So, if we go back to our initial question, is it a credible threat to
threaten British Airways to start a price war after entry?
We can answer it's not, because it would rely on sub-optimal behavior at some
point. So, Lufthansa of course knows this, and
they were thinking about changing their behavior somehow.
So, they commit now to a price war and they do it by signing a contract with
Star Alliance, specifying a penalty of 500 if Lufthansa do not start a price war
after Deutsche BA's entry. And the question we ask then is, is that
now a credible threat? Does it now make sense?
Does BA, Deutsche BA, now believe that Lufthansa would actually start a price
war? Well, again, let's have a look at the
game. And we know that if no contract is
signed, these are going to be the payoffs.
Now, If Lufthansa signs this contract, if they commit to this contractual penalty
of 500, what's going to happen?
It's going to change the payoffs if Lufthansa's not running a price war if
Deutsche BA enters the market. It's going to change it from 400 to minus
100. And so payoffs actually could become
worse once they sign a contract. However, what's the outcome of the game
then? Well, again, if we're looking for
for sub-game perfect Nash Equilibria, we have to look at this
sub-game. And within this sub-game, given the
contractual penalty, Lufthansa can now choose between not starting a price war
and making minus 100 or starting a price war and making zero.
So, for them now, the best response to Deutsche BA entering the market becomes
to start a price war. And if that is something that British
Airways can anticipate then British Airways will respond in
anticipation by not entering the market. So, the Nash Equilibrium now is
the second one and we would expect this one to be played.