4. Game Theory, Exchange, and Trust

I started this blog in medias res, with markets, yet markets are not really a proper starting place. A novelist might begin with a crisis, to get the reader interested, then fill in the backstory afterwards. So here. A market, as represented by a supply-and-demand chart, is already a rather complex and advanced institution. A lot of assumptions are cooked into it. There must be a system of property rights, else suppliers have nothing to sell, nor customers, to pay with. Property rights must be transferable. There must be some kind of money in place, to facilitate the transaction, and to have units in which to denominate prices. The classic supply-and-demand chart is not a model of barter trade. There must be some kind of standardization of goods, for it to make sense that the quantity axis is a continuous variable.

Game theory is a method that enables economists to study simpler, more primitive and fundamental situations. It has applications far beyond economics, for example in international relations and evolutionary biology. Unfortunately, it is most often used in economics to model competition among firms. The Cournot model and the Bertrand model are the oldest and most venerable of this type. I don’t think game theory is very useful in understanding competition among firms. It starts by simplifying to the point of surreality, then, when it starts the long road back to realism, immediately sinks into a swamp of intractability. It can deliver a few basic concepts, e.g., what collusion is, but it can't get you very far. I think I have a better approach to understanding competition among firms, which is a key starting point for my reinvention of economics. I'll get to that later. But game theory still has an important role.

Game theory starts with players, rules, and outcomes, then analyzes the strategies by which rational players will try to achieve their goals, usually concluding with predictions about what will occur if scenarios resembling the game arise in the real world. In common parlance, the word “game” usually refers to things like checkers or chess, which are too complex to be solved. Game theorists deal in games vastly simpler than that. For example, consider the TRANSACTION GAME shown below:

Here's what every economist or good econ undergrad knows about diagrams like that shown above. (Begin review) The above graph is called the “extensive form” of a game. The game flows from top (the beginning) to bottom (the end). Each of the nodes (the blue circles) represents a scenario that might arise in the course of play, in which one of the players can move. Each of the lines branching out from a node represents a move that is available to the player in question in that scenario. The text boxes next to the nodes say whose move it is, or at the end, says “payoffs” to indicate that the game is over and it’s time to count the gains and losses. The payoffs refer to the overall benefit or loss that the players enjoy as a result of the game. They are denominated in dollars and listed in the order that the players moved, i.e., ($customer payoff, $seller payoff). I’ve numbered the decision nodes to facilitate analysis. (End review)

The narrative behind this game is as follows. A seller has something that a customer values at $15, but which is only worth $10 to the seller. They’ve discussed a price of $12 and found it mutually agreeable. But someone has to move first, and the assumption here is that it’s the customer. The customer either pays, or does not pay. Then the seller either provides the good, or does not provide the good. If no transaction occurs, no gain to either results, i.e., each gets a payoff of $0. If the customer pays, but the seller does not deliver, the customer loses his $12, the seller gains it. In the unlikely event that the seller provides even though the customer didn’t pay, the customer gets the full $15 value, and the seller suffers the full $10 cost. Finally, if the transaction goes through smoothly, with the customer paying and the seller providing, both gain, with $3 of benefit going to the customer ($15 value minus $12 price) and $2 of benefit going to the seller ($12 price minus $10 value).

So, what will happen?

To “solve” the game, we use backward induction. If we arrive at decision node 3, the seller’s best option is not to supply the good. Supplying it gives him a payoff of -$10, which is much worse than his payoff, $0, for doing nothing. That’s a good place to begin the analysis, because the game is then over, so there’s nothing more for the seller to consider. So we can make a confident prediction. If the seller is rational, he’ll decline to provide the good to the non-paying customer.

But now look at decision node 2. Even though the customer paid, it’s still in the seller’s interest not to supply the good! After all, if he supplies the good, he only gets $2 of benefit. But if he declines to supply it, he gets the full $12 the customer paid as benefit. So we predict that a rational seller will just take the customer’s money. Now we can go back to decision node 1. The customer, having analyzed the seller’s optimal strategies at nodes 2 and 3, predicts that “pay” will give him a payoff of -$12, “don’t pay,” a payoff of $0. He doesn’t pay, and the seller doesn’t provide. We’ve solved the game.

