Week 4: Sustaining Cooperation

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Week 4: Sustaining Cooperation

“Group Rationality And The Rationality of Individuals…Why is Group Rationality Different From Rationality of Individuals?…Group Rationality vs. Rationality of Individuals in Biological Evolution…Group Rationality vs. Rationality of Individuals in Social Thought…How to Enforce Socially Desirable Outcomes…Cooperation of gas Stations in Long-Term Relationship Part I: Need For Cooperation…Cooperation of Gas Stations in Long-Term Relationship Part II: Mechanism of Cooperation…Reputation And Brand Name…Cooperation in Loosely Knit Organization…Summary of the Course…: Final Message…”
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Summaries

  • 4-1 Group Rationality And The Rationality of Individuals
  • 4-2 Why is Group Rationality Different From Rationality of Individuals?
  • 4-3 Group Rationality vs. Rationality of Individuals in Biological Evolution
  • 4-4 Group Rationality vs. Rationality of Individuals in Social Thought
  • 4-5 How to Enforce Socially Desirable Outcomes
  • 4-6 Cooperation of gas Stations in Long-Term Relationship Part I: Need For Cooperation
  • 4-7 Cooperation of Gas Stations in Long-Term Relationship Part II: Mechanism of Cooperation
  • 4-8 Reputation And Brand Name
  • 4-9 Cooperation in Loosely Knit Organization
  • 4-10 Summary of the Course
  • Final Message

4-1 Group Rationality And The Rationality of Individuals

  • Okay? So let me begin by talking about the difference between what is rational for the society, and what is rational for each individual.
  • That is, what is good for society is not equal, not always equal to, or quite often not equal to, what is good for each individual, okay? To achieve what is good for society, we need to cooperate.
  • It’s best for society if we keep the park clean, okay? So, we need to cooperate to keep the park clean.
  • You have an incentive to leave some garbage behind you, okay? So, this is one example, very familiar example where, what is good for society is not equal to what is good for each individual.
  • It’s best for our society that all countries cooperate to stop global warming.
  • Okay, again, what is good for society as a whole is not equal to what is good for each individual.
  • So let’s recall the, famous game prisoner’s dilemma which makes this point, very clear.
  • Okay, so if they cooperate and to do not tell the truth they are in prison for one year.
  • If you compare those two outcomes, mutual cooperation and mutual defection, obviously, mutual cooperation is better for them, okay? And, but what happens if you defect and your opponent is going to cooperate.
  • Okay, so let’s suppose you are player one, and your opponent is player two.
  • The society, for the society as a whole, mutual cooperation is much better.
  • Okay, so this example clearly shows that, what is good for the society is different from what is good for each individual.
  • Okay let me first define what is good for society.
  • Now let’s examine how we can define what is good for society.
  • Okay, so let me explain it by means of this simple diagram.
  • So society consists of two players, say player A and B. And the, this grey area here represents possible payoffs in the society, okay? The question is how we can define what is best for the society.
  • But this, it’s a little bit tricky question and it’s easier to define your point.
  • So let me define, what is not best for society first.
  • Okay? So obviously at this starting point, you know, black point is not socially optimal, because we can make everybody happier.
  • Okay, what about this red point here? Again, this is not socially optimum.
  • So by moving from here to here, you can make society better.
  • This red point here is not best for society.
  • So those two points, red point and black point, are not the best of our society because it’s possible to make society better.
  • On the other hand, the yellow points here on those yellow points, there is no better point for society.
  • So the conclusion is, what is best for society is not a single point. Those yellow points here, which correspond to downward sloping part of the boundary, represents the set of what is best for society.
  • Okay? And, those best points for society are sometimes called efficient points or efficient outcomes.
  • Okay, so those yellow points represent the set of best points for society efficient outcome.
  • Group rationality means that players should select one of those best points for society.
  • Nash equilibrium waits inside.
  • Group rationality is different from rationality of individuals, okay? So, I use this diagram again and again, so please remember what usually happens in the game.
  • The price of anarchy is the measure of inefficiency of Nash equilibrium, gap between what is rational for the society and what is rational for each individual.

4-2 Why is Group Rationality Different From Rationality of Individuals?

