So we're discussing how to analyze games, and we discussed some of
the considerations around symmetric versus asymmetric, single shot versus repeated.
I'd like to raise a couple standard challenges you often see in
these types of competitive games.
At the heart of a lot of them is a debate, if you will, or
a tension between cooperation versus competition.
And how do we resolve that, especially when we have this kind of
negative outcomes if we fail to cooperate and go to a competitive outcome?
This ultimately gets to issues around trust and communication.
How might we build that with our rivals?
How might we build that with our partners to avoid these competitive outcomes?
Now one way to think about this is through what is probably the most classic game,
which is called the Prisoners' Dilemma.
The Prisoners' Dilemma gets its name from the following scenario.
Imagine you have two bank robbers.
These bank robbers are brought in by the police under suspicion
of robbing the bank.
The police officers put the two suspected bank robbers in separate rooms, and
they begin to interrogate them.
Now what's the decision problem faced by each of these suspected bank robbers?
Well, one, if they keep their mouths shut there's a good likelihood that they might
get away with the bank robbery.
However, the police give them incentives to rat out,
basically argue and tell about the other one, so
that they can then maybe get some leniency in sentencing.
Now of course, the problem is the one prisoner doesn't know what the other
prisoner is going to do and
might be more likely to take the deal and rat out the other prisoner.
And as a result, they might both end up admitting to the crime and
then ultimately spending time in jail.
Now what's the analogy here to the real world and
to the markets that we might observe?
Well, consider two firms competing on price.
They're debating whether to engage in a price cutting or not.
Now if they engage in a price cut, there's a chance they can gain greater market
share and do quite well for themselves.
So here we have a payoff matrix between the two firms
where the decision is very simply to either cut prices or not cut prices.
If they both decide not to cut prices, they'll actually do very well and
make $100 within the market for some foreseeable time period.
However, there's an incentive to cut your prices while the other one does not.
The idea being that if I cut my prices, I'll increase demand.
Even though the prices are lower, I'll engage more sales and, as a result,
can profit more.
So in our little example here, if Firm 1 cuts their prices and
Firm 2 does not, they make $200.
Firm 2, however, starts to lose money because now they're not
price competitive within the marketplace here.
This is a symmetric game, so the payoffs to Firm 2 are the same as they are for
Firm 1 in these kind of off-diagonal situations.
However, we have this bad competitive outcome that if both engage in
a price cut, we end up with getting $0 for both players.
What makes the Prisoners' Dilemma a dilemma is that,
if you think about it from the perspective of each one,
we have a tendency to go to the cut-cut situation, so consider the following.
Firm 1 says if Firm 2 cuts their prices, I actually prefer to cut mine because
I'd rather get $0 than the negative 30 I would get in that situation.
And then similarly, if Firm 2 decides not to cut their prices,
I would also prefer to cut my prices because $200 is better than $100.
So in essence we have a dominant strategy by Firm 1
to cut their prices regardless of what Firm 2 does.
Now it's a symmetric game, using the same logic for
Firm 2, they'll also cut their prices.
And so we end up here in the competitive outcome of both of us cutting our prices.
