Game Theory: Introduction

today we're going to be starting our discussion of game theory game theory is one of the major developments intellectually of the 20th century and it's something that has been studied by economists mathematicians political scientists philosophers and I think we're really only at the beginning stages of understanding the implications of game theory for human behavior and for ethics for political philosophy for a variety of other realms now it has very definite limitations and we don't want to be blind to those limitations it's going to explain certain features of behavior of certain features of strategy certain features of ethics I don't think it's going to explain everything some people do I think that's a confusion but in any case we're going to look at it because it does contribute a lot to our understanding of well not only what people do but what they ought to do I want to start with Aristotle's idea of what the function of a human being is what is the function of man yes what are we for what's our purpose what's our goal well in the end he says it's a question of what differentiates human beings from other animals what makes you different from a dog a raccoon a mosquito well in the end he says this you have an active life of the element that has a rational principle in other words rational activity now it's hard to say exactly what that comes to I don't think there is a very clear or very good definition of rationality but on the other hand there is surely something that differentiates us from lower forms of animal life I think dogs cats raccoons etc actually have some degree of rationality after all they can solve problems they can figure out things they know when it's time to be fed its head etcetera on the other hand it seems to me that there is something that is distinctive about human beings we're capable of constructing rational plans if I say what's your plan for the next four years you can maybe give me an answer maybe not but at least you can consider the question right you can't do that with a dog well what's your plan for the next I mean the dog doesn't know what its plan is for the next hour let alone what this is for the next several years so the complexity of human planning of human activity is far greater now what is involved in all of that well at the very least decision making and so game theory is from one point of view the theory of decision making how do we make decisions how do we formulate strategies so it's really all about strategic thinking now it's unusual to put this in an ethics course because you might think wait strategy well there's an obvious connection right strategy is how you should go about addressing a problem ethics is about what you ought to do how you ought to make decisions so there's an obvious overlap here there's a connection between strategy and ethics in a way that I think people often ignore we always they're deciding upon actions with a purpose a goal in mind and in short we're formulating a strategy and so ethics is in part about how to address these kinds of strategic problems anyway game theory focuses on that and it focuses on studying conflict as well as cooperation trying to understand how people in groups address problems so one thing that's distinctive about it is we don't just think about one agent how you should act for example we think okay you're interacting with other people game theory is about social behavior about the way in which we interact with others who are also decision-makers and since at least a huge amount of ethics has to do with how we get along with other people there's a connection there too and we think suppose we have multiple intelligent decision makers who are trying to behave rationally well how does their interaction matter that's something that game theory focuses on it was originally developed by John von Neumann and Oskar Morgenstern the big book on it is the theory of games and economic behavior the first edition is shown there here's the Edition I have as you can see it's pretty and it's very mathematical it started with von neumann's attempt to understand poker and become a better poker player actually it's pretty useless for poker pokers too complicated and so my son-in-law is a very good poker player he competes in the World Series of Poker and things like that I have nothing to contribute to him but in theory I'm afraid so if that's your hope yeah it's gonna be frustrated but it is useful for all sorts of other things and in fact it began to attract a lot of attention in the 40s and in the context of the Cold War people immediately start thinking wait this allows us to game scenarios for nuclear conflict on other kinds of conflict and so it's something that was studied heavily at the RAND Corporation and by the military in the years after the Second World War 11 game theorists have won Nobel prizes in economics so it's also something that is at the forefront of economic thinking now here's one way of thinking how it connects to ethics I want to the picture there is Thomas Hobbes who in a sense had the same kind of attitude about the connection between ethics and strategy the whole idea is this self-interest rational pursuit of self-interest can actually give rise to ethical norms we often think of self-interest and ethics as competing as going at things at loggerheads and sometimes they are we're trying to do what's right but we have this real desire to do what's wrong there are cases where self-interest can conflict with ethics but on the other hand if you think about the larger framework of our interaction with other people you can start to think well wait a minute actually it's pretty rational to be in a system governed by ethical norms go back to Hobbes is question would you rather be in a state of nature he's thinking primarily about a state without a political authority at all but suppose you ask it about ethics would you rather be in a society where nobody had any ethics in relating to other people or would your rational pursuit of self-interest and other people's rational pursuit of their self-interest lead to us all agreeing to observe certain norms to get along better well the idea is it would be rational to actually adopt these norms of behavior and in fact cooperation would emerge in not only setting up those rules of behavior