  • Okay, so one of the most important messages of game theory is that group rationality, what is good for society, is different from what is good for each individual.
  • Group rationality is different from rationality of individual players, and Nash equilibrium is quite often not efficient, okay.
  • Okay, so let’s consider a simple situation where society consists of two players A and B, Andy and Becky.
  • Here is Andy’s payoff and Becky’s payoff.
  • Let’s consider a very simple situation where the society benefit for the society is just a summation of players’ payoffs.
  • Okay, society’s payoff is a summation of Andy’s payoff and Becky’s payoff.
  • So let’s say this is Andy’s profit, $100. And this is Becky’s profit, $300. And the society’s benefit is the sum of those two numbers, $400. Okay, a puzzle is the following.
  • Well, game theory shows that individuals maximizing those payoffs, it’s not equal to maximizing total payoff.
  • This is a puzzle because if, you know, Andy is maximizing his payoff, and Becky’s also maximizing her payoff, automatically it seems to me that the, society’s payoff is automatically maximized.
  • Because society’s payoff is just a summation of Andy’s payoff and Becky’s payoff, okay? Game theory somehow shows that this doesn’t happen.
  • There are basically two reasons why Nash equilibrium is different from maximizing society’s benefit, okay? The first reason is the following, okay? So, Andy is trying to maximizing his payoff by acting alone, okay? Andy’s effort alone cannot create social benefit, okay? The same is true for Becky.
  • Now let’s consider the situation where each player alone can create some social benefit, okay? In this case, Nash equilibrium is inefficient if the benefit you are creating is not coming to you, okay? So you alone can create some social benefit, but benefit is not coming to you, okay? So in such a situation the outcome is often socially inefficient.
  • Okay, so let me go back to this simple diagram, Andy’s payoff and Becky’s payoff, okay.
  • So the first example to make my point is the famous game of I scratch your back, and you scratch my back, okay? So if we both scratch our backs it, it’s better.
  • Okay, if I, as Andy, scratch your back, it’s costly to me.
  • Payoff is decreasing, but Becky’s payoff is increasing.
  • Altogether, the society’s payoff is increasing.
  • Okay, so in this situation, each individual, say Andy, doesn’t have any incentive to cooperate.
  • Y’s payoff is very low but Becky’s payoff is very high.
  • Okay, scratching is costly so Becky’s payoff decreases a little bit, but Andy’s payoff increases.
  • Altogether, compared to the original situation, their payoff increases, okay? So, even though each individual doesn’t have any incentive to cooperate, if they cooperate, they may be better off.
  • Okay, so at the best point maybe you can increase your payoff by taking antisocial behavior, which reduces total payoff to the society.
  • Okay, you are not paying the cost of your bad behavior.
  • Country B’s payoff decreases, and in total the global payoff may be decreasing, okay? So this pollution is antisocial behavior which reduces total benefit to the society.
  • In total, society’s payoff may be decreasing.
  • Okay, so if cost of cheating may be paid by if cost of cheating is paid by other players, you have an incentive to cheat.
  • Okay, rational individuals may want to cheat at the best point for society.
  • Okay, so let me summarize the second reason why Nash equilibrium is inefficient.
  • Rational individual who maximizes his own payoff ignores the effects to other players, okay? So therefore, a rational individual may not take a good behavior that greatly benefits others if it’s costly.

