| Chapter 2 | |
| Learn about the Ultimatum GameÑ | |
| or else | |
| We hope youÕve gotten some insights from our discussion of the PrisonerÕs Dilemma. WeÕve got one more game theory concept to talk about, and, donÕt worry, this one doesnÕt involve any criminals. But weÕre not finished with the topic of greed. | |
| ItÕs called The Ultimatum Game [Guth 1982]. Like the PrisonerÕs Dilemma, it starts with a story. There are three participants: The Benefactor, the Donor and the Recipient. You play the Recipient. | |
| The Benefactor offers to give the Donor $100 and says to him: | |
| ÒYour job is to decide how to divide up the $100 between you two, the Donor and the Recipient. You, the Donor, make the decision. You can divide it up any way you like, but you have to make only one offer. If that offer isnÕt accepted by the Recipient, neither of you gets anything.Ó | |
| Now, hereÕs the question: WhatÕs the minimum offer you, the Recipient, should accept? | |
| Same ground rules here as in the PrisonerÕs DilemmaÑjust one round (we can think about the iterated case separately), no discussion between the Donor and Recipient, and putting emotions aside for the moment. | |
| Most people, if placed in the position of the Donor, would make the simple choice to divide it 50-50 and offer you $50. Most people would consider a 50-50 offer fair, and accept. So whatÕs the problem? | |
| HereÕs the game theory answer: Any non-zero offer should be accepted by the Recipient. Even if itÕs only one cent. | |
| What?! That wouldnÕt be fair!!! | |
| Remember, from the perspective of game theory, weÕre putting aside for the moment the emotional aspects of loyalty, trust, empathy and fairness that come into play when real people are involved in real situations. WeÕre just considering whether the financial outcomes are advantageous or not. Indeed, when experiments are tried with real people, their sense of fairness does indeed kick in for most people, and the actual offers are mostly close to fair [Christian 2016]. | |
| Think about it this way. If the Donor is just a little greedier, they might think, ÒSince IÕve got my hands on the $100 right now, I can take a $10 ÔcommissionÕ and the Recipient wouldnÕt have much alternative but to accept. So IÕll offer just $40.Ó. This might still feel acceptable, although the Recipient would probably feel a little annoyed at being taken advantage of. | |
| Now suppose the Donor ups the commission to $20? Still, the Recipient would have to accept. And so on. Even the offer of a single cent would have to be accepted, since the alternative is nothing. Even a cent is better than nothing. ThatÕs the Ultimatum. | |
| ItÕs like the PrisonerÕs Dilemma in that each player can choose to Cooperate (make a fair offer, accept an offer) or Defect (make an unfair offer, refuse the offer). But itÕs different than the PrisonerÕs Dilemma in that the game is not symmetric. The Donor has the upper hand. | |
| Here are the choices: | |
| The decision the Recipient has is between the top row (accept offer) and the bottom row (reject offer). In the table, since $50 > $0 and $1 > $0, the Recipient should accept any positive offer, no matter what it is. | |
| But this situation is not the same as the PrisonerÕs Dilemma. The TRaPS Inequality is not satisfied. Remember the TRaPS Inequality is: | |
| Temptation > Reward > Punishment > SuckerÕs payoff | |
| But here weÕve got: | |
| You might think, ÒHey, the Recipient has some leverage, too. They can always decline the offer, in which case the Donor loses out, too. The Recipient could use the threat of declining the offer to negotiate the commission down to a minimal level.Ó | |
| And, indeed, in some real world situations, this happens. When emotions come into play, many Recipients will decline an offer even when itÕs to their financial advantage, out of spite against being exploited, or out of a sense of standing up for fairness in that situation. | |
| But, like in all game theory scenarios, when weÕre analyzing the situation, we try to put aside our emotions and speculation about Òwhat the other guy is thinkingÓ. Suppose youÕre the Recipient, but the Donor isnÕt another person, but a computer program. In that case, youÕll realize you canÕt Òteach it a lessonÓ by refusing, so your decision boils down to either taking the $1 or getting nothing. | |
| LetÕs look at it from the DonorÕs point of view. The Donor has to choose between the two columns in the table, the Fair offer and the Unfair offer. Since $99 > $50, the Donor will prefer the unfair offer. The Donor doesnÕt know how insistent on a Fair offer the Recipient will be. But thereÕs no difference in the case of the Recipient rejecting the offer, where everybody gets zero. So the Donor Òmight as well tryÓ for the Unfair offer. The RecipientÕs possible leverage vanishes. Unless the Recipient actually has a viable alternative to accepting the DonorÕs offer, the Recipient is stuck. | |
| Trickle down theories | |
| Back in the real world, the Ultimatum Game shows us whatÕs wrong with things like Òtrickle downÓ theories of economic development. The political Right often advocates policies that directly benefit big businesses and rich individuals. As for smaller businesses and lower-income individuals, the Right claims that they will indirectly benefit through Òmaking the pie biggerÓ, even if theyÕre only entitled to a much smaller share of it. Some grain of truth to that. | |
| But if itÕs the rich factions who get to decide the split, then what weÕve got is an Ultimatum Game, where the 1% play the Donor and 99% the Recipient. By the results of the Ultimatum Game, the lower income segments have no choice but to accept anything offered by the rich, no matter how small. | |
| YouÕll notice that the answer to the question of whatÕs the minimum the Recipient should accept is still, Òany positive offerÓ regardless of the amount the Donor was initially given. Still, anything is better than nothing. Increasing the initial amount from $100 to $200 wonÕt affect what the Recipient gets. Nothing assures that the RecipientÕs share will be computed as a percentage of the initial outlay. So much for Òmaking the pie biggerÓ. | |
| ThatÕs why, for example, we have Minimum Wage laws in the US. How are peoplesÕ salaries set? To quote an ad from a popular negotiation course, ÒYou donÕt get what you are worthÑyou get what you can negotiate.Ó In negotiation theory, your leverage in a market is determined by your BATNAÑBest Alternative to a Negotiated Agreement [Fisher 1981]. | |