but enforcing them and finding ways of cooperating within those rules so you can think about the sense in which both exert out of self-interest you can also think about institutional arrangements what kind of institutions do we want how do we want to structure an organization for example or for that matter a whole society in such a way as to encourage cooperation or discourage it I mean there are good things and bad things about cooperation sometimes cooperation is very good sometimes it's bad and it's important to keep that in mind I mean it's easy to think of examples of cooperation that are good right give me some examples of good cooperation marriage okay good you have to cooperate with the other person cooperation is a good thing within any kind of relationship other examples good cooperation yeah good you got a team project you split up the work you all cooperate and do your share and that's a very good thing but are there bad instances of cooperation Oh like hey you know those two are hard workers they'll do all the work lets us goof off right that would be people cooperating to push those people into doing all the work that would be a bad sort of cooperation other examples good bank robbers like hey we worked together man you all right your job is killed guard my job is to drive the getaway car you're going to set the explosive you're gonna go in and you know get the loot out of the safe then all of that would be an example bad cooperation yeah ooh tragedy of the Commons problems yeah so think about ways in which I mean sometimes that arises because people don't cooperate and we'll talk about those problems a lot next time but sometimes they can arise out of cooperation suppose we are a bunch of businesspeople who agree to fix prices for example it's like hey you know you've been you've been selling your airline tickets for less than we're putting on our website why don't we all agree to raise our prices we'll all make more money that would be an example of a bad sort of thing a price price fixing cartels can be like this right a cartel is often a bad form of cooperation the Mafia is a bad form for operation hey you don't like me I don't like you but we'll like those guys together okay okay that's bad that's a bad form of cooperation now so in short we want to encourage the good kinds discourage the bad kind there are different kinds of games and one of the things you have to do at the very outset of analyzing a problem in these terms is understand what kind of game you're playing so today I want to talk about two distinctions the first between a zero or a constant sum game and really mathematically they're equivalent and then mutually beneficial or for that matter of mutually harmful games but ones where in short if one person wins it comes at somebody else's expense as opposed to games where both people can benefit or both people can lose and then we want to talk about the distinction between simultaneous and second sometimes you and I have to play at the same time without knowing what the other person is doing at other times you move first than I move and that makes a fundamental difference do I know what you are doing right in the one case I don't you and I let's say we're I don't know we're well we're going to talk about examples in a moment but a simple thing as we'll talk about is a game of two finger amoral where we have to hold up one or two fingers and then one of us is odds and one of us is evens and I don't know what whether you're gonna hold up one or two fingers when I make my play and so that's a case of a simultaneous game we have to do it together it's not very fair if we say okay yeah I'm evens yeah now you go right then you know exactly what to do other games are sequential in chess it's not like we both move at the same time without seeing what the other person is doing I white moves then black moves and so on so it's sequential so anyway we'll talk about each of these in more detail a zero-sum game is a game where well there's a constant amount being allocated among the players and each player's gain or loss is balanced by a loss or gain from other players okay so the total sum remains the same now it might be that it's just zero I win you lose and the average of that is just sort of the same as it was before but it might be that let's say we're carving up a pie and it's the same amount of pie if I get a bigger piece you get a smaller piece and it's like the pie doesn't grow or shrink as a result of what we do in cutting it so those are cases where you might say the total amount of utility whether it's 0 or some other sum is left unchanged it might be a positive thing or it might be a negative things like ah we have this debt where are we gonna get the money from we take it from other parts of the budget and it's the same amount we have to take it's just a question of where we allocate the losses so all of those would be examples of zero-sum games now these games are strictly competitive one person's benefit comes at the expense of other people and in that way they're good for modeling conflict or the question of distribution of a fixed pie fixed amount of something so what are some examples of zero-sum games or constant some games in practice war ah is war a zero-sum game okay some people are shaking their heads No why not okay good there could be ways in which it might be mutual you there might be mutually beneficial there are beneficial solutions to conflict like a treaty there might be mutually damaging ways of going and the amounts of damage might change a lot right I mean something that escalates to a nuclear war would presumably be a lot more negative than a war fought by conventional means other things being equal and then that might be more damaging than a limited conflict by proxies in some remote region of the world and so on so there are lots of degrees of lost degrees of harm and if you're doing a war game it's not simply like oh we win you lose it can be look we both suffer horrendously we both kind of benefit we both suffer a little so that's not a constant sum but what would be an example of a zero-sum game yeah ah tell us more about what that is what's the ultimatum ah good good good yes so they actually do this experiment with often with undergraduates you guys are the guinea pigs of the psychology world the behavioral