4-3 Group Rationality vs. Rationality of Individuals in Biological Evolution

  • Okay, so let’s consider we have several species A, B, and C and the specie A has maximum fitness, that means A has the largest number of offspring, okay, lots of, you know, kids created by species A, and if that is true, if species A has maximum fitness, greatest number of offspring’s, then the society is eventually dominated by species A, okay? So this is a very simple idea of the survival of the fittest or a natural selection, right? So the old idea says that evolution leads to maximum fitness of a species.
  • If species doesn’t maximize its fitness, it’s going to extinct, okay? Evolution selects species which maximizes its fitness, okay? So there seems to be nothing wrong about this idea.
  • We have already seen how we can apply because of the game theory to biology, okay, so the new idea is the following, in each species, such as wolves there are a variety of different genes in the same species and those genes play a game, and successful genes have more offspring.
  • Okay, so if a gene produces a successful behavior, it’s going to produce lots of copies, and eventually evolution leads to a Nash equilibrium played by those genes.
  • So the new idea says that evolution leads to a Nash equilibrium of the game played by genes, okay? So what’s the difference between this new idea and the old idea? Well let’s suppose genes play a game that is very similar to Prisoner’s Dilemma.
  • Okay, so there are two genes cooperate, cooperating gene C and the defecting genes D. And Prisoner’s Dilemma says society’s benefit is largest, the fitness of the whole society is maximized if cooperation strategy C is adopted, but defection is always better than C. So let, let’s examine what’s going to happen in this hypothetical situation, possible strategies are cooperation or defection.
  • The destination of biological evolution is a Nash equilibrium played by a game played Nash equilibrium of a game played by selfish genes.
  • So genes are randomly matched to each other to play a game like this.
  • So if you compare cooperating situations CC, you have lots of offspring’s, so each gene can produce three copies of itself and, but in this situation where everybody is defecting, this defecting gene in this society of defecting genes only, they can produce only two offspring’s, okay? So if society is here, you know, the gross of population is very low but if society is here, the gross of society is very large, okay? The fitness of the society as a whole is maximized here, and this is a bad situation.
  • So originally we’re in this happy situation and society is growing fast, ‘kay? Each gene of corporation is producing three copies.
  • Suppose now mutant comes in, okay, so lots of people are playing C, so D is most likely eh, is matched with C, but in this situation his payoff is 4, so that means why lots of existing gene C are producing three copies but the defecting gene is producing more than three gene copies, okay? So a defecting gene, if defecting gene invades a pool of of cooperating genes, his offspring is larger than the existing gene, so each gene D produces four offspring’s.
  • No matter what your opponent is going to do, defection is always better for you, okay, so gradually the population of D, relative share of D, should be increasing because D is producing more offspring’s, okay? So the proportion of D is increasing, and increasing, and in the end, society is trapped in this bad situation, all right? This is exactly what happened in my hypothetical example.
  • So remember that each individual, say a bird, carries a gene, either C or D, and if a bird has gene C the birds may be cooperating, okay, and they the cooperating birds can defend their nest together.
  • What about a defecting gene? If a bird has defecting gene the bird shirks.
  • Or in another example, maybe cooperative gene tells you to work hard, and defecting gene tells you to shirk.

4-4 Group Rationality vs. Rationality of Individuals in Social Thought

  • Now, let me talk about the impact of Game Theory to social philosophy or social thought, okay? So one of the most important messages of Game Theory is that group rationality, what is good for society, is different from the rationality of individuals.
  • Okay, textbooks are pretty expensive, so there is well organized used book markets and especially in the United States.
  • Okay, so a suppose she is going to buy a textbook and she’s willing to pay up to $80 for game theory textbook.
  • This yellow bar shows her willingness to pay $80 and this person is happy to sell game theory textbook if the price is above $20, okay? So, his minimum acceptable price is $20, but she’s willing to pay up to $80. So the difference between 80 and 20 is the benefit created if they trade.
  • So on and so forth, okay? So this downward sloping stepwise curve represents willingness to pay of various potential buyers.
  • Okay? Benefit of trade is maximized at this particular point, okay? So how we can maximize the trade from benefit? How we can maximize the social benefit? Well, we can just use competitive market.
  • Okay, so this is social maximized social benefit, and it’s maximized by using competitive market.
  • How, how many textbooks are sold and vertical axis shows the market price for the used game theory textbook.
  • Okay, so in market this minimum acceptable price is supply cut, okay? And the willingness to pay is the demand cut, okay? So if the price is high, only those few who have very high willingness to pay is happy to buy.
  • And by the same token, if market price is low, only those potential sellers whose minimal acceptable price very low willing to supply.
  • Okay, this is exactly what Adam Smith called invisible hand.
  • So economists know that in competitive market, individual rationality and group rationality are the same, okay? But some economists argue that a similar thing is, similar is true, the same logic should be true in general social problem.
  • Okay, so if the present situation is not socially optimal, by definition, it’s possible to make everybody happier.
  • Rational individuals must agree to make everybody happier, okay? So, if present situation is not socially optimal, people move toward, you know, better situation.
  • Okay, so this generalization, this social philosophy says that it’s best to give rational individuals freedom to choose, okay? And then, outcome is always best for the society because of those three reason.
  • Conservative economists were not at all convinced, okay? Then in the 1980s, game theory became a dominant model of research in economics.
  • So Game theory says that, well, there is nothing wrong about one, two and three, okay? One, two, three make perfect sense.
  • The agreement reached in number three may not be sustainable, okay? So there’s nothing wrong in one, two, and three, but the conclusion, there is a gap between those reasoning and conclusion.
  • Okay, so basically this naive argument is wrong because agreement reached in number three may not be sustainable.
  • Okay? So the naive idea of Laissez-faire says that if you give rational individuals freedom to choose then, it automatically produces the best outcome as a society, okay? So, that’s the idea but, if you apply this idea to global warming, it’s silly, right? So if you give that rationale, you know, countries, freedom to choose any pollution level, ‘kay, the outcome is not best for the society.