But wait a minute. That can't be right! Our conclusion seems to be that buyers and sellers face an insurmountable barrier of mistrust that makes it impossible for them to transact. In the real world, buyers and sellers transact all the time. What's the use of this model?

First, it's useful for theory to draw attention to a solved problem, because we might forget that it's there. Sellers could be “opportunistic” and “defect” from the cooperative game that is a commercial transaction. Buyers could preempt this and not transact in the first place. Why doesn’t this happen?  

Here are four important reasons:

• Law: People may transact honestly because they fear punishment by the government if they don't.
• Virtue: People may transact honestly because that is one of the moral principles by which they regulate their own conduct.
• Reputation: People may transact honestly because they want to foster a reputation for honest dealings, so that they will get more opportunities for profitable transactions in the future.
• Habit: People may transact honestly because it doesn't occur to them to do anything else.

Now, of these four, virtue stands out as particularly desirable and excellent. It's generally good to have as many reasons to transact honestly in play as possible, but law, reputation, and habit all fail in predictable ways and/or are expensive to sustain.

If social trust is based on reputation, young people and newcomers start out in a kind of catch-22. Can't transact unless trusted, can't earn trust except by transacting. Moreover, when a major change makes future transactions unlikely-- during certain disasters, or when one is about to move out of town-- reputation may suddenly lose value and cease to be worth investing in, so one walks away from unpaid bills when one is moving.

If social trust is based on law and fear of the government, the prevalence of honesty will be proportional to the efficiency of the police. Whenever people think the police aren’t watching and can’t easily be called in, they’ll start cheating each other. Moreover, law and government give rise to a “who guards the guards?” problem. If the police have enough power to prevent people from cheating each other, they have enough power to rob people blind.

If social trust is based on mere habit, it can be disrupted by simply putting bad ideas in people’s heads. If a wicked novel is circulated that glorifies cheaters and liars, people might start imitating it. And people are always reasoning and imagining, so if there’s an opportunity to benefit by dishonest dealing, it will probably at least occur to people as a possibility sooner or later. 

But if people are virtuous, they will transact honestly regardless of the incentives they face. That makes social cooperation easier to establish, and less vulnerable to disruption.

Perhaps the transaction game won’t be taken as proof of the economic importance of virtue, because the problem to which it draws attention, and to which virtue is offered as a solution, seems so trivial to solve in practice. But it’s not. In physical marketplaces and stores, when both the buyer and the seller are simultaneously present in person, and the good in question is tangible and portable, and its valuable properties are readily ascertainable, the transaction process is easy. But when the transaction is remote, executed by mail or online, or when the good in question is intangible, like intellectual property rights in a book or a piece of music, or not portable, like real estate, or many of its useful properties are hard to ascertain, or the good or service is to be delivered in the future or on an ongoing basis over a period of time, trust is often an important problem, and many mutually beneficial transactions fail to take place because the potential transactors cannot establish sufficient trust.

One nifty feature of game theory is that a game with the same structure can be adapted to describe many different situations. Consider an Employment Game:

In this Employment Game, the employee can do something for the employer that is worth $1500 to him, while the employee values at $1000 the leisure he would sacrifice by taking the job. There are, therefore, potential gains from trade. The employer considers hiring the employee for $1200. However, he will not be able to supervise the employee effectively, perhaps because the work involves the use of some discretion or special skills, or because the employer is too busy to be present while the job is being done. Moreover, he has to pay the employee even if the work is not done, maybe because the employee can always credibly claim that he was prevented from accomplishing the task by flawed instructions or inadequate materials, or maybe because the employer will only be able to ascertain the quality of the work sometime after the fact, well after the wages are due to be paid. So the employer uses backward induction. If he doesn’t hire the employee, the employee presumably won’t do the work, so he gets a payoff of $0. But if he does hire the employee, the employee is still better off if he doesn’t do the work, since he still gets paid and can do what he likes instead of working.