economics world but they do this kind of thing they bring you in and they're two people it's a you two and the experimenter gives you ten dollars and says now you can give him any portion of that ten dollars you want and you both get to keep the money provided that he agrees but if he says no deal then neither of you gets the money okay so what do you do now from one point of view you could say well okay if he keeps the ten bucks and says yeah I got it you get nothing presumably he's gonna say well screw you you know so he's gonna say No Deal now suppose you offer him one dollar it looks like rationally speaking well he's better off by a dollar right and so wouldn't that be reasonable shouldn't he agree if he doesn't agree he has no money if he does agree he has one dollar at least but lots and lots of and some people think that way but a lot of people will say No No Deal I want my share now if you offer him five dollars almost certainly he'll agree you're splitting it evenly right seems fair unless he's really you know he might be saying no I get the nine you get the one right but most people will go along with it even split but how far does it go right and so behavioral economists study this kind of thing to find out how much inequality people will tolerate in that situation and it's it's sort of interesting as long as the other person gets three most people will agree to the deal but but there's a sliding scale anyway it's an interesting game but notice it is a zero-sum game there's a fixed amount in the sense that it's ten dollars however that's given that you actually divide it up in some way I suppose if we include the experimenter if if he says no deal and you get nothing when I view it as you - aha it's not zero-sum anymore you lost the ten dollar amount on the other hand if I the experimenter that looks zero-sum because he at least gets the money back so other examples of something that would be a zero-sum game yeah good cutting a cake at a birthday party you're cutting the birthday cake there's a fixed amount of cake and you are allocating it among the people if you get a bigger slice somebody else is getting a smaller yeah oh good you put your money in a pile and you play cards to do this you have in effect a little tournament tip and you find out and the winner takes all let's say that would be a case of a fixed amount it's not as if playing makes that amount if it's in the pot grow or shrink it's something that is fixed and then it's just a question of how it gets allocated and who it gets allocated to yeah elections ah is an election a zero-sum game yeah one way to look at it is to say there are only a certain number of votes and if this candidate gets more votes the other person gets less but of course more a few or fewer people might vote so really to have it be zero-sum would have to have a situation where the number of votes cast is the same if people just sit at home and don't vote then one candidate might get more votes just by attracting the people who otherwise wouldn't vote at all so if you think of percentages of the vote you get it looks zero-sum because the percentage is by definition have to add up to 100% if we're thinking of the actual total number of votes that might be a number that increases or decreases depending on the public's interest in the election by the way that itself can be gained the Austin City Council is extremely good at gaming elections in that respect here's a proposition that has to go before the voters do we want it to face a large number of voters or a small number of voters we could have a special election in the middle of May so the hardly anybody votes we could actually allocate it for the main primary or the main election in November when lots of vote on it and they often make that decision the basis of you know how they want it to come out so that's a good illustration a lot fewer people are gonna vote in the third week of May then will vote on the first Tuesday in November and you can use that to game the thing figure ha we've got a dedicated group of people who are gonna show up now that are what they'll be overwhelmed in November but they can nominate in May so it can make a big difference okay well those are examples of things that are zero-sum games they're actually a little less now everybody in the world knows mine here are some other examples oil and gas licenses you might have a certain territory you divide up the licenses among different oil and gas companies for exploration that's something that's a zero-sum game you can't create more land as a result of the way you do it promotions are like that you have a certain position open one person the company is going to get promoted into that position their promotion means other people aren't going to be promoted into that position budgets are like this you have a set amount of the budget and then it's a question of the different groups within the organization fighting for their share of the budget and you might say doing a lot of dollars remains fixed it's just a question of who gets what in the budgeting that's how things more or less work at the University departments compete within their colleges colleges to compete within the University and it's really more or less a fixed sum that is coming in through tuition and legislative appropriations and other things and then it's question of where that money goes real estate negotiations are often like that if I pay more for the house you get more right you can't get more for the house unless the buyer actually pays more elections are like that if we think about percentages of the vote or for that matter if we think about seats in Congress one party can only gain seats if other parties lose seats bargaining is often like that say we're arguing over salaries if you pay me more then you have less right this hour I'm out I'm receiving comes out of someplace contracts are often like this market share is like this companies are competing for market share there's only a certain I mean you might have more viewers on TV say or fewer viewers so that PI can expand and contract but if we're thinking of shares well if you increase your market share that means somebody else is decreasing their share yeah right right well right I mean it's easiest to think of examples like this in economic terms I absolutely agree but