4-5 How to Enforce Socially Desirable Outcomes

  • Okay, so individual has an incentive to deviate typically at a socially optimal point.
  • Design trading rules optimally so that the Nash equilibrium is efficient in the first place.
  • Change the rules, design the organization and rules.
  • First, designing the system or institution or market trading mechanism optimally, so that the Nash equilibrium is efficient in the first place.
  • If rules of the game is given, if the game is given, game theory predicts what kind of behavior is going to happen, okay, Nash equilibrium, for example.
  • So you can design the system or institution or trading rules carefully by using the knowledge of game theory in such a way that individuals have an incentive to achieve a good outcome.
  • Okay, so let me just explain briefly what market design or mechanism design has achieved.
  • So game theory has been applied to design real institutions, institutions in real society in the following examples.
  • Game theory’s used the knowledge of game theory to design an optimum mechanism to match those young doctors to hospitals.
  • Also mechanism design or market design was applied to design auction rules to allocate spectrum bands to mobile phone companies.
  • The question is, how to design the trading mechanism to allocate towards specular, spectrum band efficiently to cell phone companies.
  • Again, mechanism design was used to design good auction rules, okay.
  • The first way to achieve efficient outcome of the society is to design the system carefully, so that the Nash equilibrium, or the consequence of individual rationality leads to the good outcome.
  • Okay, second way of achieving a good outcome in society, okay.
  • By signing a legally binding contract, people can enforce an efficient outcome.
  • Okay, so you can sign a legally binding contract to enforce a desirable outcome, where individuals have an incentive to cheat.
  • If you construct a house, you sign a detailed construction contract.
  • The point here is, those contracts should be formal, legally binding one.
  • So legally binding contract means, that if contract is breached, then penalty is imposed by the court.
  • Okay if the con, the contract specifies you have to do certain things by the certain time and if you don’t obey this contract clause, you are penalized by the court.
  • At the socially optimal point, when people are cooperating, individuals may have an incentive to cheat, okay.
  • Under the legally binding contract, penalty is imposed by, by the court.
  • So this is how a legally binding contract supports cooperation or efficient point of the society.
  • This condition plays a very important role in designing you know, optimal institution or a writing optimal contract.
  • Okay, gains from cheating should be less than penalty.
  • Okay, that’s good, but we often do not sign a legally binding contract.
  • You can ask yourself or your family, how many times have you signed a legally binding contract at all? I guess for many people they explain, many people, they explain, experience very few times, you know, that they signed a legally binding contract.
  • So the use of binding contract is not widespread because, it’s costly.
  • It’s costly to prepare for detailed clauses, contract clauses.
  • Also in the, in the case where contract is breached, you have to sue the other party and litigation is very costly.
  • So in that case binding contract may don’t, may not have many power.
  • According to it, it depends on the situation, but there may be no legal system to enforce a contract.
  • We don’t have international code powerful enough to enforce contract signed by countries, okay.
  • Country signs contract but it’s a gentleman’s agreement.
  • In the case of global warm, warming, there is no legal system to enforce a contract.
  • So in that case, signing a legally binding contract is not available.
  • This is a less costly, and more flexible alternative to a legally binding contract, okay.
  • Recall how a legally binding contract works, okay.
  • If contract is breached and a legally binding contract penalty is imposed by the court.
  • That’s the basic mechanism of legally binding contract.

