Game Theory: The Competitive
Dynamics of Strategy
MANEC 387
Economics of Strategy
David J. Bryce
David Bryce © 1996-2002
Adapted from Baye © 2002
The Structure of Industries
Threat of new
Entrants
Bargaining
Power of
Suppliers
Competitive
Rivalry
Threat of
Substitutes
From M. Porter, 1979, “How Competitive Forces Shape Strategy”
David Bryce © 1996-2002
Adapted from Baye © 2002
Bargaining
Power of
Customers
Competitor Response
Concepts 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
David Bryce © 1996-2002
Adapted from Baye © 2002
Fundamentals of Game Theory
1. Identify the players
2. Identify their possible actions
3. Identify their conditional payoffs from their
actions
4. 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
David Bryce © 1996-2002
Adapted from Baye © 2002
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.
David Bryce © 1996-2002
Adapted from Baye © 2002
The Bargaining Game in
Normal Form
Union
David Bryce © 1996-2002
Adapted from Baye © 2002
W=$10
W=$5
W=$1
Management
W=$10
W=$5
500
100*
-3
-100
-3
-100
-3
-100
300
300*
-3
-100
W=$1
-100
-3
-100
-3
100
500*
“Fairness” – the Natural Focal Point
Union
David Bryce © 1996-2002
Adapted from Baye © 2002
W=$10
W=$5
W=$1
Management
W=$10
W=$5
500
100*
-3
-100
-3
-100
-3
-100
300
300*
-3
-100
W=$1
-100
-3
-100
-3
100
500*
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
David Bryce © 1996-2002
Adapted from Baye © 2002
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
David Bryce © 1996-2002
Adapted from Baye © 2002
Step 1: Management’s Move
10
M
5
1
David Bryce © 1996-2002
Adapted from Baye © 2002
Step 2: Append the Union’s Move
Accept
U
Reject
10
M
5
Accept
U
Reject
1
Accept
U
Reject
David Bryce © 1996-2002
Adapted from Baye © 2002
Step 3: Append the Payoffs
Accept
100, 500
Reject
-100, -3
Accept
300, 300
Reject
-100, -3
Accept
500, 100
Reject
-100, -3
U
10
M
5
U
1
U
David Bryce © 1996-2002
Adapted from Baye © 2002
Multiple Nash Equilibria
Accept
U
Reject
10
M
5
Accept
U
Reject
1
Accept
U
Reject
David Bryce © 1996-2002
Adapted from Baye © 2002
100, 500 *
-100, -3
300, 300 *
-100, -3
500, 100 *
-100, -3
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.
David Bryce © 1996-2002
Adapted from Baye © 2002
Sequential Strategies in the
Game Tree
• 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
David Bryce © 1996-2002
Adapted from Baye © 2002
Only One Subgame-Perfect Nash
Equilibrium Outcome
Accept
100, 500
Reject
-100, -3
Accept
300, 300
Reject
-100, -3
U
10
M
5
U
1
Accept
U
Reject
David Bryce © 1996-2002
Adapted from Baye © 2002
500, 100 *
-100, -3
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.
David Bryce © 1996-2002
Adapted from Baye © 2002
Moroni, Zarahemna and Credible
Threats (or Bush, Saddam and those pesky WMDs)
M
Payoffs
0 100*
-200 -100
Z
200 -200
M
-150
See Alma 44, Book of Mormon
David Bryce © 1996-2002
Adapted from Baye © 2002
-50
Moroni – Zarahemna and Credible
Threats
Payoffs
0 100
M
-200 -100
Z
100
Z
?
M
-175 -100
200 -200
M
See Alma 44, Book of Mormon
David Bryce © 1996-2002
Adapted from Baye © 2002
-150
-50
*
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)
David Bryce © 1996-2002
Adapted from Baye © 2002