think about we don't tend to do this in liberal arts because we're nice okay but in some departments at this university grades are allocated on a bell curve and then I might say hey 10% of the students or 15% or whatever it is we're gonna get A's actually the toughest grader in liberal arts used to have this policy it's a look I'll give you an exam and it'll be entirely determined by how you do the person who does best on the exam anybody who does within 10% of that gets an a anybody who does within 20% of that gets a B etc that turns out to be incredibly incredibly Stern more than half of his students would fail now why is that so stern well think about the way a bell curve goes often in a large class and he would teach classes of 500 people in intro psych the very best student is often extremely good right and they're way out on the tell a tale of the bell curve well 10 within 10 percent of that score now if he wasn't saying 10 percent of the class he was saying 10 percent of the score right and it might be that only two or three other people are within 10 percent that highest school which means only the people in the extreme tale of the bell curve are getting an A so but there were anyway that wasn't exactly a fixed thing in a sense you could take the smartest person in the class and pay them off like make a few mistakes just for the rest of us but many event suppose we don't do it that way suppose we say yeah 10 percent of the students will get A's or for a while in the liberal arts actually that the a former Dean had a policy that would say I'm gonna yell at you if you give more than 50% A's and B's and in that case you might say there's a fixed sum of A's and B's together that I can give out and then it's a question of who gets them but even if everybody in the class does better it doesn't matter only half the students can get those grades so that would be a kind of treating of grades as a zero-sum game no I don't do that I mean there are classes like this one where the students are very good and lots of people get very high grades there are classes where people are terrible in fact talk about a instance of bad cooperation versus good cooperation we have this program called figs first-year interest groups the advisors refer to the people in them as fig le'ts by the way anyway the fig 'let's normally within those groups cooperations very good and people in those perform better but in the time I've been here I did have one of these where it was bad cooperation there were several people in there who were just terrible students and they corrupted the others but they all cooperate so like I think one person in that entire fig group got a see all the others got D's and F's and I don't think it's at the first they didn't look like they were all terrible students but it turned out the few really a bad apples just spoiled the whole bunch and encouraged them all to have terrible work habits so that kind of thing can happen in any event normally grading isn't like that but it could be so it doesn't have to be economic now lots of games are mutually beneficial in the sense that the players can increase or decrease the total amount of utility so normally we would think war is like that Wars can be fought more or less struck t'v Lee and in fact one of the hard questions in looking at 20th century military histories why were 20th century conflicts so unbelievably destructive the First World War the Second World War the loss of life the destruction of property and so on just wharfs earlier Wars partly that's just because people had more technology to do more efficient killing but it wasn't just that and so you know you have to think yeah why were they such terrible wars that was a case of people really decreasing utility radically but also there are ways of people actually getting together and cooperating and increasing utility well in this case one players game doesn't necessarily come at somebody else's expense it might be in fact that I gain by causing you to gain and so we actually have useful cooperation so what are some examples of mutually beneficial games good economic competition right you might think well if we're thinking market share my getting more market share means you have less but on the other hand it might be that actually by introducing new project new new products and competing we're actually increasing people's interest in all of this and so we're growing the market at the same time so maybe the competition is actually improving all of our situations and similarly I I sell you some product and you like it it makes your life better I'm improving your utility meanwhile you're paying me so I'm getting a benefit out of that and so we're both benefiting in fact typically in an economic exchange that how it that's how it goes you agree to it because you're better off and this person agrees cuz they're better off and so the exchange actually makes both parties better off other examples yeah education good education is something that generally makes people better off and so you might say when a professor does the job well the professor is better off but also the students are better off a teacher who does a terrible job you know the students don't learn anything the professor doesn't do I assume doesn't feel good about it I wouldn't know of course well yeah um think about the worst teacher you've ever had and don't tell me if it's me but you know think about the ways in which that can be worse for the students but also for the professor even within a class given the holding the professor constant as it were sometimes the groups of the group of students in a class add to each other's learning a lot and other times they don't I've taught ideas of the 20th century sometimes with really good students who make comments that are terrific and get everybody else more involved more excited and people in general do better I had one class where there were two people who sat in the front row and every question I asked the class responded with some stupid joke and it was stupid I mean it wasn't funny but they always did it and so you know so you said I was a question like why we're 20th century Wars so destructive and this is meant to encourage a good discussion and if the first people to talk say something stupid then it's kind of like well now the whole discussion kind