| By definition, the people at the bottom of the pyramid have nothing below them, so they have no alternative. No leverage. Marx understood this, a century before game theory, and wrote that the lowest-paid workersÕ salaries would fall to subsistence level. And once the lowest level is fixed at near zero, then the people just one level up only have the alternative of the lowest level, so they wonÕt fare much better, and so on. Minimum Wage laws prevent this situation, and thatÕs why thereÕs so much pressure now to update the levels to present economic conditions. | |
| The Right does have a counter argument, which is that market forces will always generate another alternative. If workers are unhappy with their wages, some entrepreneur will always arise to provide an alternative. WeÕll call this counter-argument, the Imaginary Friend argument. Markets do indeed provide some incentive for this to happen, and sometimes it does. But how realistic is the assumption that that alternative will always be there when needed? | |
| ItÕs like the old joke among economists: | |
| Two economists are walking down the street and one sees a $10 bill on the sidewalk. He reaches down to pick it up, and the other grabs his hand to stop him, saying ÒWait! If that were a real $10 bill, somebody else would have already had the incentive to pick it upÓ. | |
| Incentive, by itself, isnÕt enough to cause something to happen. The fact that the Recipient is getting a raw deal in the Ultimatum game might indeed provide some incentive for an external entrepreneur to provide another alternative. But if that alternative doesnÕt actually materialize, the Recipient is still stuck. | |
| How long will it take for the alternative to appear? How much actual, quantifiable effect does it have on the situation? The entrepreneurial mechanism of generation of alternatives is generally far less reliable and effective than the dynamics of the Ultimatum Game. And the rich make money on the spread. | |
| The Right is fond of the image of the lone productive entrepreneur or small business owner. But in the real world, it usually takes a group of people working together to produce significant economic value. So when that economic value actually appears, and the group has to share it amongst themselves, how do we decide who gets what? | |
| In small groups of homogeneous, friendly people, splitting it equally usually satisfies everyone. In larger, more varied groups, however, the power relationships of the Ultimatum Game kick in, so the answer is: The first ones to get paid usually keep most of it, and they distribute the dregs down the line. ThatÕs why your Estate Grown Organic Tanzanian Peaberry Coffee costs $18.99 a pound and the poor farmer in Tanzania gets $0.17 per pound. | |
| Imagine that making a product takes a sequential Òsupply chainÓ of 10 people, each of whom takes input from the previous worker, and spends an hour of work producing the output to be fed to the next worker. You donÕt get the finished product until all 10 workers have done their jobs. Each workerÕs contribution is essential and there are no practical alternatives that could replace someone in the chain. EverybodyÕs contribution is basically indistinguishable. | |
| But now, the consumer buys the product and pays the last worker in the chain, whoÕs the only one that has the finished product. The last worker has all the money and the discretion to divide it up with the rest of the team. That last worker can play an Ultimatum Game with everybody else and offer only the minimum necessary to keep everybody else from rejecting the offer. Enjoy your seventeen cents, Mr. African Coffee Farmer. | |
| Hildalgo refers to this as Topocracy [Hidalgo 2015], where what you receive is determined more by your position in the supply chain than by your effort or the value you produce. The longer the supply chain, the worse it is, which is why disintermediation, cutting out the middlemen, is one of the most effective routes for changing the situation. | |
| The Ultimatum Game mixes poorly with another feature of our capitalist economy: the Law of Supply and Demand. The beauty of this Law in an idealized capitalist economy is that it performs price discoveryÑas the economic textbooks say. It sets the price high enough to incentivize the vendor to produce the product, but low enough so that the customer still agrees to buy the product. But that only really works well if supply and demand are approximately in balance. At the extremes of supply and demand imbalance, you have an Ultimatum Game situation. Then, itÕs Ultimate Game that really sets the price, and the Law of Supply and Demand takes a back seat. | |
| Take for example, the idea of co-pays for medical services covered by medical insurance. In the old days, the idea was that insurance, in order to give you peace of mind, would cover the entirety of expenses. Then the idea of a co-pay was introduced, ostensibly to make sure the patient had some Òskin in the gameÓ and wouldnÕt use medical services unnecessarily. | |
| But at what level should that co-pay be? Unfortunately, medical services arenÕt really like a consumer item like clothing. Generally, when you need them, you need them. You usually only have a very limited discretionary ability to Òforgo the luxuryÓ, or shop around for alternatives. Attempts to turn medicine into a market by imitating the marketing techniques for other consumer goods are laughable. LetÕs see, should I choose the medical plan that has the ad with a kindly old doctor smiling at a baby, or the one that has a beautiful young woman running through a field of ßowers? | |
| EconomistsÕ term for this is that thereÕs little elasticity of demand, and therefore, no really effective competition. The choice youÕre really faced with is Òyour money or your lifeÓ. | |
| The temptation for medical service providers is to slowly raise the co-pay to the point Òthe market will bearÓÑwhich is to say, the same level that would be bearable by the customers in the total absence of insurance. The insurance becomes worthless. This hasnÕt taken place widely yet, but you can certainly expect co-pays to slowly creep up unless government regulators, or industry self-policing groups are vigilant. | |
| ThatÕs a general problem with Capitalism. If sellers charge Òwhat the market will bearÓ, then, by definition, prices will always be just short of unbearable. Do we really want to live in a world where everything is always on the edge of being unbearable? | |
| The lesson is, for trickle down theories to work, someoneÕs got to be constantly checking the water pressure. |