Game theory and competitor analysis

Paul C. Godfrey

Mark H. Hansen

Brigham Young University

Why should we care what competitors are doing?

• One firm’s changes always evoke responses by competitors – A feature of markets as systems

– Sometimes the response is to do nothing (rational or irrational)

• Game theory helps model rational behavior– Behavioral analysis helps model “irrational” behavior

– Fundamental knowledge of competitors helps understand likely responses

Game Theory

• Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others. Initially developed to analyze competitions in which one individual does better at another's expense (zero sum games), and expanded to where there are joint gains to cooperation (Wikipedia, accessed 12/08)

• Game theory has several key assumptions– The players are rational maximizers

– The players have full information about each other

– The payoffs are known

Game Theory

Simultaneous Games

Enter

Don’tEnter

Don’tEnterEnter

In-n-Out

Five Guys

200, 175

0, 300

325, 0

0, 0

Five Guys and In-n-Out aredeciding, at the same time,whether to enter the market

Is there a dominant strategy forFive Guys? In-n-Out?

Game Theory

Sequential Games

In-n-Out

Enter

Don’tEnter

0, 300

Five GuysFight

Accommodate

50, 150

150, 200

Five Guys is already in the market, In-n-Out is deciding whether to enter

The prisoners dilemma

• Two people are picked up by the police on suspicion of robbery and placed in separate cells. The evidence is sketchy and so the district attorney attempts to elicit a confession from each person separately. The district attorney presents each with the following payoff matrix, represented as years in jail.

• What will the accused persons do?

Player 2

Not Confess Confess

Player 1

Not Confess

1,1 5,0

Confess 0,5 3,3

The centipede game

There are two players, A & B, who alternate in making choices. That is, A makes the decision in round 1, B in round 2, and so on. In each round, the player must decide whether to end the game by moving down, or continue the game by moving across. Below each round is a payoff matrix, showing the points awarded to A & B if the game ends in that round. The objective of the game is for each player to maximize their own payoff.

The Centipede Game, Structure

Player A M P

Player B N Q

Decision Player

A B

1 2

The Centipede Game, 1

Player A 1 0

Player B 0 2

Decision Player

A B

1 2

The Centipede Game, 2

Player A 1 0 4 3

Player B 0 2 1 100

Decision Player

A B A B

1 2 3 4

The Centipede Game, 3

Player A 1 0 4 3 102 101

Player B 0 2 1 100 99 102

Decision Player

A B A B A B

1 2 3 4 5 6

The Ultimatum Game

• You are given $5. The condition for keeping the money is that you have to propose a split between you and the other player and the other player has to agree to your split. If he or she agrees, you split the money. If he or she refuses, neither of you get the money.

• What split will you propose?

So, what do these games teach us about competitive behavior?

Questions to Ask About Competitors

Future goals

At all levels of management

Assumptions

Held about themselves and industry

Current Strategy

How do they currently compete?

Capabilities

Where are they strong? Weak?