of goes off the rails so anyway you know the group can act in a way that improves the group's outcomes or decreases other examples yeah good conformity to laws if we all conform to a certain law and it's a wise law at any rate then it looks like everybody benefits from that but we can also start breaking that law on that maybe makes other people more inclined to break it and so people's behavior can make people worse off too okay well there are lots of examples of this it's easier than zero summons examples so lots of cases where people cooperate or for that matter of collude that's sort of a bad form of cooperation cartels we've mentioned medical records somebody came up with this example to this one time it may be if we have a system of keeping medical records that's highly effective it helps make people healthier because doctors have the information they need nurses have the information everybody puts it in and such on the other hand you could have a system of doing this that's bad either because it's misleading or because it takes up so much people's time that they don't have time to actually treat patients at cetera so that can make us all better off or worse off student-professor interactions but do beware of third party effects because sometimes people can affect the behavior of others in ways that are unexpected a lawbreaker for example might not only lets say steal somebody's property and create harm in that way but might create all sorts of other harm all of a sudden the rest of us start getting worried it upsets us we think oh we're in some danger too we start having to buy locks security cameras etc there can be big Gipp costs imposed on third parties now let's talk about that other distinction between simultaneous games and sequential games so in a simultaneous game players are choosing actions without knowing what the other players are to choosing so I have to make a decision about what I'm going to do and I don't yet know what you're doing we have to make our decisions at the same time and then we see what happens when we put them together but you act in ignorance of what I'm doing I acted in ignorance of what you were doing now we might know the history of what we've done in the past but in terms of what we're the play we're making now we have to play at the same time as it were without knowing the other person's play so what are some examples of simultaneous games yeah uh yes a prisoner's dilemma we're gonna be talking about that a lot next time but the idea will have to be the prisoners are taken in separate into separate rooms in question by the police and you have to make a decision how much information do you reveal about things and do you in particular give evidence against the other person in the other room and that is something you have to decide without talking to the your fellow criminal in the other room the police really do this kind of thing they normally take people into separate rooms and question them separately both to try to trap them in lies but also to give them increased pressure to confess and implicate the other person and again we'll talk about the details next time but yeah that's a case where you have to decide what you're doing without knowing what your fellow prisoner is doing it becomes something totally different if you're there in the room together and you can kind of confer but in this case you can't I did have a student one time who said after class when we talked about this I've been in trouble a lot with the law this is exactly what they do they put you at a prisoner's dilemma that's why it's called that anyway other examples of things where you have to decide what to do without knowing what the other person involved is doing yeah good stock market you decide whether to buy or solve a stock and you can look at the history and know what it's been doing even in the last few minutes but you don't know who's going to be willing to buy or sell at that moment do you make the decision and so the stock market is something that is like this you make a decision and other people are deciding on buying and selling at the same time and you aren't quite sure how that's going to come out other examples yeah college applications can be like that yeah it depends on the system now some colleges have rolling admissions and so that can be different you can apply to a place find out oh I didn't get in because apply for this other place but but yeah the way it often goes there's a certain deadline and you have to submit all the applications by more or less that deadline and then there's a certain time you hear Moll and at the time you're applying you don't know what's happening with others and then when they announce their decisions they don't know what those people are gonna do so so yeah it can when it's done that way it really looks like a simultaneous game other examples yeah okay good yeah a lot of TV is based on this kind of thing where you have to decide on a strategy somebody else is doing it you can't see what happens until you put them together yeah that's that's true yeah I mean imagine well actually if you've ever watched the survivor show there's a huge amount of coalition forming in collusion going on until of course it gets down to the last two and then it's like there's nobody else to collude with and so then it can look more like a simultaneous game but but you're right until then there's all this collusion happening and that is going to complicate these pictures a lot in fact often in game theory what we'll do just because we're looking at it an introductory level is looking at two players so we don't have to worry about the collusion part but you're right in real complex situations with lots of players they're forming coalition's with other parties and so on think about a european-style democracy we're actually taking control of the government isn't a question that any one party can do on its own you have to form coalition's with other parties that can make things a lot more complicated and then it can be much more well it's interesting yeah sometimes that becomes more sequential because you for Macklowe coalition with that party and then this party scrambles to form a coalition with that one but sometimes it can really be simultaneous you walk in to the vote and you see how the vote goes and it can all be happening