0:03

Great to have you here.

As we've learned already, companies are players.

They're not necessarily happy about the equilibrium in the prisoner's dilemma.

So in a prisoner's dilemma kind of situation, they could increase their

joint profits if they would somehow be able to

coordinate their behavior. However as we've seen in in the previous

session, a coordination is not easy to establish and maintain.

So in this and the subsequent videos, we'll have a look, and analyze games that

are played repeatedly, and we will ask how repetition can support

coordination. Okay, so what do we mean by repeated

games. Repeated games basically take into

account the fact that interactions between two players, between multiple

players, can take place not only once but a repeated number of times.

So before we even get started at the very beginning, we would like you to think

about some real life examples of games. So which of these are one off games, and

which are played repeatedly. Just have a look at the at the couple of

games that are going to follow, and I'll see you after this brief quiz.

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Okay, so as we've seen sometimes interactions just take place a couple of

times in a row. And the way in which that changes the

dynamics of the game or that changes the dynamics of

competition between two players is by making the future matter.

So, for once for example A, player A, if we have a game between A and B, player A

can threaten player B or vice versa. So if A does not behave cooperatively

this time, in one instance of the game, then B will retaliate the next time.

And of course, the other way around, okay?

So that would be a possibility in which playing a game multiple times changes the

outcome of the game. But what we're going to do is we're going

to take a very analytical look at this and see if this kind of threat can

effectively enforce cooperation. And to do that we have to distinguish

between two different types of repetitions.

First one's finite repetition, where it's clear from the beginning how often the

game is going to be repeated and when the game ends, okay?

So we simply know what the outcome or what the end point of the game

is. And once we have the end point, then

we're going to work towards this end point.

2:37

If we have infinite repetition, then there's no defined end to the game, the

number of repetitions is unclear, and we can therefore never tell if one round is

the last round of a particular game. And let's take one particular example of

a finite repetition game. And that's the installation of street

lights for the Olympics. This is the 2012 Olympics in London and

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we had a situation, well and this was a situation that of course

was repeated in lots of different ways and lots of different small

settings, but, we had a situation where an organizing committee had to order

500 street lights from a contractor. And that contractor was supposed to

install them time over time leading up to the Olympics.

Why is this a finite game? It's a finite game because the Olympics

will start at a certain date and by that date the streetlights have to be

installed. After that, there's no future, if you

wish. So the contractor manufactures the street

lights and installs them in the Olympic park.

And he's capacity constrained so that every month only 100 street

lights can be manufactured and installed. This means that the overall process of

installing 500 lights will take five months, okay, and we can think of this as

a game that's repeated five times. Alright it's the same game

over 100 street lights just playing it five times and its over after these,

after the fifth iteration. So one month before the olympic start all

street lights will have to be installed. So we're going to take this into a

game setting, and keep in mind that whenever we put up the numbers these are

fictitious numbers, and not necessarily reflective of reality.

So what are the actions that our two players can take?

Alright, so we have the contractor and the organizing committee.

So every month, the contractor has to decide about delivery.

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The organizing committee, will also have two strategies at their disposal.

They can decide if they want to pay the agreed price of 30,000.

So that's the price that they initially had agreed with the contractor, or if they

negotiate the price down to 20,000. Now what do we mean by

renegotiating the price? It's about basically finding some small

fault or some slightly late delivery, something that isn't entirely up to

specifications that you can either let go or you can decide to play hard ball about

it and lower prices in form of a penalty, of a contractual penalty

from 30,000 to 20,000. Okay, so these are the two strategies

each for the contractor and the organizing committee.

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So, what's going to happen in each of these instances?

So, if the contractor delivers high quality, and the organizing committee

pays the price of 30,000. Delivering high quality, means, it's

worth 45,000, so if the organizing committee pays 30,000, then what's left

for the organizing committee is a value of 15,000.

If the cost for the contractor are 15,000 and he is paid 30,000 then that's going

to leave him with a surplus of 15,000. Okay, and by the same token if the

contractor delivers high quality, and the organizing committee simply pays a lower

price then the payoff for the contractor is

going to be 5,000, the payoff for the organizing committee

is going to be 25, because they negotiated the price down to 20,000,

which leaves them with 25,000. Contractor delivering low quality and the

organizing committee paying full price means that there's no surplus left for

the organizing committee and the contractor gets 18,000.

And if the contractor delivers low quality and the organizing committee

renegotiates the price. Then, profits are going to be

8,000 for the contractor and surplus is going to be 10,000 for the organizing

committee. So, as you can imagine the fairest or

the most sensible outcome for this game would be if the organizing committee

paid the full price, and the contractor delivered high quality.

But you can also see that there's an incentive for both of them to actually

not stick to that agreement. So keep in mind that we play this game 5

times. So one thing that might help is the

threat of doing something in the future if the

other party does not behave according to the rules.

So the contractor, for example, could threaten the organizing committee and

say, well, if you ever renegotiate the price in a given month, then we will

continue delivering low quality from there onwards.

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The threat on the part of the organizing committee would be well if you the

contractor ever deliver low quality in one month then we will renegotiate the

price in all subsequent months. Okay, and so the question we're asking

here is, if this is going to be helpful in enforcing cooperative behavior.

Just having outlined the situation, what we're going to do in the next video,

is we're going to look at these these threats, and at the effectiveness

of this threats to enforce cooperation. So stay tuned and see you in a minute.