Game Theoretic Rivalry:
Best Practice Tactics
Chapter 9
• Greater attention in business is being given to tactics
and strategy to achieve competitive advantage.
• This chapter predicts rival firm behavior as if they
were games.
» Sometimes being the first-mover offers advantages.
» Sometimes credible threats affect opponents' behavior.
» In oligopolistic industries, the interdependence among
firms is most keenly felt.
2005 South-Western Publishing
Slide 1
Business Strategy Games
• When an oligopolistic rival alters its product or
pricing, our firm must react or adapt.
• Best would be proactive behavior that could
anticipate actions.
• A simultaneous game occurs when all players must
chose their actions at the same time.
• A sequential game is one in which there is an
explicit order of play.
» A sequential example is when one firm has
announced a price cut, your decision to respond or
not is sequential.
Slide 2
Simultaneous vs Sequential Games
Table 13.1 page 550
Discontinue
Service
of Trucks
• A Truck manufacturer and a
retail truck dealership (with
Truck Manufacturer
service repair trucks)
Price Increase No Price Increase
• Payoffs for the retail
distributor are in the lower
$0
$2,000
triangles
• Neither player has a
dominant strategy
$0
$3,000
• If the truck manufacturer
raises price, the best
Retail Dealer
decision is to continue
service of trucks a the retail
$5,000
$0
dealerships
• If the truck manufacture
doesn’t raise price, the best
$2,000
$0
decision is to discontinue
the service
• This shows that sequential
decisions influence
outcomes
Continue
Service
of Trucks
Slide 3
Game Tree
An Illustration of a Sequential Game
• A game tree is like a decision tree. It is a
schematic diagram of decision nodes.
• Solutions to games parallels board games
like chess.
• One way to solve a decision problem is to use endgame reasoning, where we start with the final
decision and use backward induction to find the
best starting decision on the game tree.
Slide 4
Two Accountant Firms Bid
Illustrated as a Sequential Game Tree
• Alpha & Daughters () is the incumbent auditor at $200
per hour.
• Omega & Sons () could bid the same or less (say $50
increment reductions) to unseat the incumbent in year 1.
Alpha Matches $150
$200
$150

Alpha wins bid
Omega wins bid
Alpha Cuts price to $100
If this pattern continues, the price could be
driven too low for either firm
Slide 5
Subgames in Game Trees
• Since game trees have several branches, we can examine
the concept of equilibrium in each part of the tree, called a
subgame
» example: If Alpha always matches any cut by Omega
(tit for tat style), this would be a “branch” or a subgame.
• When all players make their best reply responses then the
game is in a Nash equilibrium.
• Looking to the end-game, it may be that both offering $150/hour is
an equilibrium
• If keep cutting prices, this ends in losses.
» Optometrists, accountants, insurance, and other homogeneous
suppliers of services seem to recognize this.
» Avoid price wars through recognition of its outcome
Slide 6
Business Rivalry
as a Sequential Game
• The first to introduce a product, lower price,
etc., often achieves recognition and an
advantage, called a first-mover advantage.
• When games last several periods, the actions
by firms in one period can be punished or
rewarded in future period.
» If a new firm enters a market, the threat is that the
incumbent firm may drop prices down to levels that
are unprofitable.
Slide 7
First Mover Games
• Andrew Carnegie:
The first person gets
the oyster, the second
person gets the shell.
civilian
civilian
-10, -10
B
military
30, 15
• Some markets are too
A
military
15, 30
-10, - 10
small for multiple firms.
• First number in each pair
is for firm A.
In a simultaneous game, both
• Game with Military and
would want the civilian market. But
Civilian markets for
in a sequential game, the first to get
“water-land vehicles”
the civilian market preempts it. The
(DUCKS).
other firm takes the military market.
Slide 8
Credible Threats & Commitments
• A credible threat is a conditional strategy that is
perceived as a possible penalty in a noncooperative
game.
» Its existence sometimes induces cooperative behavior
» Example: If you cut your price, I will cut my price too! If
believed, the parties tend to avoid price wars.
• A credible commitment is a conditional strategy for
establishing trust by promising to make the promisegiver worse off by violating that trust
» such as a reward for good behavior in a noncooperative game.
» Example: If any of my products fail to work, I will pay the
buyer three-times their purchase price in recompense!
Clearly, this commitment makes the firm worse off if they sell
shoddy goods.
Slide 9
Mechanisms for credible threats
and commitments
• contractual side payments, but these may
violate antitrust laws.
• use of nonredeployable assets such as
reputation.
• entering alliance relationships which would
fall apart if any party violated their commitments.
• using a "hostage mechanism" that is
irreversible and irrevocable can deter breaking
commitments.
» Examples are "double your money back
guarantees," and "most favored nation" clauses.
Slide 10
Hostage Mechanisms
in Local Oligopolies
• Circuit City’s offer: If you find a lower advertised
price, you’ll get that money back
• ‘Double the Difference Price Guarantee as a credible commitment
• This makes Circuit City cut prices whenever local
TV stores cuts prices
» Local stores realize that they won’t undercut Circuit City
» Customers realize it is unlikely to find lower prices
» If potential entrants ( Best Buys, Silo, Freddy’s, etc.) think they
can get a foothold in area, they know that Circuit City’s pricing is
a credible commitment.
Slide 11
The Tactical Advantage of
Licensing and Leasing
• There is a tactical advantage in leasing and
renewal licenses between sellers of major capital
equipment and their customers.
• The renter fears that the equipment will become
quickly obsolete.
• The seller is in a better position to know what
changes are occurring in technology.
• A lease or license works for both parties in the
contract.