4-6 Cooperation of gas Stations in Long-Term Relationship Part I: Need For Cooperation

  • Every morning those gas stations post prices, right? 3, $3.5 per gallon, and so on.
  • Okay, different prices means, that all customers go to the cheaper station, okay? Because gasoline is gasoline.
  • So unit cost is the wholesale price which those gas station pay to a gasoline company.
  • Horizontal axis, I measure the quantity of gasoline, and vertical axis measures the price.
  • Let’s say unit cost of sale is $2 per gallon, okay? So what could be best outcome for those two gas stations? Well, they can charge a price that maximizes their total profit.
  • For one unit of gasoline, the profit is a difference between $3, the price, and $2 cost, ‘kay? For each unit the profit is $1. And this is the quantity solved, which is determined by market demand.
  • You choose the price so that you maximize the size of this area, total profit.
  • So by slightly undercutting the price gas station 1 can steal all customers from station 2.
  • Since the price is not changing so much, effectively gas station 1 is stealing all the profit of, from 2, gas station 2.
  • Okay, so by slightly undercutting the price from optimal price of $3, gas station 1 can almost double its profit.
  • So each gas station is tempted to undercut the price to increase, or steal the profit from the other gas station.
  • Each gas station has an incentive to undercut supplies and to steal customers from the other station.
  • Well, you can see that even if the price is not optimal, say $2.5, then the same logic applies.
  • Each company, or each gas station can undercut the price and steal the other station’s profit.
  • The only Nash equilibrium in this situation is that they charge the price which is equal to the cost, and they are both earning zero profit, okay? Obviously, this is a Nash equilibrium because each player cannot possibly gain any positive profit.
  • If other company, or if other gas station, if is charging price too, and if you increase your price, nobody comes to you, okay? So your profit remains to be zero.
  • If you undercut the price, all customers come to you.
  • The Nash equilibrium of price competition game predicts zero profit for those companies.
  • This prediction should be true when they play the price competition game only once, okay? So they post the price today, and they get some customers today, and that’s the end of the game.
  • The important point you should notice is that those two stations are not playing this price competition game only once, ‘kay? They are located side-by-side, and they play this game of price competition again and again, today, tomorrow, the day after tomorrow.
  • In reality, they play the price competition game every day, and that’s what I call long-term relationship, okay? And in the long-term relationship a positive profit may be achieved.
  • So let’s think about how to formalize this situation, long-term relationship of two gas stations, okay? Well, you have the same players, gas stations 1 and 2.
  • Repeated game has the same set of players, playing the same game again and again, okay? By analyzing this dynamic game, instead of analyzing price competition in one day, we can see that those gas stations can actually sustain positive profit.
  • So let me briefly explain the intuition about how they can sustain high price in dynamic price competition, repeated game.
  • Well the following could be a very plausible considerations of those two gas stations, okay? Well, I can undercut the price today, and I can certainly increase my profit today by stealing customers from the other gas station.
  • That’s true, okay? But if I do that, if I undercut the price today, then it may trigger very harsh or cutthroat price competition in the future.
  • Other you know, gas station, may react and price in the future may, may go down, okay? And if that happens, after all, that’s not going to be good for me, so therefore, even though I can gain something today, then future, you know, consequence is really bad. So overall, you know, I’m better off by refraining from undercutting the price.

4-7 Cooperation of Gas Stations in Long-Term Relationship Part II: Mechanism of Cooperation

