Game Theory: The Competitive Dynamics of Strategy

David Bryce © 1996-2002Adapted from Baye © 2002

Game Theory: The Competitive Dynamics of Strategy

MANEC 387MANEC 387Economics of StrategyEconomics of Strategy

David J. Bryce


The Structure of Industries

Competitive Rivalry

Threat of newEntrants

BargainingPower of

Customers

Threat ofSubstitutes

BargainingPower of Suppliers

From M. Porter, 1979, “How Competitive Forces Shape Strategy”


Competitor ResponseConcepts from Game Theory

• Sequential move games in normal form– Simultaneous vs. sequential move games –

hypothetical Boeing v. McDonnell-Douglas game (bullying brothers)

• Sequential move games in extensive form– Backward induction– Subgame-perfect equilibria


Fundamentals of Game Theory1. Identify the players2. Identify their possible actions3. Identify their conditional payoffs from

their actions4. Determine the players’ strategies – My

strategy is my set of best responses to all possible rival actions

5. Determine the equilibrium outcome(s) – equilibrium exists when all players are playing their best response to all other players


Simultaneous-Move Bargaining

• Management and a union are negotiating a wage increase

• Strategies are wage offers & wage demands• Successful negotiations lead to $600 million

in surplus, which must be split among the parties

• Failure to reach an agreement results in a loss to the firm of $100 million and a union loss of $3 million

• Simultaneous moves, and time permits only one-shot at making a deal.


The Bargaining Game in Normal Form

UnionM

anag

emen

t 500 -3 -3 100 -100 -100

-3 300 -3-100 300 -100

-3 -3 100-100 -100 500

W=$10 W=$5 W=$1W

=$10

W=$

5W

=$1

*

*

*


“Fairness” – the Natural Focal Point

UnionM

anag

emen

t 500 -3 -3 100 -100 -100

-3 300 -3-100 300 -100

-3 -3 100-100 -100 500

W=$10 W=$5 W=$1W

=$10

W=$

5W

=$1

*

*

*


Lessons in Simultaneous-Move Bargaining

• Simultaneous-move bargaining results in a coordination problem

• Experiments suggests that, in the absence of any “history,” real players typically coordinate on the “fair outcome”

• When there is a “bargaining history,” other outcomes may prevail


A Sequential Game - Single Offer Bargaining

• Now suppose the game is sequential in nature, and management gets to make the union a “take-it-or-leave-it” offer

• Write the game in extensive form – Summarize the players – Their potential actions – Their information at each decision point – The sequence of moves and – Each player’s payoff


M

10

5

1

Step 1: Management’s Move


Accept

Reject

Step 2: Append the Union’s Move

M

10

5

1

Accept

Reject

U

U

Accept

RejectU


100, 500

-100, -3

300, 300

-100, -3

500, 100

-100, -3

Step 3: Append the PayoffsAccept

Reject

M

10

5

1

Accept

Reject

U

U

Accept

RejectU


100, 500

-100, -3

300, 300

-100, -3

500, 100

-100, -3

Multiple Nash EquilibriaAccept

Reject10

5

1

Accept

Reject

Accept

Reject

*

M

U

U

U

*

*


Step 7: Find the Subgame Perfect Nash Equilibrium Outcomes• Outcomes where no player has an incentive

to change its strategy at any stage of the game, given the strategy of the rival, and

• The outcomes are based on “credible actions;” that is, they are not the result of “empty threats” by the rival.


• Final player chooses the option that maximizes her payoff

• The previous player chooses the option that maximizes his payoff conditional on the expected choice of the final player, and so on

• This is backward induction – work backward from the end “sub-game,” each player makes optimal choices assuming that each subsequent rival chooses rationally

• The equilibrium is called sub-game perfect

Sequential Strategies in the Game Tree


Only One Subgame-Perfect Nash Equilibrium Outcome

100, 500

-100, -3

300, 300

-100, -3

500, 100

-100, -3

Accept

Reject10

5

1

Accept

Reject

Accept

Reject

M

U

U

U*


Re-Cap• In take-it-or-leave-it bargaining, there is a

first-mover advantage.• Management can gain by making a take-it

or leave-it offer to the union. • Management should be careful, however;

real world evidence suggests that people sometimes reject offers on the the basis of “principle” instead of cash considerations.


Moroni, Zarahemna and Credible Threats

MSpare

Attack

-200

-50

200

-150

MSpare 100

-100

0

-200Z

Deliver/Oath

Don’t Deliver

Payoffs

Attack

*

See Alma 44, Book of Mormon

(or Bush, Saddam and those pesky WMDs)


Moroni – Zarahemna and Credible Threats

MSpare

Attack

-200

-50

200

-150

MSpare 100

-100

0

-200

Z

Take Oath

Don’t Deliver

Payoffs

Attack

*Z Don’t Take

MSpare

Attack

Deliver

?100

-175 -100

See Alma 44, Book of Mormon


Summary and Takeaways• The reasoning of game theory supplies

a useful way to predict the outcome of competitive interactions

• By diagramming a game, players can identify their best potential strategies

• Threats of retaliation must be credible• Incumbents may be able to deter

entrants by making major strategic commitments (credible threats)

Game Theory: The Competitive Dynamics of Strategy

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