nm0763: right well as you can see er i'm all wired up for the benefit of er 
posterity er the synopsis of this lecture is in the handout that i gave out at 
two o'clock today and i'm going to be discussing the issue of sequential games 
er an aspect which in a way develops er quite nicely some of the issues that so 
far er have as it were cropped up er in the course of these lectures but have 
frankly er rather been fudged and the key er issue that we really fudged is 
exactly in what order er the moves are made within a particular game so what i 
now want to just review one or two basic concepts er that relate to 
representing games in a sense a more explicit form er this form is known as the 
extensive form of the game and it differs from the normal form bit of jargon 
this the normal form basically is the form of that matrix or bi-matrix that 
we've been working with in previous lectures we put up a table of rows and 
columns er we have a pair of numbers in each of the cells in the table 
and that's how we represent the game we then proceed to analyse the game as if 
each player decided on their strategies independently of what the other s-, 
player decided but it's quite possible that in many cases a game could be 
played in such a way that one player moves first and the other moves second in 
which case the most important point would be that the player that moves second 
would know the decision that the first player had already made and there are 
then two possibilities here one is that because the second player is better 
informed than that is he knows what the first player's already decided whereas 
the first player when he made his move did not know what the second player was 
going to do that therefore this gives an advantage to the second player so you 
could say well the sequence will matter er because whoever moves second is in a 
stronger position because they have more information but actually there's 
another side to this and this depends on the following issue 
and that is suppose that each of the players did know the other player's pay-
offs you might be able to work out if you knew the other player's pay-offs what 
they would do under certain conditions given that they knew what you had done 
and therefore you might as it were have a degree of power because by moving 
first you could frame the context in which the second decision was made and if 
you knew the other player's pay-offs you could then work out before you made 
your move how the other player would respond so it's by no means clear when 
players do make moves whether the advantage lies with the first mover or with 
the second mover it all depends to some degree on the nature of the game the 
structure of the pay-offs on the one hand and how much the players know before 
the game starts about each other's pay-offs and that brings me to the second 
point about the information set because the information set is basically what 
each player knows and er in a game 
played out sequentially the information set changes because as the moves are 
made new information on what moves have been made is added to the information 
set and what this means is that the information set changes as the game 
proceeds now in one sense that then makes the whole analysis much more 
complicated but in another sense it it actually makes it in some respect 
simpler too the reason that it makes it in some sense simpler is this that if 
there is a a final stage of the game then you can imagine what the players 
would be doing at this final stage of the game if there were a definite last 
play er a last step in the game then both the players would presumably know 
everything that had happened up to that stage and you could then construct a 
series of scenarios if a certain sequence of moves had occurred and the players 
knew this in the final step they would be equipped with the following 
information and would behave in the following way so you can construct 
a range of scenarios to work out in principle how the various players would 
move at the final stage of the game depending on what had gone before and then 
if the players themselves could work out what was likely to happen at later 
plays they could make their own earlier plays in the knowledge of what the 
consequences of those plays would be for later stages of the game and that is 
basically what is meant by the concept firstly of backward induction that is to 
solve games that are in a sequential form what one does is begin with the final 
stage and work backwards towards deciding what each player will do at the 
outset and the allied concept of subgame perfection is that at any stage in a 
game each player will look ahead at all the scenarios that could develop as a 
result of alternative decisions by they might make at that stage and therefore 
subgame perfection basically means that each player er works er with full use 
of the information they have at any stage as to what 
the repercussions of that move might be in the context for example of a game of 
chess er a chess player who is operating with backward induction and subgame 
perfection basically tries to identify all the possible endgames that might 
