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.

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 Pepsi’s.

The country is at war, but remains segregated along racial lines, with blacks economically and socially disadvantaged.

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

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.

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?

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?

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.

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.

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.

The choice labor faces

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.

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.

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.

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.

The first rule of strategy: Backward induction

A follower’s 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.

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.

A further reduction

Taking expected values we are left with a very simple game tree.

Cheetah should stay out, and Eagle should enter.

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.

Air service -redrawn

The game is equivalent to the picture on the right.

Both firms must move before the state of demand is revealed.

Air service – further reduction

Taking the expectation over the payoffs yields a further simplification.

Now Cheetah will enter confident that Eagle will stay out.

Philips and Sony compete in the introduction of CD playersIn 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.

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.

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.

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.

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.