0:04

Right, welcome back. So, in the last video, we used a game

tree to systematically develop and approach a competitive situation in which

firms take decisions. But they don't do it simultaneously, but

they do it one after the other. In this video, we're going to use the

game tree and a technique we call backward induction to find the optimal

strategy for the firm that has to decide first.

0:30

So, let's have a look. So, we know that Mars have the first

choice. They have the choice of signing the

product placement contract or not signing it.

And if they sign it, the game is over. Hershey's does not have a choice.

Whereas if they don't sign it, then Hershey's gets to decide if they want to

accept or not accept the deal. As the game played out, we found this

result. So, Mars declined and Hershey's accepted.

This turned out to be a loss maker for Mars.

They lost half a million and Hershey's won by $200,000.

Okay. So, what we're going to do is we're

going to apply that concept of backward induction and try to go back and see if

this is an outcome that is optimal in any sense

or, and or, if it's something that we should have expected.

1:30

But let's first see what backward induction is in the first place.

Backward induction is the process of simplifying a sequential game.

You remember looking for dominant strategies.

You remember looking for dominated strategies and eliminating them.

It's a bit like that, right. So, you're trying to simplify a

particular type of game. We're eliminating actions at the final

node and we work our way forward. So, anything that isn't going to be

played is something we can ignore from the game, just like a dominated strategy.

2:25

So therefore, we will always rely on a rational rival never to

choose these actions. Okay, anything that doesn't maximize my

own profit is not something that I'm going to choose.

Okay? So, let's take that example again.

Let's take the chocolate wars again, and see if this is the right outcome, if this

is an outcome we expected. Okay, so if Mars chooses to sign, then

there's no contest, no choice for Hershey's, status quo, nothing to

decide, okay. What if Mars declines the offer?

If Mars declines the offer then, Hershey's has the choice of signing the

deal, which is going to gain them 200,000, or not signing the deal, which

is going to mean business as usual, and zero change in profits.

So, for Hershey's the situation is, do I want to make 200,000 dollars or do I want

to make nothing? Yes, so of course, the best outcome, the

best solution for Hershey's is to accept the deal if offered the deal, okay.

Therefore, we can eliminate this part of the game, it's never going to happen.

And Mars should not expect this to happen because, of course, Hershey's wants to

maximize their own profits. Now, what does this mean?

It means for Mars that if they do not sign the deal, Hershey's will accept the deal.

And this is going to mean a loss of half a million for Mars.

4:02

If they accept the deal, so they sign the contract, Hershey's does not have a

choice, and it's going to mean a loss of 200,000 for Mars.

Now, comparing a loss of 200 and a loss of 500, of course, it's clear that

Mars should have chosen this strategy, so they should have signed the

deal. But I think we're probably losing out

some sort of realism here, because if you go to your manager, if you go to your

boss, and say, well, here's a product placement offer I got, and I believe it's

going to lose us $200,000. Can we please do that?

It's going to be a difficult sell, right? Typically, you would not engage in any

project, you would not engage in any contract, you would not sign any contract

that's going to lose you money. Okay?

But if you think strategically, if you think ahead and actually make that

calculation, and make that anticipation that Hershey's, if we don't accept it,

Hershey's is going to accept it, and this would be an even worse outcome,

then it all of a sudden makes a great deal more of sense to sign that deal,

okay. So, looking forward, looking ahead and

trying to think strategically what the other firm is going to do can help make

better decisions in this case, right? So, the right outcome, the outcome we

would've expected is for Mars to sign straight away.

5:26

Let's use backward induction again for another game.

Okay, it's a game of price setting. Firm A can choose a high price or a low

price. Firm B can make their decisions dependent

on what firm A has done. So, they can choose a high price if firm

A has chosen a high, or, they can choose a low price and so on

and so forth. Payoffs are 8 million for both, if both

charge a high price, they are zero for firm A and 10 million for firm B.

If firm B charges a low price and firm A charges a high price, they are 10 million

for A and zero for B. If A charges a low price and B charges a

high price, and if both charge low prices, they both made 5 million.

What is the likely outcome of that game? Well, if we look at it just like that, it

would seem reasonable that both A and B should choose high prices, because that

gives them the highest profit jointly. Okay?

But let's use backwards induction to try and see what's most likely to happen.

6:32

If Firm A has chosen the high price, Firm B will have the choice of either getting

8 million, if they choose a high price or getting 10 million if they choose a low

price. So, the best response, the best strategy

for firm B is to charge a low price here. Okay, because 10 million is bigger than

eight. If firm A chooses a low price, then firm

B can choose between charging a high price and getting zero, and charging a low

price and getting 5 million. So, the best choice for them again, is to

charge a low price. Okay.

Now, firm A is going to take a step back. They're going to try to anticipate what's

going to happen. And charging a high price means profits

of zero for them. Charging a low price means profits of 5

million for them. So, what we expect in this game

via the technique of backward induction is that firm A charges a low price

because they anticipate that firm B is going to charge a low price as well.

So, the outcome of the game would be that both firms charge a low price.

We're basically in a Prisoner's Dilemma type situation as you've seen in previous

videos where both first do something that is individually rational, but not

collectively profit maximizing. So, in this video, we've used the concept

of the previous one, game tree. We've used the technique called backward

induction to find what the optimal strategy for a firm is, okay.

We've found, the optimal strategy for firm B, for the second mover, and

from that, we could derive what the best strategy for the first mover was.

So, we're going to have an exercise on this just after this, but for

now, thanks very much and I will see you very soon.