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Introduction to practical Game Theory and its corporate applications

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Opening Experiment

- Each of you give me one buck;
- Each of you pick one number between 1 and 100. Then we take the average of all the numbers you pick, and multiple it by 60% and get number X;
- Whoever picks the number that is closest to this number X will get all the money.

An example of irrationality in reality

- Rationality is a foundation assumption for Game Theory
- If one is rational, he would assume everyone start with 50, the average between 1 and 100. So he will further reason that the final number will be 30 - however, if every one is thinking the same way, everyone will pick 30, so the final number should be 18… then he continue to think in this way again and again until he picks zero - the equilibrium point!
- However, that’s never the case in reality - in group experiments, the final number that appears most often is around 17, given a large enough sample size.
- Actual outcome depends on how smart the group is, or how smart (stupid) the group thinks their peers are;

Agenda

- Game Theory in Definition
- Game Theory in Illustration
- Game Theory in Application

Agenda

- Game Theory in Definition
- Game Theory in Illustration
- Game Theory in Application

What is Game theory? - many definitions, but you got the point

- Study of rational behavior in situations involving interdependence. (McMillan, economist)
- A formal way to analyze interactions among a group of rational agents who behave strategically (Dutta, economist)
- In war the will is directed at an animate object that reacts (Karl von Clausewitz, general)

Key elements of a game we will visit many times in today’s discussion

- Assumption for players
- Rationality (not doing crazy things)
- Self-interested (to maximize own utilities)
- The strategic environment
- Who are the players? (decision makers)
- What actions are available? (strategic options)
- What are the payoffs? (objectives)
- Rules of the game
- What is the time frame? (Repeat game vs. one-shot interaction)
- What is the nature of the interaction? (sequential vs. simultaneous)
- What information are available? (symmetric vs. asymmetric)
- What’s the nature of the conflict? (seriousness and players’ posture)

Game theory is everywhere - Economics & Business

- “Game theory is hot!” - Wall Street Journal, 13 February 1995, P. A14
- Auctioneer and bidders, such as in FCC Spectrum auctions in 1993 where government employed a game theory professor to design auction methods ;
- Labor union negotiation with employer & repeated game;
- Negotiation between buyer and seller;
- Airlines’ price wars & tacit collusion;
- Timing of launch of new products in IT industry;
- Evaluation in merger and acquisitions & winner’s curse;
- Insurance companies vs. the insured & asymmetric information;
- Others ...

Game theory is everywhere - Beyond Economics & Business

- Presidential election
- International relations
- Office politics
- Dating strategies
- War
- Sports games
- Recruiting
- Everything...

Game theory is everywhere - Even hot in Pop Culture these days

- John Nash & Nash equilibrium
- 2001

- Prisoner’s dilemma
- 2002

- Game of chicken
- 2000

Agenda

- Game Theory in Definition
- Game Theory in Illustration
- Game Theory in Application

Prisoner’s dilemma - the classic game as a example throughout our discussion

A

Confess

Don’t

Don’t

3, 3

5, -5

B

Confess

-5, 5

0, 0

- Player: A & B;
- Payoffs: (a, b);
- Strategies: (don’t confess, confess)

Nash Equilibrium

- Nash equilibrium
- For every game, there exists at least one set of strategies, one for each player, such that each player’s strategy is best for her given that all other players are playing their equilibrium strategies
- key condition
- No incentive to unilaterally change my strategy
- The strategies employed can be mixed strategies
- A byproduct theorem by Nash in his proof using Topology
- For every human head, there exists at least one swirl.

Prisoner’s dilemma - the equilibrium is not necessarily the best payoffs

Person A

Confess

Don’t

Don’t

3, 3

5, -5

Person B

Equilibria

Confess

-5, 5

0, 0

Agenda

- Game Theory in Definition
- Game Theory in Illustration
- Game Theory in Application

Conventional business strategy focuses on understanding the static environment

- Who are the players?
- What strategic options are available?
- Who are the payoffs and objectives?

“3 Cs”

“Porter’s

5 forces”

“Core

Competence”

Others...

Game theory driven strategy formulation focuses on Dynamics and Change the Rules

- What’s the nature of the conflict? (seriousness and players’ posture)
- What is the nature of the interaction? (sequential vs. simultaneous)
- What is the time frame?