develop and then works back to decide which of these endgames he would like to 
get into and therefore finally arrives at the question if i make this move what 
endgame am i likely to finish up with if i make that move what endgame am i 
likely to finish up with and therefore solves the game in that way now chess is 
a notoriously complex game and one of the er attractive features of it is that 
it's in fact not normally difficult for people with finite human er rationality 
to actually approach a game of chess in that way but with the simpler games 
certainly two by two games of the kind that we've been discussing in this 
course it is possible to approach them in this way and i will in fact 
illustrate er how that can be done and er finally this 
analysis of sequential games also provides a discussion of issues relating to 
credibility and credibility is an important issue in modern economics for 
example we're told that the independence of the Bank of England gives 
credibility to monetary policy we're told that er for countries that enter in 
to treaties through the World Trade Organization give credibility to their 
competition and trade policies because if they were to change them at some 
future time they would suffer severe penalties and everybody knows this we also 
discuss in industrial economics issues about whether particular strategies 
towards entry deterrents are credible if a firm in an industry says to a 
potential entrant if you enter i will cut price and that will put you out of 
business is that threat actually a credible threat which will keep out the 
entrant or is it a not credible threat because if the entrant were to actually 
enter they would call the incumbent firm's bluff then the 
incumbent would then be faced with the situation well given that they've 
entered that we all know they've entered it's no longer er rational for me to 
carry out my threat so by looking ahead at later stages of the game one can 
investigate what kind of promises commitments threats and so on can economic 
agents make to one another and which of them will be discounted as being not 
credible I-E not rational in the light of what will later materialize and which 
of them can be identified as being er rational so let's start on this er by 
going back to er a very simple issue of some games we've already looked at the 
first game we've looked at is the prisoner's dilemma and in the prisoner's 
dilemma as you will i hope recall er the strategy of cheating in a one shot 
game is always dominant now what that means is that if you say to one player 
okay you go first the other player will then go after neither player minds what 
the other player is going to do because 
whatever the other player does whatever the other player does it always pays 
them to cheat so the prisoner's dilemma is a special type of game in which the 
sequence of moves doesn't actually matter because each player has a dominant 
strategy whatever the other player does they do the same thing so knowing what 
the other player's going to do doesn't alter the way they will act at all but 
there are other games we've looked at where the sequence does matter and the 
simplest example of this is the battle of the sexes game where we have Jack and 
Jill er going either to the wrestling or to the opera and we have two possible 
scenarios that we can distinguish here in the first Jack makes the decision 
announces what he's going to do and leaves Jill to respond and in the second 
Jill moves first now the essence of this as i say is based on the idea that 
each player may have a knowledge of the other player's pay-offs so let's 
suppose in this case that Jack knows not only Jack's 
preferences but also Jill's preferences and that Jill knows not only Jill's 
preferences but also Jack's preferences suppose now we er look at the game and 
represent it in this er what's called the extensive form the extensive form is 
usually portrayed in the form of decision trees so if we look at this first 
decision tree what this says is we start up here and the first person to move 
to make a decision is Jack and Jack makes a decision either to go wrestling or 
to go to the opera that decision then becomes known it's obviously known to 
Jack because he made it but it also becomes known to Jill and when that 
decision's made then Jill er can decide whether to go wrestling or go to the 
opera but under these circumstances if Jack knows that er Jill is er aware of 
his decision then he can calculate what Jill will do because he can say if i go 
wrestling then given her pay-offs Jill will want to go wrestling too because 
although she doesn't much like the wrestling she'd rather g-, be same place i 
am rather than somewhere completely different so if i go wrestling then Jill 
will go wrestling too on the other hand if i go to the opera Jill will also go 
to the opera she likes going to the opera but she'll go there just to meet me 
how nice 
so in that case Jack knowing Jill's preferences knows that whatever he does it 
will pay Jill once she knows what he's done to do the same but he can then use 
this information to his own advantage because by moving first he can say aha i 
