Lecture 1B Perfect Information

1
Lecture 1BPerfect Information

• In games of perfect information players take
  turns making their moves, knowing what the
  players who have moved before them have chosen.
  Every perfect information game has an extensive
  form in which all the information sets are
  singletons. There are no dotted lines joining
  nodes. Thus all the strategic interactions are
  sequential.

2
Pepsi versus Coca Cola

• After struggling through the Great Depression of
  the 1930s Pepsi finds its soft drink sales are
  stalled in the 1940s.
• Coke is the industry leader, and its products
  command a premium price over Pepsis.
• The country is at war, but remains segregated
  along racial lines, with blacks economically and
  socially disadvantaged.

3
Who are the main players in this episode?

• Pepsi shareholders
• Coke shareholders
• Management at Pepsi
• All-black sales team working in Pepsi
• White cola demanders
• Black cola demanders

4
What options or choices face the main players?

• Pepsi could target its product line to African
  American consumers, Pepsi could target a new
  product line to African American consumers, or
  Pepsi could pursue another strategy, such as
  expanding its operations in Canada.
• Coke could respond aggressively or passively to
  any marketing initiative taken by Pepsi.
• White consumers might be alienated by a marketing
  campaign that targets African American consumers.

5
How do the players evaluate the consequences of
their choices?

• If Coke responds to an advertising campaign both
  firms will sell more cola in return for lower
  profits.
• If Coke does not respond to Pepsi, how much value
  will be added or lost to each company?
• If the white community is alienated by both
  companies targeting the African American
  community, would Coke be hurt more than Pepsi?

6
Where are the sources of uncertainty in this
unfolding drama?

• Will white cola drinkers be alienated by the
  introduction of a marketing campaign that targets
  the African American community?

7
Answering the four critical questions in an
extensive form game

• If both companies target blacks, the probability
  of alienating whites is higher than if only Pepsi
  does.
• Moreover as the company with the bigger white
  market share, Coke has more to lose in this case.

8
Day labor

• In Los Angeles and other places employer
  contractors routinely hire workers directly off
  the street for a fixed wage for the day.
• Contractors can offer different salary rates to
  laborers, but they cannot directly control the
  level of effort their laborers work.
• Contractors would prefer to extract strenuous
  effort from laborers for low wages, but laborers
  prefer the opposite, high wages and low effort.

9
Employment and effort

• In this game a laborer is willing to give up 8 a
  day to provide moderate rather than strenuous
  effort, and a further 6 in return for low
  effort.
• The employer is willing to pay 88 to extract
  strenuous rather than moderate effort, and loses
  a further 66 if the worker puts in low versus
  moderate effort.

10
The choice labor faces
11
Reduced game for the employer

• The solution to this game explains why most
  employment is not contracted in this fashion.
• In 45-976 we examine strategic interactions
  within the workplace in greater depth.

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Regional markets

• A prominent feature of geographically based
  markets, such as personal services, retailing,
  distribution, and travel is that the regional
  markets overlap.
• Thus competition in one market can spill over
  into the next, creating a cascading effect.
• Perhaps nowhere is this more evident than in the
  airline industry.

13
Airline pricing cascades

• In this example, American competes with Delta,
  Delta also competes with United, United competes
  with Delta, and US Airways, while US Airways only
  competes with United.
• Thus the payoff to US Airways is unaffected by
  rivalry between American and Delta.

14
The first rule of strategy Backward induction

• Sometimes called a rollback equilibrium the
  principle of backwards induction shows how finite
  games of complete information can be solved.
• Rule 1 Look ahead and reason back.

15
A followers advantage

• Through orders bookings and sales, first entrants
  typically learn about potential demand earlier
  than later entrants.
• If these data cannot be kept confidential, then
  followers can use the data.
• Over on the right we see that Eagle decides
  whether to enter or not, only after seeing what
  Cheetah has done and the effects on demand.

16
Folding back and simplifying the game tree

• If Cheetah begins an air service then Eagle will
  enter only if demand is high.
• If Cheetah does not create the service, then
  Eagle will not get the information on demand.
• In that case we can exchange the order of the
  moves of Eagle and nature.

17
A further reduction

• Taking expected values we are left with a very
  simple game tree.
• Cheetah should stay out, and Eagle should enter.

18
The value of withholding data on demand

• Now suppose Cheetah can prevent Eagle from having
  access to data on the profitability of its new
  route.
• In this case Eagle can see whether Cheetah
  entered or not, but not the state of demand.

19
Air service -redrawn

• The game is equivalent to the picture on the
  right.
• Both firms must move before the state of demand
  is revealed.

20
Air service further reduction

• Taking the expectation over the payoffs yields a
  further simplification.
• Now Cheetah will enter confident that Eagle will
  stay out.

21
Philips and Sony compete in the introduction of
CD players

• In 1982 Philips could commit immediately to
  building a CD processing capacity in the US or
  postpone its decision and continue to import from
  Europe.
• Philips knew its leading competitor, Sony, might
  enter if Philips postponed its decision, but that
  Sony would become informed about demand before
  Philips.
• The numbers are taken from a study by A. M.
  McGahan 1994.

22
An alternative representation of the Philips
Sony CD production

• This is a perfect information game because we can
  exchange the order in which Sony and popular
  buyers move.
• Using the first rule one can prove that Philips
  should wait, and then build (if demand is high),
  because Sony will stay out.

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Silicon valley circa 1996

• Just after TCPIP protocol was settled, a euphoria
  enveloped programmers and investors, who thought
  the internet would turn the world into a global
  village.
• Notice that in this game the venture capitalist
  has the same information as the innovator.

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The extensive form redrawn

• Redrawing the same game to reflect the
  uncertainty of both parties, we see that this is
  a perfect information game.
• If 10p 2(1-p) 5, that is p 3/8, then the
  innovator should request funding, and the venture
  capitalist should fund the project.
• Otherwise the innovator should ignore the
  opportunity.

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Lecture summary

• We discussed how to take a business situation and
  put it in a form amenable to strategic analysis.
• We derived our first rule of play. In perfect
  information games look ahead and reason back.
• We showed that there are many games that have
  perfect information, although it may not appear
  that way at first.