  • Now let me explain how those two gas stations can maintain high price in long-term relationship.
  • So high price may be sustained in long-term relationship by the following kind of consideration.
  • Well, I can undercut the price today to steal customers from the, you know, next, gas station and I can certainly increase my payoff today.
  • If I do that may trigger a fierce price competition in the future.
  • After all that is not good for me, so let me just stick to high pricing.
  • I’m going to show you how to formulate this basic idea in the formal model of repeated game played by two gas stations.
  • So you start with high price, $3 per gallon, and if you keep on charging the same high price, $3 per gallon, if nobody has deviated before.
  • If anyone has deviated from $3, then you set price equal to cost.
  • Okay, so let’s examine the nature of this strategy.
  • What happens if two gas stations follow this strategy, okay? So, item number two, number one, number two says that, in the equilibrium, okay, nobody deviates and the high price of three is maintained every day, okay.
  • In the equilibrium, cooperation, high price, $3 is maintained every day.
  • If anybody deviates from $3, if anybody undercuts supplies, then they set price equal to cost forever.
  • Okay deviation triggers cut-throat price competition.
  • In the gas station example after a deviation, they set price equal to cost.
  • What is this? Well, this is the Nash equilibrium of the price competition played in every single day.
  • Stage game is the price competition game which they play every day.
  • Okay, so if anyone deviates, play Nash equilibrium of the stage game.
  • Like, cut-throat price competition in gas station example forever.
  • In gas station example, if you undercut you can increase your payoff.
  • Okay let me closely examine the condition under which trigger strategy is in equilibrium.
  • So let’s suppose that cooperation that means charging a high price of three in gas station example.
  • Let’s go back to the gas station example and let’s suppose cooperation charging a high price of three, gives each gas station $100 every day.
  • Well, so if you consider, say, gas station A, this is what gas station one, let’s say, gas station one is going to earn.
  • Any period starting from, say, March 1, March 2, March 3, this gas station is earning $100, okay.
  • Okay, so let’s examine what happens if he deviates, gas station 1 deviates on March 1st. By slightly undercutting the price, okay, gas station can almost double its profit by stealing customers from gas station two.
  • His profit almost doubles if, he slightly undercuts the price.
  • What happens in the future? Well, this cheating triggers cut-throat competition and the gas stations start charging very low price.
  • So before going to what, what’s going to happen in the future let’s calculate the game today.
  • If you undercut the price by cheating your profit doubles so the gain from defection is the difference of those two numbers, and you can gain $100 today by cheating, okay.
  • Now let’s examine what’s going to happen in the future, okay.
  • This cheating triggers cut-throat price competition in the future, and all future benefit is gone.
  • So how can we evaluate those stream of losses coming on March 2, March 3 and March 4 and so forth? Okay.
  • Let’s think about the value of $1 in March 1st and dollar of $1 in the distant future, say December 31st. Okay.
  • Okay, so the future loss is here, d is the value of $1 in tomorrow.
  • Okay, so therefore, gas stations can cooperate and maintain a high price by possibly by a trigger strategy in their long-term relationship.

4-8 Reputation And Brand Name

  • It’s the quality of dinner it’s very expensive, $50, is it high quality? Or is the dinner low quality? The problem here is well, you know the quality only after eating, right? So your consideration is well, maybe I will be cheated, you know.
  • How can the restaurant assure high quality and earn high profit in this kind of situation? Okay, and if you come to this restaurant every day, it’s very easy to sustain high profit and high quality situation.
  • So if you come to this restaurant every day, your trigger strategy may support high quality.
  • Well if you are served a low quality dinner once, you just stop coming, okay? And since you are, you are usually coming to this restaurant every day, you are very value, valuable customer.
  • First, you cannot observe quality of product or service, and you can only discover the quality after consuming the product or service.
  • Quality is unknown, but quality matters a lot.
  • You may expect a high quality and buy the product, but actually the quality of the product maybe very low.
  • Buying a car you know, quality of the car matters a lot same problem.
  • Okay, you don’t get surgery many times, and quality matters a lot.
  • Maybe you are seeking legal consulting of a lawyer and you encounter the similar problem? How do they sustain high quality and get high profit.
  • Let me explain how reputation and brand name solve this basic quest, basic problem of, you know, sustaining high quality and high profit.
  • When a restaurant has a good reputation, customers believe high quality.
  • Okay, therefore restaurants can, the restaurant can charge a very high price and earn high profit and actually high quality dinner is served.
  • Why? Okay, if restaurant cheats and provide low quality dinner, what’s going to happen? Well, you can write you can use your Twitter or you can, you know, say bad things about restaurant over the internet.
  • If restaurant loses good reputation, what’s going to happen? Well, customers expect low quality a restaurant cannot charge high price.
  • This is an important list, the customer’s expectations fulfilled, quality, quality is actually low because once reputation is lost, it’s very difficult to get it back. So since reputation is already low and it’s going to be low for a long time restaurant has no incentive to provide a high quality dish because it’s costly.
  • So let’s examine the basic mechanism to sustain high quality and high profit by means of brand name or, or reputation.
  • Suppose the restaurant in the restaurant example can gain by providing cheap, low quality food.
  • The gain is 250 today, okay? So if restaurant reduces the quality of dinner today it can get extra profit of $250. But then restaurant loses its, its reputation and their daily profit is going down by $100 every day in the future.
  • Same mechanism should be operating to sustain good outcome, high quality and high profit.
  • Restaurant, expensive clothes, car, house doctor for surgery, lawyer for legal consulting, quality is, quality of service or goods matters a lot.
  • You cannot verify the quality before buying in those, all those instances, and therefore you may be cheated. But, high quality is assured and the producers or sellers can maintain high profit by means of reputation or brand name.
  • As you can see in those examples, usually there are good company with good reputation whose quality is high and they are earning high profit.
  • Companies with low reputation or no reputation, or companies without any brand name, supplying low quality product and earning low profit.