can go wrestling because i know that even though Jill would rather go to the 
opera if she knows i am going to the wrestling she'll go to the wrestling too 
so as long as he makes sure that Jill knows the decision the ability to move 
first means that he can go to the wrestling er and then Jill goes to the 
wrestling and he's better off he gets a pay-off of two whereas if he'd gone to 
the opera he could predict that Jill would go to the opera but he would only 
get a pay-off of one so here is an example of first mover advantage the 
advantage here is that although Jill is better informed Jack can anticipate 
Jill's responses to his actions and therefore he can as it were endogenize 
Jill's response to his action er in in deciding what he 
will do and if Jill moves first instead then we get a different result because 
now if Jill can work out how Jack will behave from her knowledge of his 
preferences then the situation is as follows Jill moves first and if she goes 
to the wrestling she can predict that Jack will go to the wrestling because he 
likes to meet her and he likes wrestling but if she goes to the opera Jack will 
go to the opera because although he doesn't much like opera he'd rather go 
there than miss meeting her all together so Jill knows that if she goes to the 
opera Jack will go to the opera provided he knows she's gone to the opera and 
she will then er get a pay-off of two whereas if she goes wrestling Jack will 
go wrestling and she will only get a pay-off of one so Jill will then go to the 
opera so the decision is different according to the sequence in which the game 
is played so sequence does in fact matter now the only difficulty with this is 
that it imposes a sequence in 
which one does go first and the other then knows about it this extensive form 
representation would be a good deal more useful if it also contained the 
previous kind of game where the two players didn't know what each other had 
done er within it as well and so what people have done is to take this 
sequential er approach but to introduce a particular refinement of it which is 
to group together particular er nodes in the decision tree where people in fact 
do not have the information about the decision that has been made so if we 
wanted to portray simultaneous moves that is moves where neither party knows 
the other what we can do is suppose that they actually take place in sequence 
but that the first decision is not known to the person who acts later so we 
allow a temporal sequence but we allow a veil of ignorance to surround the 
initial move and that veil of ignorance is illustrated by drawing this line 
round these two points implying that Jill cannot 
distinguish between them in other words Jack's moved first he's made his 
decision Jack knows what he's done but Jill doesn't under these circumstances 
we're back to the previous er indeterminacy er in the outcome we're back to the 
previous situation of multiple outcomes because if Jack moves first but but 
Jill won't know what he's decided then Jack can't really infer exactly what 
Jill will do unless he has a theory about what beliefs Jill forms in the 
absence of any information on what he has done and that takes us straight back 
to the probability calculations that we've been using in the previous lectures 
but the point is this with the aid of this er device we can now represent any 
game involving simultaneous moves as a game involving sequential moves and 
therefore this extensive form of the game which portrays games in the form of 
decision trees is indeed more general and where we are dealing with truly 
sequential moves it's much more advantageous er than the er alternative 
approach what i now what to do is simply give an example of a sequential game 
and link it in to the point that i made about the credibility er of commitments 
and and and threats within the context of a sequential game i am going to take 
this game because it's a microcourse from microtheory and we're going to look 
at a standard issue in industrial organization er an entry game and what i'm 
going to do is i'm first going to look at the game in the ordinary normal form 
that we've used before and see how far you could get using that ordinary normal 
form and the equilibrium concepts that we've been employing up till now i'll 
then argue that this game is inherently sequential and that to represent it as 
if the moves were simultaneous er is really quite misleading and that a good 
deal of additional insight into what actually goes on in these situations er 
can be obtained if you switch er to using the extensive form which allows for 
people to make their moves in their natural 
sequence so let's portray the game in the following way the entrant has a 
choice of two strategies one of which is simply not to enter the other of which 
is to enter the incumbent er has a choice of strategies if entry occurs that is 
he can either acquiesce in the entry or he can fight it if he acquiesces then 
basically he accepts that the market power that he had before is to some extent 
diminished by a rival or alternatively he can fight and fight basically means 