Slide 12
Entry Deterrence and Accommodation
• Building excess capacity deters entry. Potential entrants fear that
the price will be driven down to zero if they entered.
• The building of extra capacity is an action in a sequential game to
forestall entry. This is called a precommitment game.
• Customers may be inclined to buy from the newest firm or from
incumbent firms. Several customer-sorting rules include:
» Brand loyalty to incumbents ─ that favors incumbents and firstmovers.
» Efficient rationing – customers prefer low prices. This is favorable at
times to low-cost entrants.
» Random rationing – customers buy from incumbents or entrants
randomly, so long as the price is the same.
» Inverse intensity rationing – the most price sensitive customers buy
up all of the capacity of the low priced producers. An example might
be People Express airline that was the low price provider (now
defunct!) See Appendix 13A.
Slide 13
Theory of
Contestable Markets
• The theory of contestable markets holds that,
with no barriers to entry, even a monopolist must
be aware that charging higher prices will
encourage entry.
• Hence, a contestable market will tend to have
zero economic profits and competitive prices,
even if there are only a few firms.
• Potential entry (rather than number of firms)
matters most to the profitability of markets.
Slide 14
Brinksmanship and Wars of Attrition
• Brinksmanship is a strategy taken that threatens, unless
the other party concedes
» Unions threaten strikes, unless they attain the contract they
want.
» If they get what they want, the strategy works. But the results
can sometimes be disastrous for a union, if the firm or
government doesn’t budge
• Wars of Attrition occur in sequential games if firms drop
out as time goes on
» New product introductions lead to multiple firms competing.
As some lose money on their venture, they pull out.
» A slippery slope is the tendency for wars of attrition to generate
mutual losses that worsen over time.
» As each party ‘hangs tough’ losses mount for all firms.
Slide 15
Simultaneous Games
• A sealed bid auction is a simultaneous game.
Every bid is opened at the same time.
• A dominant strategy is the best decision, no
matter what anyone else does. It is an action
(strategy) that is better in each "state of the
world."
• When no Nash equilibrium exists, it is useful
to hide one's strategy by randomly changing
strategies. This is a mixed Nash equilibrium
strategy.
Slide 16
Nash Equilibrium
$450
• When all players make their best
reply responses (so changing
Carnival
$450
$300
their choices cannot improve
their position) then the game is in
a Nash Equilibrium.
$275
$375
• Royal Caribbean’s payouts are in
the bottom triangles.
$350
$50
Royal
• The cooperative solution is for
Caribbean
both to charge $450, but
$60
$185
Carnival has a dominant strategy
of charging $300
$320
$175
• Knowing this, Royal Caribbean
also charges $300. The outcome
is the Prisoner’s Dilemma again.
• {$300, $300} is a
Nash Equilibrium
$300
Slide 17
No Nash Equilibrium
High Price
• Some games have no Nash
Equilibrium.
• Pepsi’s payouts are in the bottom
triangles.
• The cooperative solution is for
both to charge a high price
COKE
High Price Low Price
• Both Coke and Pepsi have an
incentive to switch to a low price.
$13,000
$16,000
• But {Low Price, Low Price} is not
an equilibrium, since both are
$12,000
$9,000
better off switching to a high
PEPSI
price.
$10,500
$8,000
• Coke and Pepsi may want to
randomize their pricing
• Notice at your grocery store, that
$14,000
$6,300
each week either Pepsi or Coke is
on sale, but not both.
Low Price
Slide 18
Escape From Prisoner's Dilemma:
Repeated Games
• If the games are repeated, there is greater
expectation that firms will achieve the
cooperative solution.
• Each firm "shows" by its behavior each
period that it wants to cooperate.
• Firms that expand production "show" that
they do not want to cooperate.
Slide 19
Two Period Games
• Same duopoly payoffs as
before
• Probability, p, that the
game goes to period 2
• If keep small output both
periods, payoff is:
100 + p 100
• If produce a large output in
first period, payoff is:
150 + p (20)
• Therefore, the greater
probability that the game
continues, the more likely
it is for firms to cooperate.
FIRM 2
Small Output Large Output
Small Output
100, 100
10, 150
150, 10
20, 20
FIRM 1
Large Output
Expect to reach cooperative
solution if:
100 + p 100 > 150 + p (20)
or 80 p > 50 or p > 62.5%
Slide 20
Examples of
Repeated Game Strategies
• a grim trigger strategy which has an
infinitely long punishment.
• alternatively, the punishment can last for
a period.
• For multi-period games, there usually is
some period of punishment that can
induce cooperation.
Slide 21
trembling hand trigger
• For non-infinite lived games, if you are one period
before the end, the best strategy is to act
noncooperatively.
» Yet this logic works for two periods before the end, and
tends to unravel a cooperative, multi-period game.
• Some game theorists have wondered if the slight
defections could go unpunished, called a trembling hand
trigger strategy.
• If the rival acts noncooperatively once, perhaps you can
forgive. But fool me twice, and then watch out!
Slide 22
Other Strategies in Multi-period Games
• When games involve 3 or more players, coalitions of
players can "win" the game. These n-person games have
complex solutions.
• A tit-for-tat strategy can lead to cooperation. If two
cruise ship firms were competing on the price of
staterooms, one ship line could match the price
announced by the other. Each time the other cut its
price, the other would too. Soon the first cruise line
‘learns’ to pick a price that is best for both lines.
• A conspicuous focal point is an outcome that attracts
mutual cooperation.
» In a price war between Newsweek and Time, it may be that a
newsstand price of $3 per issue is best for both. If this is a
focal point, they may end up at this point.
Slide 23