Firm behavior in concentrated market

structuresOutline

•The prisoner’s dilemma

•Advertising rivalry

•Bundling

•Mixed bundling

•Tying

Game theory

Game theory is useful for illustratingthe principle of seller interdependence

and also for analyzing the behaviorof firms in tightly concentrated

market structures

Prisoner’s dilemma

Ralph and Gertie have been charged with bank robbery. But lacking a confession,

the DA can only get a “recklessendangerment” charge to stick. So the

police play one suspect off against the other.

Let’s make a deal

OK, Ralph. Confess,rat on Gertie, and you get a

reduced sentence of one year in prison.

What will Gertie do?

The payoff matrix

StayMum

Confess

StayMum

2 years, 2 years

8 years, 1 year

Confess 1 year,8 years

5 years,5 years

Ralph

Gertie

Confess is the dominantstrategy in this case,

since it gives the shortest sentence irrespective of whether the other prisoner

selects the “confess” or “stay mum” strategy

Dominant strategy

A dominant strategy yields the best possible payoff for any strategy selected by the other player(s).

6 years for Ma1 year for Pa

4 years for Ma2 years for Pa

8 years for Ma0 years for Pa

5 years for Ma3 years for Pa

Confess

Confess

NotConfess

NotConfess

Pa

Ma

Ma has “1st mover” advantage. Does this game have a predictable outcome?

Price wars in a duopoly

The preceding is what we call a “non-cooperative” game.

Cooperation among duopolists is a strategy that maximizes joint profits—as the Cournot model

will verify. So why do price wars break out?

The payoff matrix for a running shoe duopoly

HighPrice

LowPrice

HighPrice

$10 million,

$10 million

$5 million,$12 million

Low Price

$12 million,$5 million

$7 million, $7 million

REEBOK

NIKE

Notice that “low price” is the dominant strategy

Pizza Planet and Luigi’s are rivals in the market for home-delivered pizza. Each rival seeks to gain an advantage through advertising (product differentiation).

Advertising is presumed NOT to affect market demand--only market share.

Market share depends on the intensity of advertising relative to one’s rival.

Advertising rivalry

Let

P = $15

Q = 100 pizzas (market quantity-demanded)

AC (w/o advertising expense) = $5.

Hence:

/Pizza = (TR - TC)/Q = ($1500 - $500)/100 = $10

If neither seller advertises, each will sell 50 pizzas and earn a profit of $500. However, advertising could potentially increase sales to 75 pizzas.

Pizza Planet and Luigi’s may selecta “low” strategy (meaning a

$100 outlay for advertising) or a “high” strategy

($200 outlay for advertising)

The payoff matrix for a pizza duopoly

LowAdvertising

HighAdvertising

LowAdvertising

$400, $400

$150,$550

HighAdvertising

$550,$150

$300, $300

LUIGI’S

PIZZA PLANET

Notice that “high advertising” is the dominant strategy

Bundling

Bundling is the practice of selling two or more products as a package

•Cable TV companies (such as Cox Cable) bundle the Food Channel with CNN and ESPN.

•Lawn services bundle fertilizer service with weed killing service.

•Film distributors bundle “flops” with “hits.”

Bundling films

A distributor has 2 films to distribute (X and Y) to 2 theater chains, each of which has 500 multi-screen theaters.

Chain 1 is willing to pay up to $13,000 per screen per week for film X and $6,000 film Y.

Chain 2 is willing to pay up to $7,000 per screen per week for film X and $11,000 for film Y.

The differences are explained by regional variations in how films play.

We assume the distributor does not engage in price discrimination.

The incentive to bundle

TheaterChain Film X Film Y Bundle

Chain 1 $13,000 $6,000 $19,000

Chain 2 $7,000 $11,000 $18,000

The bundle column indicates the maximum amount each chain would pay per screen per week for a bundle containing films X and Y.

The results

•You can verify that, without bundling, the optimal price for film X is $7,000 and the optimal price for film Y is $6,000. The unbundled maximum revenue is:

R = ($7,000 1,000 screens) + ($6,000 1,000 screens) = $13,000,000

•You can also verify the distributor could maximize revenue from both films by bundling them at a price of $18,000 per week. The bundled revenue is given by:

R = ($18,000 1,000 screens) = $18,000,000

Mixed Bundling

Firms often offer customers the option to purchase products as a bundle or to buy them separately. This policy is called mixed bundling.•Now we add a third chain (with 500 multi-screen theaters) that attaches a low value to film Y (assume film Y is “Horror on Prom Night” and Chain 3 has a number of theaters in retirement communities).

•We now assume that the distributor has a marginal cost of $5,000—the cost of printing an additional copy of each film.

Mixed bundling options

TheaterChain Film X Film Y Bundle

Chain 1 $13,000 $6,000 $19,000

Chain 2 $7,000 $11,000 $18,000

Chain 3 $15,000 $2,000 $17,000

MarginalCost

$5,000 $5,000 $10,000

Mixed bundling resultsThe best “pure bundling” option is a price of $17,000. Profits () from this strategy are given by:

= ($17,000- $10,000) 1,500 screens = $10,500,000

You can verify that this strategy is superior to a price of $18,000, where Chain 3 is “priced out” of the the market.

The best “mixed bundling strategy” is to set a bundled price of $18,000 and a separate price of $15,000 for film X and $12,000 for film Y.

= [($18,000 - $10,000) 1,000 screens] +

[($15,000 - $5,000) 500 screens] = $13,000,000

Tying

Seller requires as a condition of sale of good X that the customer also buy good Y.

Good X is the “tying” product.

Good Y is the “tied” product.

The practice of tying allows a firm to leverage its

dominant position in the tying product to foreclose

the market in the tied product.

Examples of Tying

•Xerox copier leases required lessee to purchase all copying paper from Xerox.

•IBM once had a policy to give price quotes for “full line” systems only —i.e., CPUs and plug-compatible peripherals.

•Microsoft licensing agreements with Dell, Compaq, Gateway, and other PC makers stipulated that the Internet Explorer icon appear on the desktop after the initial boot up sequence. These licensing agreements created a barrier to entry into the browser segment (or so claimed the DOJ).

•International Salt tied industrial rock salt to the lease of salt dispensing machines.