game” but not the outcome

Equilibrium

- The likely outcome of a game when rational, strategic agents interact
- Each player is playing his or her best strategy given the strategy choices of all other players
- No player has incentive to change his or her action unilaterally

- Outline:
- Model interactions as games
- Identify the equilibria
- Decide if they are likely to occur

Equilibrium Illustration

The Lockhorns

1970

Cigarette Advertising on TV- All US tobacco companies advertised heavily on TV
- Surgeon General issues official warning
- Cigarette smoking may be hazardous

- Government may recover healthcare costs

- Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits.

Strategic Interaction

- Players: Reynolds and Philip Morris
- Strategies: Advertise or Not Advertise
- Payoffs: Companies’ Profits
- Strategic Landscape:
- Each firm earns $50 million from its customers
- Advertising costs a firm $20 million
- Advertising captures $30 million from competitor

- How to represent this game?

What to Do?

If you are advising Reynolds, what strategy do you recommend?

Solving the Game

- Best reply for Reynolds:
- If Philip Morris advertises:
- If Philip Morris does not advertise:

Dominance

- A strategy is dominantif it outperforms all other choices no matter what opposing players do
- Games with dominant strategies are easy to play
- No need for “what if …” thinking

DominanceA Technical Point

- Strict Dominance:
Advertise is strictly dominant forReynoldsif:

- Profit (Ad , Ad) > Profit (No , Ad)
- Profit (Ad , No) > Profit (No , No)

- Weak Dominance:
Advertise is weakly dominant if:

- Some inequalities are weak (),
- At least one is strong(>)

- By “dominant” we will mean “strictly dominant”

Dominance

COMMANDMENT

If you have a dominant strategy, use it.

Expect your opponent to use her dominant strategy if she has one.

Prisoner’s Dilemma

- Both players have a dominant strategy
- The equilibrium results in lower payoffs for each player

Optimal

Equilibrium

Cigarette Advertising

- After the 1970 agreement:
- Cigarette advertising decreased by $63 million
- Industry Profits rose by $91 million

- Prisoner’s Dilemma
- An equilibrium is NOT necessarily efficient
- Players can be forced to accept mutually bad outcomes
- Bad to be playing a prisoner’s dilemma, but good to make others play

How to Win a Bidding War by Bidding Less? Current share price ≈ $60 Expected post-takeover share price ≈ $60 Macy’s offers $70/share Do you tender your shares to Macy’s?

- The battle for Federated (1988)
- Parent of Bloomingdales

- contingent on receiving 50% of the shares

How to Win a Bidding War (continued)

- Robert Campeau bids $74 per share not contingent on amount acquired
- Campeau’s Mixed Scheme:
- If less than 50% tender their shares, each receives:
$74 per share

- If more than 50% tender their shares, (if X% tender), each receives:

- If less than 50% tender their shares, each receives:

The Federated Game

- To whom do you tender your shares?

How to Win a Bidding War

- Each player has a dominant strategy: Tender shares to Campeau
- Resulting Price:
(½ x 74) + (½ x 60) = $67

- BUT: Macy’s offered $70 !

Dominant Strategies

“The biggest, looniest deal ever. ”

– Fortune Magazine, July 1988

on Campeau’s acquisition of Federated Stores

- What if players do not have dominant strategies?

Pricing without Dominant Strategies

- Two bars (bar 1, bar 2) compete
- Can charge price of $2, $4, or $5

- Customer base consists of tourists and natives
- 6,000 tourists pick a bar randomly
- 4,000 natives select the lowest price bar

- Marginal costs are close to zero

Tourists & Natives

- Example scenario:
- Bar 1 charges $4, Bar 2 charges $5
- Bar 1 gets:
3,000 tourists + 4,000 natives

= 7,000 customers x $4 = $28K

- Bar 2 gets:
3,000 tourists + 0 natives

= 3,000 customers x $5 = $15K

Successive Elimination of Dominated Strategies

- Does any player have a dominant strategy?
- Does any player have a dominated strategy?
- A strategy is dominated if there is some other strategy which always does better
- Eliminate the dominated strategies
- Reduce the size of the game
- Iterate the above procedure

- A strategy is dominated if there is some other strategy which always does better
- What is the equilibrium?

Dominance

CAVEAT

Expect your opponent to use her dominant strategy if she has one.

BUT

Be sure you understand your opponents’ true payoffs.

(Do you know what really motivates them?)

No Dominated Strategies

- Often there are no dominated strategies
- Some games may have multiple equilibria
- Equilibrium selection becomes an issue
- Method:
For each player, find the best response to every strategy of the other player

- Games of Coordination
- Games of Assurance
- Games of Chicken

Games of Coordination

- Joint ventures and supplier choice
- Two firms engaged in joint venture
- Must use the same supplier, but each firm has a preferred supplier

Firm 2

Games of Assurance

- Joint research ventures
- Each firm may invest $50,000 into an R&D project
- Project succeeds only if both invest
- If successful, each nets $75,000

Firm 2

The Right Game to Play

- Why do we “solve” games?
- To know which one to play!
- How do internal corporate changes impact the outcome of strategic interaction?

- Some games are better than others

Your Value to a Game Added value provides benchmark Change the Game!

- Your added value =
the size of the pie when you’re in the game

minus

the size of the pie when you are not

- Added value limits how much you can get
- You cannot receive much more than your added value

- You should receive close to your added value

- You can increase your payoffs by increasing your added value OR decreasing the added value of other players.

Capacity Constraints

- Can decreasing others’ added value increase our profits?
- Can decreasing total industry value increase our profits?

Summary

- Games have predictable outcomes
- Notice dominant & dominated strategies

- Select the right game to play
- Seemingly internal corporate changes can impact the outcome of strategic interaction

- Looking ahead:
- Sequential Games:
How do games unfold over time?

- Sequential Games:

Download Presentation

Connecting to Server..