The only unrealistic thing about the Employment Game is that the employer is completely unable to supervise the employee and make him work, or to withhold payment if he doesn’t. Usually, employers have some ability to monitor employees and punish shirkers. But it’s quite common for an employer not to know what a reasonable pace of work is, and/or not to be able to observe an employee all the time. Employers typically won't know, even when they are observing, whether employees are exerting himself to the best of his ability. And while it’s hard to quantity the exact extent of the phenomenon, it seems certain that many employment arrangements that would be mutually beneficial fail to occur because the potential employer doesn’t sufficiently trust the potential employee. This has little to do with unemployment, by the way. A fully employed economy may nonetheless be full of unrealized employment opportunities, which if realized, would crowd out existing, less valuable jobs. Mistrust causes, not unemployment, but weak labor demand and low wages, as employers forego creating high-value but trust-requiring jobs, in favor of low-value jobs amenable to close supervision and performance monitoring.

The structure of the Employment Game is exactly the same as that of the Transaction Game, and the lessons are the same, namely, that a trust problem will prevent mutually beneficial exchange from occurring, unless it can be solved by forces such as law, habit, reputation, or above all, virtue. In this case, the virtue needed is a “work ethic” on the part of the employee, who, once hired, will hopefully feel honor bound to serve the employer to the best of his ability for the duration of the job.

A third example, the Investment Game, will highlight the generality of the model, and is interesting in itself.

In the Investment Game, an entrepreneur has a bright business idea, but lacks the money to execute it. He needs $1 million, but can-- if he works hard-- earn $1.5 million (over and above the opportunity cost of his labor) over two years. The investor considers lending him $1 million, to be returned plus $200,000 interest after two years. The investor will make $200,000, and the entrepreneur will make $300,000.

I modified the game somewhat since the entrepreneur can’t implement his business plans unless the investor invests. But it is essentially the same. The investor foresees that while it’s advantageous for the entrepreneur to invest and make a profit, it’s even more advantageous for him to get the money and abscond, $1.2 million richer than he was before. So the investor does not invest. Of course, rather than abscond, the entrepreneur might live off the investment capital, then declare his business bankrupt. As before, the trust problem will prevent a mutually beneficial exchange, unless it’s solved through law, reputation, habit, or virtue. If it fails to occur, the entrepreneurial opportunity fails to be exploited. If such entrepreneurial opportunities fail to be exploited, returns to capital fall, and economic growth slows.

Now, it is quite difficult to make a game-theoretic model that sheds a realistic light on competition among firms, which is full of complicating factors like imperfect information and decisions being made continuously and simultaneously. But it is very easy to use game theory to elucidate ethics, and to show why justice and generosity make the world a better place. Indeed, it’s difficult to make game-theoretic models at all, without constantly bumping up against the conclusion that fairness, gratitude, altruism, pity, and so on make it much more likely that game-like scenarios will end in favorable outcomes.

So let me jump to conclusions. No, just kidding: not to conclusions, but to a hypothesis. It’s not the sort of hypothesis that would appear in a textbook, in part because textbook authors are reluctant to entrust undergraduates, who are apt to believe everything they hear, with tentative hypotheses, which their young minds will turn into facts and dogmas. I am genuinely tentative. I merely suggest. The following is only a hypothesis.

Call it the theory of Development as Virtue. The Transaction Game, the Employment Game, and the Investment Game, between them, shed light on why some nations are so rich, and others so poor. It’s because people in rich countries are more virtuous. They are less inclined to cheat each other when exchanging goods and services. They are endowed with a stronger work ethic so that they perform well on the job without close supervision. They are more inclined to fulfill their fiduciary duties to investors when entrusted with the leadership of companies. These virtues facilitate mutually beneficial exchange in markets for goods and services, labor, and capital, resulting in far more productive economic activity than in poorer, less virtuous countries.

Rich countries also benefit from having better-designed laws and more honest governments, widespread good habits, and effective reputation systems that motivate people and companies to do right for the sake of a good name, which is the key to getting continued opportunities. But they owe all these things to a more fundamental factor, namely, virtue. Good laws arise from the agitation of honest, engaged citizens and the labor of relatively non-corrupt legislators striving to serve the public interest. Honest government results from cops and judges and bureaucrats refusing bribes, and being content to live on their salaries, and avoiding conflicts of interests and favoritism too. Good habits become widespread and stable when virtue has so thoroughly banished certain vices and sins that people stop even thinking of them as possibilities. Reputations are more accurate and worth investing in if, when people talk to each other about other people, they try hard to be just in what they say.

It’s only a theory, to enter the lists against other theories as we move forward. But it’s plausible enough to add urgency to the question of how economics relates to ETHICS.