4-9 Cooperation in Loosely Knit Organization

  • Okay the basic mechanism to sustain cooperation is basically the same as in the gas station example we have seen in, in the previous lecture.
  • It’s possible to sustain cooperation’s, it’s possible to sustain cooperation, theoretically.
  • Sustaining cooperation in a loosely knit organization is not only theoretically possible, but we found a remarkable real-life example.
  • Okay, theory of cooperation in loosely-knit organization.
  • Let me start with theoretical possibility, okay? Loosely-knit organization can be formulated as a special kind of repeated game called OLG repeated game.
  • In long term relationship, good behavior is reciprocated by the same person.
  • A wonderful example we found was, what’s called the Community Union.
  • Actually, my co-author Shia Obayasi was first to notice that community union was a wonderful example of overlapping generation gain.
  • Okay, community union is a labor union with a very unusual form.
  • Let’s explain the structure of Community Union.
  • The definition of Community Union, Community Union is a labor union which admits individual affiliation.
  • If the company has a labor union, the union can represent you and fight against the firm.
  • Let’s suppose the, the company doesn’t have any labor union.
  • One thing you can do is join Community Union by yourself, okay, even if no other people in this company are joining Community Union, you alone can be a member of a Community Union.
  • Okay? Single affiliation is allowed in community labor union.
  • Community Union can exercise it’s legally protecting, protected rights to negotiate with this firm to result the labor dispute between you and the company.
  • Okay, so lemme explain a typical life of a member of a Community Union.
  • So first you have a problem with your company, dispute happens, and then you join the union as a single member from the company, and that union can negotiate with the firm, and if negotiation if an agreement is reached in the negotiation, then that’s the end of the story.
  • If agreement was not reached in negotiation, then labor union can, you know, organize protest activities.
  • Because it’s based on legally protected rights of labor union.
  • Union can organize protest activities and also a union can sue the company in litigation.
  • A union can perform those activities and then the dispute is resolved and then the member usually exit fro, from, from the union.
  • Each member only stays in the union for one or two years.
  • So we conducted a case study about one of the labor unions called the Tokyo Managers’ Union.
  • In the fiscal year of 2012, altogether, company, the union had 105 entries and 108 exits.
  • What’s the duration of each member? Well, each member stays in union on average 1.92 years, okay? So this union has a structure which is, you know, closely related to Overlapping Generation Game.
  • Each player stays in the union roughly 1.92 years.
  • Okay, so did they cooperate? Well, mainly cooperation happens here in protesting activities, and attending court session, and attending the labor relation commission meetings.
  • How is cooperation sustained in the union? Okay, so how is cooperation sustained in the union? Well, the basic mechanism was already explained.
  • Okay? If he deviates, future generation punishes you.
  • One possible way of sustaining cooperation in union.
  • Okay, so this is theoretically possible but this is not the mechanism in the union.
  • Okay, so let me tell you one important thing here, theory of repeated games show that there are lots of other ways to sustain cooperation.
  • Okay? So the challenge here, is to find out the mechanism actually used in the area? Okay what about the possibility of Reputation mechanism that we, we have seen? If yellow player is doing good thing, he maintains good reputation and people who have good reputation are going to rewarded by future generations.
  • Okay? Originally, we suspected that this could be a mechanism in the union.
  • Okay? People don’t know each other’s reputation well in, in this community union.
  • What’s the difficulty of sustaining cooperation in this union? Well.
  • Okay? So you can interpret this situation in two completely different ways.
  • Okay? So if one is not helping someone, there are two interpretation and maybe it’s defection or maybe it’s punishing a defector.
  • By conducting a detailed interview with one member we, we discover a very clever simple equilibrium, that can sustain corporation, in labor union.