precipitate a price war with a view to damaging the rival's th-, d-, dama-, 
damaging the entrant's profitability so i've got here a structure of pay-offs 
what does this structure of pay-offs symbolize well firstly if the entrant 
stays out the entrant is the row player so their numbers are the first in these 
pairs if the entrant stays out then he gets no profits i mean that's just a a a 
null strategy so there's nothing for the entrant if he stays out so far as the 
incumbent is concerned he retains his 
dominant position in the market and so he gets a handsome return of thirteen 
units so that's just fine for the er incumbent firm if the entrant enters then 
the incumbent can acquiesce that means that the incumbent simply switches if he 
was a monopolist to some form of duopolistic behaviour so perhaps instead of 
having strong monopoly power there's now some degree of tacit duopolistic 
collusion the result is that the two firms share a rather diminished profit 
they share a diminished profit a total profit of six as opposed previously to 
the profit of thirteen that the incumbent had all for themselves alternatively 
the e-, incumbent can fight and if the incumbent fights then basically he drops 
the price very dramatically saying to the incumbent basically there's no way 
you are getting a foothold in this market unless you're prepared to buy market 
share at a loss-making price as a result of which he can inflict a loss of five 
on the entrant but only at the expense of 
inflicting a loss of five on himself now if we just look at this in its present 
form er as a two by two game er with sequential moves then we would proceed to 
calculate the equilibria er in the usual way i'm only interested here in pure 
strategy equilibria so we can do that quite simply in terms of best responses 
er and we can suppose to begin with that the entrant stays out er if the 
entrant stays out then the incumbent doesn't have to do anything so it doesn't 
really matter whether he acquiesces or fights er either is a response because 
nothing has happened so both of these are underlined they're both possible 
responses to the entrant staying out that's a weakness of the normal form it 
doesn't really capture the fact that these strategies only really come into 
being if the entrant really does enter but technically both of these are best 
responses to the er entrant's play out strategy so far as the incumbent is 
concerned if the entrant enters this is quite important it pays to acquiesce 
because three is better than minus-five so if the entrant were to enter and the 
incumbent er knew that he had then the incumbent would acquiesce 
so far as the entrant is concerned if he thinks the incumbent will acquiesce 
then he'll enter because if he stays out he gets zero but if he enters and the 
incumbent acquiesces he gets three so if he thinks that the incumbent will 
acquiesce then entry will occur alternatively if he thinks that the incumbent 
will fight then it's better to stay out because he will get zero if he stays 
out but incur a loss of five if he goes in and so if we now just look at where 
the equilibria are we see that there are two equilibria in one of which entry 
er is combined with acquiescence and the other is that the entrant stays out 
because in some senses the the table suggests that the entrant that that the 
incumbent will be prepared to fight now that discussion isn't is partly 
adequate it's partly adequate because it does capture one insight it captures 
the insight that if the entrant were to enter it would pay the incumbent to 
acquiesce which is an important result but it's also er 
a bit unsatisfactory and it's unsatisfactory because the method of analysis 
we're using suggests that as it were the moves are simultaneous but in fact 
when you think the situation through this is inherently a sequential game 
because inherently what happens is that the entrant makes a decision and then 
the incumbent can decide the incumbent can decide what to do once he knows 
whether or not entry has occurred that is to say there's no reason for er the 
incumbent to start fighting an entrant who hasn't actually appeared so really 
er what we need to do is to move to the sequential form in order to get a more 
realistic picture what this sequential form does is it recognizes that the 
entrant does indeed move first and the incumbent then moves second and the 
incumbent only has a choice if the entrant enters so so this representation 
based on the extensive form with its decision tree says okay the entrant makes 
the first decision the entrant stays out there's nothing 
more to be said the er incumbent firm retains its market power the entrant gets 
nothing but if the entrant enters then the incumbent has the choice and that's 
where the pay-offs come in he can then either acquiesce or he can fight now how 
will this game then be played given that the sequence of moves is in this way 
well if we invoke the assumption that both players know the other player's pay-
offs as well as their own then the entrant can calculate what the incumbent 
will do because the entrant knows these pay-offs he knows both all the numbers 