at once other examples of this yeah life yeah good life is often like this right you don't know what other people are doing at the same time you make your commitment and so that's I mean it in a certain sense you face situations like this every day and that makes that's part of what makes life complicated you have limited information here are some examples I was able to think of sometimes proposals people submit proposals let's say for grants or for projects or other kinds of things and a bunch of other people are submitting proposals at the same time you don't know what they've done yet they don't know what you've done submitting college applications can be like that there are auctions where it has this form now some auctions are open and it'll be like you know ah who'll give me $50 for this small statue of Aristotle that's at red you bid and you know what other people are bidding and so on you can see their hands going up but other auctions are closed and sealed bid you know you just say hey here is here is a bit of property submit your bid and that's something where you don't know what the other people are bidding football play calling is like this okay at least if you've got a decent team they they don't the offense and the defense are there and deciding on the play they're about to run separately and you might know the history of what people have been doing but at the time the offense calls its play in the huddle they don't know what the defensive formation is gonna be yet and the defense doesn't know what the offense is called when they set up their formation so you've got a situation where it's a simultaneous game yeah that's true that's true they can audible so that the audible is a way of trying to turn this into a sequential game so I see where you are in the field now I do this ah good good good yes exactly so you should cheat I mean normally literally in baseball for example it's a simultaneous game in the sense that the pitcher and catcher communicate about what pitch to throw and then the batter gets set and is expecting a certain kind of pitch but this to a large extent has to decide on certain things before that pitch is even thrown I mean the batter can react to some things but how long is 60 feet six inches away how quickly does that ball get to home play often it's less than half a second and so that's not much time to make a decision and move the bat around into any position so to a large extent the batter has to decide am I going to try to swing at this or am I going to take this pitch before they have any real information about whether it's a changeup a curve a fastball etc and that means it has the features of a simultaneous game however if you have somebody on second base and they manage to steal the catcher sign or let's say you have a camera back in center field and some teams have done this then you say aha curveball and if you have a way of signaling that to the batter that can be a huge advantage right so watch those third-base coaches this sort of you know all that has a meaning you know some of it has a meaning there's a lot of other garbage in there so that you don't know what has a meaning or not but some of that is going to be you know telling the batter might be take whatever but it might be an anchor ball coming up etc so so yeah that's a way of often it's to your advantage if you can turn the simultaneous play into a sequential one in that way by getting more information very helpful of course similarly a team can give away information there was a year if you followed Texas football a few years ago when it was the same thing every time first down oh we're to throw a screen pass second down since that didn't work we're going now it's second and long they expect us to pass so we're gonna running up the middle then third down well now we've gone nowhere into place so we'll just throw it randomly down the field and that happened again and again and again I mean people in the stands were calling the plays you know it was like Oh first and ten okay X screen yeah that didn't work when you know the offensive coordinators name it's a bad sign okay people were so angry in any event voting is like this you cast your vote you don't know yet what other people are doing in the past in the voting booth a battle is often like this you weren't formulating your battle plan in a way you don't know what the enemy commanders are planning invitations are like this you invite people to the party at the same time and they might all have to respond to the invitations without knowing who else is accepting and so forth and exams of course are like this you put down your answer you don't know okay ideally you don't know what other students are saying it responds to that exam question of course you might anyway okay so in a sequential game you choose actions before or after the other players and lots of games are like this I already mentioned chess white moves black sees what white has done and then responds okay later players have information about previous choices and I move independently of you you know what I've done when you respond hey quick examples of that in our last few seconds yeah that's right in basketball you get to see where the other players are as you're deciding where to go it's not like you have to decide okay I'll do this without knowing what they're doing you get to get constant information about what the defense is doing yeah ah good yes you often can see what they've done as you go around the table it's not like you all have to commit at the same time yeah negotiations can be like this that's right you propose something then you respond etc etc it's not like you both submit your things now if you're both going before an arbitrator you may have to do it at the same time but an ordinary negotiation isn't like that ah I'll pay you $250,000 to 52 etc you're you're doing this back and forth so that's a sequential situation alright next time we're going to look at the games that really have some philosophical power to them after we consider a couple of simpler examples just so we can get some concepts under our belts

Channel: Daniel Bonevac

Views: 7,983

Rating: 4.9298244 out of 5

Keywords: Game theory, Zero Sum Games, Simultaneous Games, Sequential Games

Id: DLl--A0gV3w

Length: 42min 36sec (2556 seconds)

Published: Mon Mar 25 2019