4-10 Summary of the Course

  • Game theory provides a generally applicable principle, a governing principle, which can be applied to any social problem.
  • Political campaigns, negotiation, market competition, traffic allocation, struggle for existence of animals and a parlor game like poker.
  • There might be a general theory which can be applied to all those social problems.
  • The question is to find out that this general theory, which can be applied to any social problem.
  • Okay, game theory found out that by the same mechanism, which assure us the existence of a vortex point on coffee surface.
  • So by the same mathematical reason that a vortex point exists on coffee surface, game theory discovered that any social problem has a point where players are doing their best.
  • Nash equilibrium is a point where players are doing their best against others.
  • What does game theory do? Well, given any social problem like negotiation, political campaign, traffic allocation, any social problem can be formulated as a mathematical model of game.
  • Okay, so a mathematical model of game specifies players and the possible strategies and their consequences, payoffs.
  • Any social problem can be formulated as a mathematical model of a game, and then, by using of the power of mathematics, game theory computes, or finds out, Nash equilibrium.
  • What is Nash equilibrium? Well, Nash equilibrium is a stable situation in a social problem where each player can no longer improve his payoff.
  • So basic prediction of people’s behavior in such a problem by game theory is Nash equilibrium.
  • So in low rationality case, you can accumulate through your experience in the same game or similar game, and you can adjust your behavior by trial and error.
  • Well, even if players have no intelligence, their behavior may be described by game theory.
  • So strategy of a plant may be determined by the gene and the genes are playing a game.
  • So the outcome of biological, e, evolution is very much like, Nash equilibrium of a game played by genes.
  • So even for zero-intelligence case, game theoretic prediction sometimes work.
  • The third message is about the prediction power of game theory.
  • So game theory provides you with generally applicable principle.
  • The card game we played in the first week and the penalty kicks in soccer game.
  • What about the policy choice of Democrats and Republican? Well, the very simple game theory model predicts that Democrats and Republicans should choose exactly the same policy, and the reality, policies are different.
  • So you should remember that sometimes game theory works amazingly and sometimes it doesn’t really work.
  • Well, if it doesn’t give you perfect fit, as it really, is game theory really useful? Well I would argue that even though the fit is not perfect, game theory is useful by the following two reasons.
  • Okay? Prediction power of game theory is not perfect, but game theory is useful because of the following two reasons.
  • The simple game theory framework shows that they should choose exactly the same policy, but in reality, their policies are different.
  • Is game theory completely useless? I would argue to the contrary.
  • Okay? Game theory is pretty useful in this particular example, because it gives you very useful insight.
  • ‘Kay? Prediction doesn’t work perfectly but you can gain very important insight from game theory.
  • Game theoretic model actually, you know, make it clear, one of the driving forces of political campaign.
  • Okay? So game theory is useful in gaining insight what is one of the main driving forces of policy choice of two big parties.
  • What determines the policies of Democrats and Republicans? Well, this is a very general and vague question and without the help of game theory, you don’t know where to start.
  • Game theory assures you that you can always find the Nash equilibrium and the Nash equilibrium tells you that they play, they should choose exactly the same policy.
  • So now you can ask, if parties are not choosing the same policy, what could be the reason? Starting with Nash equilibrium and comparing it with reality and, you try to fill the gap.
  • That’s one of the reasons why game theory is useful if the, fit is not perfect.
  • Well, there is no reason to believe that people always play Nash equilibrium.
  • Well, why? If model behavior is not a Nash equilibrium, somebody can gain by deviating.
  • Okay, so the last message, one of the most important messages of game theory is that, there is a conflict between group rationality and rationality of individuals.
  • Game theory shows how we can possibly overcome this problem.
  • Well, that’s it, and I hope you have enjoyed my course, and I also hope that you will learn more about game theory in the future.

Final Message

  • I suppose now you are ready to think like a game theorist.
  • Now I’d like to give you some remarks on some guides to study game theory.
  • In Coursera, there are two good game theory courses given by Matt Jackson and others, called game theory and game theory two.
  • Also there are some good mathematical game theory textbooks, and I’d like to recommend a few of them, okay.
  • So this is my favorite game theory textbook, I use for graduate students and advanced undergraduate students.
  • It’s a book by Robert Gibbons, and the title is Game Theory for Applied Economists.
  • The book says for applied economists, but I’d like to recommend this book for all of you, because this book teaches you four basic solution concepts.
  • Solution concept for static game without any timing, and solution concept for basic dynamic game with timing.
  • Okay, and there’s also a recent text book by Steven Tadelis just called Game Theory, and this is also a good reference if you have a math background.
  • For most levels, this is the book to read. And also, there are lots of applications of game theory and all those fascinating extension and applications of advanced game theory can be found in this wonderful book called Game Theory, by Jean Tirole and Drew Fudenberg.
  • Well, I hope you have enjoyed our course, and I wish you continue learning more about the wonderful world of game theory.

Return to Summaries.

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