so he can say well right once i enter once i've entered the incumbent knows 
i've entered and if he acquiesces he gets three and if he fights he gets minus-
five so once i've entered he will acquiesce i know that he will acquiesce 
suppose then that the incumbent says to the entrant if you enter i will fight 
what does the entrant do just discounts it one-hundred per cent it's just cheap 
talk it means nothing why because the 
entrant knows the incumbent's pay-offs and knows that although the entrant 
would like him to believe that he would fight the threat is not credible 
because once the entrant has entered and the incumbent knows it it won't pay 
him to implement his threat it'd be stupid of him to implement his threat only 
if there were further plays in which reputation effects became important might 
the incumbent wish to implement the threat for the sake of what might happen in 
some subsequent entry context but if we ignore the the repetition of the game 
then basically the incumbent's threat has no credibility the incumbent's threat 
has no credibility because it's not in line with the structure of pay-offs that 
the entrant knows so what does the entrant do well the entrant knows that if he 
enters the incumbent will acquiesce and therefore he'll get a pay-off of three 
whereas if he stays out he will get a pay-off of zero so he enters so in fact 
we have a unique 
equilibrium we had er multiple equilibria in that rather unsatisfactory 
analysis based on the normal form once we introduce the sequential structure 
explicitly we move to a plausible and unique equilibrium of entry followed by 
acquiescence the question then arises as well is there anything that the 
incumbent can do about this i mean we've seen that the incumbent can't just 
make threats because they won't believ-, be believable under these conditions 
is there anything the incumbent could do well people who've studied these 
situations have argued yes there are certain things the incumbent can do and 
basically er the kind of thing that the incumbent can do is to say well look 
part of the problem in the story i've just told is that the entrant gets to 
make the first move and therefore frames the decision that i then have to make 
and he knows that that that he can frame my decision suppose that i as 
incumbent could do something could could i could make the first move 
before any entrant appears could i do something before the entrant appears in 
such a way that when an entrant looks at the situation they'll say oh dear i 
don't want to enter because under the conditions the incumbent has set up it 
will pay him to fight is there something the incumbent can do while he's 
incumbent before the entrant appears that w-, can be set up to give credibility 
to threats that they lacked under the present situation well we can make one or 
two observations one thing is this that that if the incumbent is going to do 
this thing at the outset it should ideally be irreversible because if for 
example the incumbent does something but if the entrant enters it just pays the 
incumbent to undo it then of course it's as if it'd never been done so it's got 
to be something that the incumbent does at the outset the entrant comes in but 
the the the incumbent can't then simply say ah well forget that i'll go back to 
what i was doing before because the 
entrant would know that and would know then that the circumstances would revert 
to the original ones so the incumbent if he's going to deter the entrant has to 
do something and do something in a clearly irreversible fashion what's the most 
irreversible thing most people can do in an industry is invest invest in highly 
specific capacity capacity that has no use outside the industry so what you do 
is you build a plant and you build it in such a way that its scrap value or its 
value in producing any alternative product is virtually zero 
so that means that once you've built this plant you might as well operate it 
now under what conditions would that work that would work under conditions 
really in which firstly the equipment itself is very rigid not flexible 
specific not versatile but secondly why you would want it in the first place 
one reason why you might want it is that although it costs you a lot of money 
to buy it it brings down the marginal cost of production to a very low level 
because what this means is that by investing in this very specific equipment 
that will reduce variable costs by incurring large sunk costs it means that 
once you've put that spent that money you can't get it back you're simply left 
with very very low variable costs and this would mean that you could profitably 
fight a price war so an entrant therefore confronted with an incumbent that has 
made a very large irrecoverable investment in an asset that will reduce the 
marginal costs of 
production knows that if they enter they face an entrant who has an economic 
incentive very probably to actually fight a price war even if entry did occur 
and that's what this er example shows er i don't want to go through all the er 
precise er numerical details of it but suffice it to say that what we imagine 
