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\noindent
 11 November 2005.   Eric Rasmusen, Erasmuse@indiana.edu.
Http://www.rasmusen.org.


\begin{LARGE}
\begin{center}
 {\bf  US Air for Sale:  A Classroom Game for  Chapter 4}
 \end{center}
 \end{LARGE}


        On October 2, 1995, USAir, at the time  the nation's fifth largest
airline, announced that it had approached United Airlines and American Airlines
about a possible buyout.  United and American are the two largest U.S. airlines,
and both are interested in growth in the highly competitive airline market.
United and American must  now consider    what to do.

  Financial analysts for both United and American have made projections for all
the possible scenarios, on the request of the strategic  bidding consultants.
They say that United and American start in equally strong positions, but that
can change depending on who wins the auction.

  The three possible outcomes for an airline   are:


 \noindent
 {\it Neither firm bids enough for US Air to accept.} Both United and American
will maintain their strong positions, and they can expect future profits of \$50
billion each.

 \noindent
 {\it Our airline wins.}  The winning airline will become the dominant firm in
the market, and  can expect future profits of \$80 billion. The purchase cost of
US Air, however, must be subtracted from this in order to calculate net profit.
Therefore, the payoff for the firm with the winning bid is
 $$
 Payoff_{Winner}= 80 - B_{winning}.
 $$
  The minimum price US Air will accept is \$10
billion.

 \noindent
 {\it Our airline loses.} The losing firm may have trouble competing with the
larger network of the winner because of the greater variety of flights a large
airline can offer. The more, however, that the winner pays for US Air, the
better off is the loser, because the cash flow  the winner uses  to pay for the
acquisition is no longer available for other investments in new equipment and
lenders will be more reluctant to lend to the   newly enlarged firm.    The
analysts suggest that a good approximation to the payoff of the losing firm will
be
  $$
 Payoff_{Loser}= 30 + .25*B_{winning}.
 $$
   In particular, if the winner pays just \$10 billion for US Air, the loser's
profit will be  \$32.5 billion.

   \noindent
  We will look at two kinds of auction rules: ascending, and first-price.

   \noindent
{\bf  First-Price  Auction Rules:}    US Air will solicit  bids in writing from
anyone who cares to bid.  Once all bids are received, they will be announced
publicly.   If there is just one bid, it wins if it is \$10 billion or above. If
there are no bids, US Air will continue as an independent firm.   If there are
two bids, and  at least one is  \$10 billion or above,  the winner has purchased
US Air, ties being broken   by the flip of a coin.

 \noindent
{\bf  Ascending Auction Rules:}    US Air will solicit initial bids in writing
from United and American, choosing the first bidder randomly and announcing
its bid  publicly before asking  the other for a written bid.
   If there are no written bids of at least 10 billion dollars, US Air
will continue as an independent firm.   If there is at least  one bid of 10
billion dollars or above,  US Air  will allow   counteroffers, and an  ascending
auction commences.  The winner has purchased US Air.

 Students playing the game will be put into groups of three representing either
United or American. Groups will be paired up to play out the auction under the
ascending or first-price rules. First, play all the pairs  by the first-price
rules, then by the  ascending rules.




\newpage


 \bigskip
\noindent
{\bf Instructor's Notes   }

This case
was
developed by John Maxwell for G570 at Indiana University, following an
idea  of Patrick Meister and Kyle Anderson. See    J. Patrick Meister \&
Kyle J. Anderson, ``Lessons from a Failed Airline
Auction,''  forthcoming, {\it Economic Inquiry}, 2005.

 The     equilibrium of the first-price auction is for each player to bid  \$40
billion. Then,
    $$
  Payoff_{Winner}= 80 - 40 =  Payoff_{Loser}= 30 + .25*40 = 40.
 $$
 A deviation to 50 would win, but yield a payoff of only 30. A deviation to 30
would not affect the payoffs, since the other player would win with his bid of
40.




  In the  equilibrium of the ascending auction,  both
players  make  initial
bids  of less than \$10 billion, and the auction ends. The equilibrium payoffs
are  \$50 billion each. A player's optimal strategy is to make some amount less
than 10 his initial bid, but to bid higher if someone has placed an initial bid
of 10 or more, and then to bid up to 40.

 What commonly happens, though, is that some player starts by submitting a bid
of \$10 billion. Once that happens, the other player enters the bidding, and the
price rises all the way to 40.

 Note that if the  ascending auction were to be started with simultaneously
submitted written bids, there would be multiple equilibria. One equilibrium, a
pareto-dominant one,  would be to submit bids of less than \$10 billion, as
before.  Another  class  of  equilibria would be  for both players to submit
bids of between \$10 and \$40 billion, inclusive of those limits. Given that
United believes that American is going to submit a bid of \$12 billion, for
example, United thinks the auction is going to proceed all the way up to 40, and
its initial bid hardly matters.   These would be  weak equilibria, in weakly
dominated strategies, though.  If there is even an $\epsilon$ chance that
American will bid less than \$10 billion at the start, United should submit a
bid of less than \$10 billion too.




On the next page I have put some news excerpts that you should show the class
after the discussion is over. I have put them on a separate page  so you can
make this into an overhead slide or a handout.

 \newpage
\begin{Large}
\begin{center}USAIR NEWS\end{center}
\noindent
 {\bf October 15, 1995:  } ``The other suitor is AMR Corp.'s American Airlines,
which also is considering a bid either to purchase the airline or possibly
create a marketing arrangement that would pump cash into financially strapped
USAir in exchange for an instant major East Coast feed to American's
international operations.

\noindent {\bf  Crandall's Response:} AMR Chairman Robert L. Crandall would not
comment directly on American's potential interest in USAir. `I have said in the
past that the most effective way for an airline to grow is internally,' Crandall
said last week. "What I have not said and will not say today is what I would do
if others made the first step." He strongly emphasized `others.' '' ({\it The
Washington Post}, p. HA1)

\noindent {\bf November 14, 1995: } ``After more than a month of speculation
about a possible merger with United Airlines, USAir will remain independent.

   United's board of directors, facing difficulties convincing the airline's
unions and unable to meet their own criteria, yesterday declined to bid for
Pittsburgh's largest employer and ended merger discussions. A buyout could have
cost thousands of jobs in the Pittsburgh region.

   Analysts said the United decision and a statement by American Airlines that
it would not make a bid unless United moved first effectively ensures USAir's
independence for the near future. American last night reiterated its statement
but would not comment further.'' ({\it Pittsburgh Post-Gazette}, Bus. A1)

 For the full articles in ascii, go to  \\
http://rasmusen.org/GI/problems/04.usair.15oc95.txt and \\
http://rasmusen.org/GI/problems/04.usair.14nov95.txt.

\end{Large}


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