(Repeat game vs. one-shot interaction)

- What information are available? (symmetric vs. asymmetric)

- Game of Chicken
- Game of Assurance
- Game of Collusion
- Winner’s Curse

Good news: all of these rules can be changed, manipulated or influenced to our advantage

I. Change the nature of the conflict - Game of Chicken

Incumbent

Fight

Accommodate

Equilibria

Don’t Enter

10, 0

10, 0

Potential entrant

Equilibria

Enter

5, 5

-5, -5

Commitment and posture matters – Perception Is Reality

- Two Equilibria exist - but incumbent wants the equilibrium of (10, 0)
- To achieve this Equilibria, incumbent needs to convince that he will fight to death if entrant enters
- Ways of convincing the rival:
- Serious commitment such as preemptively building extra capacity in manufacturing and airline industry;
- Perception of being “tough” - bluff, PR, advertising, and etc;
- Historical behaves to make credible threats

A real event...

Radio conversation released by the Chief of Naval Operations, 10-10-95. #1: Please divert your course 15 degrees to the North to avoid a collision.#2: Recommend you divert YOUR course 15 degrees to South to avoid a collision. #1: This is the Captain of a US Navy ship. I say again, divert YOUR course.#2: No. I say again, you divert YOUR course. #1: THIS IS THE AIRCRAFT CARRIER ENTERPRISE, WE ARE A LARGE WARSHIP OF THE US NAVY. DIVERT YOUR COURSE NOW! #2: This is a lighthouse. Your call.

II. Change the timing of the conflict - Game of Assurance

Firm A

(Market Leader)

Promote/Invest new standard/product

Don’t

Equilibria

Don’t

5, 5

0, 5

Firm B

Equilibria

Promote

5, 0

10, 10

Leadership and first move matters – snowball effect in industry standardization

- Two Equilibria exist – “Invest & promote” is best for all but very risky
- Ways of getting to the ideal equilibrium (10,10):
- Market leader must commit first and make the initial move, rather than waiting for everything to happen at the same time;
- Turn simultaneous game into sequential game, and minimize uncertainty

Example: IP over voice, Java based banking and etc – all are new standards and risky today given still premature technology and services;

Do you have the right to influence the equilibrium?

Game in extensive form to demonstrate a sequential move

(10, 10)

Invest

B

Don’t

Invest

(0, 5)

A

Leader

Don’t

(5, 0)

Invest

B

Don’t

(5, 5)

III. Change the interaction of the conflict - Game of Collusion

Airline A

don’t

cut price

Repeated learning and cooperation process

don’t

(5,5)

(10,-5)

Airline

B

Equilibria

cut

price

(-5,10)

(0,0)

Airline A

don’t

cut price

don’t

(5,5)

(10,-5)

Stable

Point

Airline

B

cut

price

(-5,10)

(0,0)

Repeatability and punishment matters – tacit collusion in industry “co-petition”

- A variation of prisoner’s dilemma
- One mutually damaging Equilibria exists
- How to avoid it?
- Ways of getting to the optimal equilibrium (5,5):
- Signaling: announce commitment of price level through press and advertising;
- Punishment: if A cuts price in period 1, B will cut prices in the next 3 periods in a row no matter what A does;

Example: card issuers undercut each other though 0% APR, fee waiving and other measures - are there any ways that you can slow down this path to non-profitability??

IV. Change information flow of the game - Winner’s Curse

- What is winner’s curse?
- Lack of information or asymmetry of existing information on the bidder or buyer side make the winner actually a loser
- Examples
- Auction
- Merge & Acquisition
- LBO
- Others

Winner’s Curse in action - one example in bidding

- In dotcom heydays, brick & mortar A, as one of the bidders, wants to acquire Internet startup B of the same industry, with assumed 50% added synergy generation;
- You know, accurate evaluation is almost impossible here: in A’s assessment, the highest potential value is $100MM and the actual outcome could be evenly spread between 0 and $100MM;
- So A bid $50MM and won -- a perceived total value of $50MM*(1+50%)=$75MM;
- But in fact B wouldn’t sell itself unless offer is equal to the highest potential it feel it can reach; So the highest actual value of the acquisition is $25MM*(1+50%)=$37.5MM, far below the prices A pays for!

An example of how to avoid Winner’s Curse

- Before 1960s, American oil companies who won the drilling right in certain area always later found themselves in the business of losing money;
- After 1960s, American oil companies who participated in bidding:
- always only offer a fraction (0.65 ~ 0.75) of their estimated value in bidding for overseas drilling rights
- spend money in testing in adjacent fields;
- those who see critical strategic benefit in certain fields took out full-page ads to signal their intention so others stayed out;

Example: how should we gather and benchmark information to make right decision in acquisition and vendor selection?

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