going on here is that the incumbent sinks er nine units of cost into er a 
specific er i-, i-, i-, i-, into a specific piece of equipment and what this 
specific piece of equipment allows the entrant th-, allows the incumbent to do 
is to fight a price war without making er any er losses and if you then er 
study the pattern of pay-offs er what you find is that the modification of the 
pay-offs effected by the investment in the er specific piece of capital 
equipment means that the entrant's best response to entry the incumbent's best 
response to entry is to fight that then translates into the fact that the 
entrant who has the full information available knows that the incumbent now 
faces 
a situation where the best response to entry is to fight now also the incumbent 
knows that the entrant will know that he has invested in the equipment and so 
the incumbent knows that if he buys the equipment the entrant looking at the 
consequences of entry will see that the consequences of entry will be a fight 
and therefore the implication of this is that if the incumbent invests the 
entrant will be deterred from entry because if the entrant tries to enter he 
will incur losses because it will pay the incumbent to fight on the other hand 
if the incumbent doesn't invest then he knows that he's back with the game we 
just discussed back with the game where the entrant will not stay out but will 
enter and where it will then pay him to acquiesce so what he has to do as the 
incumbent er is to work out er what er the best strategy is if he doesn't 
invest then entry will occur and he will acquiesce on the other hand if he does 
invest then the entrant will stay out and he 
won't in fact have to fight now the incumbent's er pay-offs are the second in 
these pairs of numbers and if he doesn't invest and entry occurs and he 
acquiesces he gets a pay-off of three whereas over here if he invests then it 
will pay the entrant to stay out and he will get a pay-off of four yeah 
sm0764: why do we not count on the bottom right on the slide 
nm0763: yeah 
sm0764: why do we not count the investment on that one 
nm0763: because of the er saving in costs that's effected by utilizing the 
investment the investment is a specific investment that reduces marginal costs 
that reduction in marginal costs is of particular value when you are wishing to 
expand capacity dramatically in order expand output dramatically because you 
have effected a major reduction in price so so the so the outlay on sunk cost 
is recovered by savings in variable costs under the conditions where the 
entrant enters the market and you fight if you decide not to fight then you 
don't drop the price the output doesn't need to increase and therefore you 
don't get substantial 
savings so the savings only accrue in the event of a fight occurring you 
undertake the investment in order to give credibility to fighting but you don't 
in fact have to fight because your threat is credible so this is in fact an 
argument why firms will invest in unused capacity the final punchline of this 
model is with the firm investing capacity in order to reduce marginal cost 
which will give it a return in the case that it has to fight but the very fact 
that it has invested in reducing marginal costs means that its threat to fight 
an entrant is credible and that keeps the entrant out so what the incumbent has 
done is invest in capacity with the specific objective of not using it not 
having to use it to its full capacity in other words incumbent firms it is said 
it may invest in highly specific excess capacity specifically to keep the 
incumbents out and this as it were is quite useful because it explains a 
paradox that one or-, does observe in a number of 
industries where they appear to have made investments that are unnecessarily 
specific unnecessarily large and not properly utilized and yet the firms are 
relatively profitable and the question why do they do it one answer may be that 
in fact it's not a case of a firm being incredibly inefficient and still 
managing to make a profit it actually makes a profit because although the 
wasted capital underutilized capital is socially inefficient privately it's 
efficient because it supports credible threats against entrants and therefore 
sustains the incumbent's monopoly power and so another consequence of that is 
the social costs of monopoly not only include the costs of higher prices the 
distortion of er buyers and consumers' decisions the social costs of monopoly 
are not merely to be found 
in in price distortion and the distortion of consumer buying decisions they're 
also to be found in the fact that monopolized industries may well er employ 
excess and overspecialized capital for the specific purposes of deterring entry 
from the industry so those who are concerned er with er amplifying or finding 
the maximum possible social costs of monopoly often employ these kinds of 
arguments to suggest that the social costs of monopoly are found not only er on 
the consumer side of the situation but also on the capital investment er side 
of an industry as well okay it's quarter to five er i've had er six hours of 
lecturing today and i'm going home