So, hi everybody and we're almost through with the first unit.
In the previous videos, we've introduced the concept of sequential games.
In these games we have one player deciding first and another player
following with his or her decision. So, in this last video lecture for today,
we're going to look at whether the player who decides first has some sort of
strategic advantage and if he can influence the decision of
the second player to its favor. So, for this, lets have a look at the
market for domestic flights in Germany a couple of years ago.
So, within Germany, we had Lufthansa as a monopolist on domestic flights.
So, whenever you wanted to fly from Munich to Berlin then Lufthansa was the
carrier that you had to choose. And with deregulation, there came other
firms that were thinking about coming into the market.
And interestingly, these were not necessarily start-ups, but these were
also giants in other parts of the world. And British Airways, as one of the
largest airlines worldwide, also considered entering the market.
They did consider entering the market through a subsidiary called German BA, or
Deutsche BA. And of course, Lufthansa, having been a
monopolist for a long time, were not happy with this and threatened British
Airways to start a price war after entry. And so the question we're asking is if
this was a credible threat. Is this something that British Airways
should've believed when Lufthansa announced it?
So, let's try and represent this as a game and a sequential game in particular.
So, we have Deutsche BA deciding if they want to stay out of the market or if
they want to enter. At that point, the decision comes to
Lufthansa. If Deutsche BA stays out of the market,
then Lufthansa has nothing to do. They just carry-on as they did before.
If Deutsche BA enters the market, then Lufthansa has two choices.
They can either start a price war, as they've announced
or they can decide not to start a price war, so they just change their mind
and say well, we're going to keep prices as is.
And we're going to share the market with Deutsche BA.
Now again, let's have a look at some fictitious numbers for payoffs for Deutsche
BA and Lufthansa. If Deutsche BA does not enter the market,
and nothing changes for Lufthansa then Deutsche BA of course gains profits of
zero. Because nothing changes for them, and
Lufthansa make their monopoly profits, which we assume to be 1,000.
If Deutsche BA comes into the market, then, if Lufthansa starts a price war,
Deutsche BA makes losses of 500 and Lufthansa makes profits of zero.
If Deutsche BA enters and there is no price war then both share the market and
they get profits of 400 each. So, with this in mind let's revisit the
concept of a Nash Equilibrium. A Nash Equilibrium, as we know, is a
combination of two behaviors, one for each player, for which none of the
players has an incentive to deviate unilaterally.
So, that means that if we keep the other player's strategy as given, no player of
the two has an incentive to change what they're currently doing.
So, if we look at this game tree, let's try and find the Nash
Equilibria. The first one is going to be Deutsche BA
entering the market and Lufthansa not starting a price war.
Let's have a look. Well, if Deutsche BA has entered the
market, then Lufthansa can choose between starting a price war, getting profits of
zero, and not starting a price war and getting profits of 400.
So, if they choose whatever maximizes their profit, given the strategy of the
other player Deutsche BA, then it's best for them not to start a price war.
Now given that, Lufthansa does not start a price war, what's Deutsche BA's best
strategy? Well if they enter the market they get
profits of 400, if they stay out of market their going to get profits of zero.
So the best strategy given that Lufthansa does not start a price war is to enter
the market for BA. Okay?
So that's the first Nash Equilibrium that we found.
There is however a second Nash Equilibrium as well and that's this one
here. So let's have a look.
If Lufthansa starts a price war here, then Deutsche BA can
choose if they want to enter the market and make profits of minus 500 or if they
want to stay out and make profits of 0. So, their best strategy is not to enter
the market given that Lufthansa starts a price war.
How about Lufthansa? If Deutsche BA stays out of the market,
it doesn't even matter what Lufthansa does at this point.
So, they're indifferent between starting a price war and not starting a price war
because they get profits of a thousand anyway.
So, this is as good an answer as any. Meaning that there is no incentive to
change your behavior, given that Deutsche BA does not enter the market.
So, the second Nash Equilibrium is no market entry from Deutsche BA and a price
war from Lufthansa. So, which one of those is the one that we
believe more? Which one of those seems more rational,
more sensible somehow? Well, let's have a look at this part of
the game. We call this sub-game.
So, if Deutsche BA has entered the market, we're going to have to ask the
question, what's the best strategy for Lufthansa?
They can choose to start a price war and get profits of zero
or they can not start a price war and get profits of 400.
So, the profit maximizing behavior in this sub game is not to start a price
war which means that the second Nash
Equilibrium alright? The equilibrium based on the red lines
here, is not one that we would believe. Because Lufthansa does not behave
optimally at this point in this sub-game. So, in other words if we play the game we
would expect that Deutsche BA enters the market because they expect Lufthansa not
to start a price war if push comes to shove.
Because it's profit maximizing, it's optimal for Lufthansa to do that.
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.
So, to answer that question, does that contract serve as a credible threat?
Yes it does. So, British Airways should believe that
kind of threat, whereas they didn't believe the previous type of threat
because it was cheap talk. Okay, so to wrap up, what did we do in
this session? Well in this sessions we looked at a
sequential game again and we showed that commitment in a particular way,
can change the way the game is played.
And in particular for Lufthansa it was important, that they changed their
payoffs so that they don't play whatever they don't like
if a particular contingency arises. So, the contingency here was that British
Airways enters, and they sort of felt, well, we need to force ourselves to commit
to a price war. And they did that by signing
that commitment, signing that contract
with Star Alliance. So, that's one way in which you can use
strategic thinking and in which you can use commitment strategies,
to actually improve your payoffs in a competitive situation.
So, for now stay on till the wrap up, and thanks very much for staying through the
first session. Thanks.
And see you very soon.