Slide 12005 South-Western Publishing

• 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.

Game Theoretic Rivalry: Best Practice Tactics

Chapter 13

Slide 2

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 3

Simultaneous vs Sequential Games Table 13.1 page 550

• A Truck manufacturer and a retail truck dealership (with service repair trucks)

• Payoffs for the retail distributor are in the lower triangles

• Neither player has a dominant strategy

• If the truck manufacturer raises price, the best decision is to continue service of trucks a the retail dealerships

• If the truck manufacture doesn’t raise price, the best decision is to discontinue the service

• This shows that sequential decisions influence outcomes

Truck ManufacturerPrice Increase No Price IncreaseD

iscontinue Continue

Service

Serviceof Trucks

of Trucks

Retail Dealer

$0 $2,000

$5,000 $0

$0 $3,000

$2,000 $0

Slide 4

Game TreeAn 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 end-game reasoning, where we start with the final decision and use backward induction to find the best starting decision on the game tree.

Slide 5

Two Accountant Firms BidIllustrated 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.

If this pattern continues, the price could be driven too low for either firm

$200 $150

Alpha Matches $150

Alpha Cuts price to $100

Alpha wins bid

Omega wins bid

Slide 6

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 7

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 8

First Mover Games • Andrew Carnegie: The

first person gets the oyster, the second person gets the shell.

• Some markets are too small for multiple firms.

• First number in each pair is for firm A.

• Game with Military and Civilian markets for “water-land vehicles” (DUCKS).

Bcivilian military

Acivilian

military

-10, -10 30, 15

15, 30 -10, - 10

In a simultaneous game, both would want the civilian market. Butin a sequential game, the first to get the civilian market preempts it. The other firm takes the military market.

Slide 9

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 promise-giver 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 10

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 11

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 12

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 13

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 first-movers.» 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 14

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 15

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 16

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 17

Nash Equilibrium• When all players make their best reply responses (so changing their choices cannot improve their position) then the game is in a Nash Equilibrium.

• Royal Caribbean’s payouts are in the bottom triangles.

• The cooperative solution is for both to charge $450, but Carnival has a dominant strategy of charging $300

• Knowing this, Royal Caribbean also charges $300. The outcome is the Prisoner’s Dilemma again.

• {$300, $300} is a Nash Equilibrium

Carnival $450 $300

$275 $375

$350 $50

$60 $185

$320 $175

$450 $300

RoyalCaribbean

Slide 18

No Nash Equilibrium• 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• Both Coke and Pepsi have an

incentive to switch to a low price.• But {Low Price, Low Price} is not

an equilibrium, since both are better off switching to a high price.

• Coke and Pepsi may want to randomize their pricing

• Notice at your grocery store, that each week either Pepsi or Coke is on sale, but not both.

COKE High Price Low Price $13,000 $16,000

$12,000 $9,000 $10,500 $8,000

$14,000 $6,300

High Price Low

Price

PEPSI

Slide 19

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 20

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

FIRM 1

Small Output Large Output

Small Output

Large Output

100, 100 10, 150

150, 10 20, 20

Expect to reach cooperativesolution if:

100 + p 100 > 150 + p (20)or 80 p > 50 or p > 62.5%

Slide 21

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 22

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 23

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.