Coordination Games Are Not (Merely) Maximization Problems: Welfare Economics Reconsidered

Leeson (2019) compellingly demonstrates that the logic of maximization entails that every institution is efficient, where efficiency consists of a stable equilibrium in which gains from trade are exhausted. What he wants us to take away from this is not that we live in the best of all possible worlds (that may or may not be true) but rather to think, “So much the worse for efficiency.” Efficiency is not an operational concept in economics. I aim to rectify this problem.

The problem with efficiency is that an invocation of the idea with respect to institutions seems to commit the Nirvana fallacy (Demsetz 1981), which is another way of stating Leeson’s point. “Monopolistic markets are inefficient” — compared to what benchmark of efficiency? Perhaps a government could break-up the monopoly for a cost less than the deadweight loss of the monopoly’s existence, for a net efficiency gain. Then again, perhaps the government’s activity would be more costly. This is Demsetz’s (1964) point. Complicating the situation further, perhaps the dissolution of a monopoly does at present yield a net efficiency gain, but also precludes a future market shift that would have eliminated the monopoly at less cost, which means that, all things considered, antitrust action (or the repeal of rent-creating legislation) may generate a net efficiency loss. The same pattern of reasoning applies to all instances of market failure and of government failure: It is impossible to compare the relative costs and benefits of alternative institutional arrangements.

The problem can be made more precise. Allen (1991) gives us a working definition of transaction costs: the costs of defining and enforcing property rights. Perhaps we can attach a dollar value to the costs of enforcement — intuitively, the defensive output of locks on houses, police forces, and the like can be measured with some level of precision, as can the labor and capital costs required for their production. But what can possibly be meant by the costs of defining? What is the cost of defining a rule?

Let’s suppose this: the opportunity cost of defining a rule in one way is the value of defining the rule in the second-best way. Thus, the cost of defining a rule includes both alternative ways of defining the same rule and defining different rules entirely (sidestepping the ship-of-Theseus question, “Is it still the same rule?”). It is tempting to look at the costs of definition as an empirical question. This optimism is naive at best. We can’t identify the cost of a particular institutional arrangement because we can’t  know the set of possible outcomes that the institutional arrangement will generate, and we can’t know the set of possible outcomes for every alternative institutional arrangement. As Hayek points out, the value of liberty consists in the fact that liberty will generate outcomes that the designer of the system could not foresee (1960, 1991). It is a “fatal conceit” to imagine that we can envision every possible response to a given set of rules.

Thus the true opportunity cost of alternative rulesets must of necessity be indeterminate, where true cost is the one that rule-followers and rule-creators actually bear. The cost of definition is neither a theoretical nor an empirical question; it is an unanswerable one. But we might say instead that choosers face a given probability distribution of costs, or distribution of distributions, or that at the very least they have some conjecture or intuition (that need not match reality in the slightest) of the relative strengths and weaknesses of different rules. Economists like Leeson are inclined then to say that every institution is efficient. Given the logic of maximization, it follows that every institution is efficient: people maximize with respect to their information about benefits and costs of different institutions.

What I want to suggest is that there are cases of decision-making which cannot be properly described as maximizing. Sometimes people have no prior beliefs about the benefits and costs of an action, and yet, by the nature of the decision they confront, must act. It is in fact the action which creates conditions for belief, or perhaps taking action just is the formation of belief, but the action is not determined by some prior set of beliefs, information, or the like.

Consider the case of an aboriginal island nation, some sixty miles west of a mainland of which the islanders are ignorant. The indigenous peoples have an extremely low standard of living relative to the mainlanders. Both could benefit from exchange. Thus, in this status quo, there remain unexploited gains from trade. So it is tempting to call the situation inefficient. On the island, however, they do not have the technology to sail to the mainland; indeed, they may not know that the mainland exists. So, given that the islanders are doing the best they can with what they have, the situation is efficient. The ignorance of the mainland is just another component of the islanders’ budget constraint.

But a thoughtful islander will recognize that he does not, properly speaking, know whether there is a mainland or not. He might surmise that there is the possibility of sailing to another place and finding another people with whom he can exchange, but the islander knows neither the costs of sailing nor the benefits. He may sail east and find the mainland, or he may sail west into oblivion. The costs of each journey are radically different and his decision must be arbitrary with respect to maximization. The same can be said for the costs of making a journey at all. The same can be said of the decision to invest in the production of seagoing watercraft in the first place. The same can be said of the decision to think about investing in the production of seagoing watercraft. The uncertainty with which the islander must operate precludes him from assessing opportunity cost. The benefits that the islander might receive from sailing are wholly unknowable prior to attempting a journey.

Whatever the islander decides to do, his decision is not maximizing. He is not optimizing a consumption bundle under constraints. He is not maximizing a risky consumption bundle with known probabilities of consumption under a risky constraint with known probabilities of various costs. Whether he chooses to sail or not, he is choosing to pursue an unknown consumption bundle with an unknown probability of acquisition against an unknown set of costs with unknown probabilities of bearing those costs (Knight 1921). 

A thoughtful reflector on a given rule may recognize that he does not know whether the rule is best, and yet, he still must choose to uphold or follow the rule, or change it or disregard it. His behavior is shaped by a choice he must make about the rule. A sufficiently self-conscious chooser must make this choice, in circumstances of great uncertainty, without respect to beliefs he has about the rule: he does not have enough belief to generate a decision. Nonetheless, the logic of the situation requires that a decision be made. A decision is made that is not entirely maximizing; maximization does not summarize the entirety of the decision making process.

To sum up so far, the logic of maximization commits us to seeing all institutions as efficient. However, because it is impossible to appreciate the opportunity cost of defining alternative rules, it is better to say that all institutions are of indeterminate efficiency. In other words, people are not (always) maximizers. We should still accept Leeson’s principal conclusion: Welfare economics is unscientific. This is not because all rules are the best we could have, nor merely because we cannot know, in principle, if given rules are the best we could have, but because this fact causes some people to confront a forced decision where they must make a genuine choice about what to believe.

Two questions naturally arise from the foregoing discussion. (1) If people are not always maximizers, how do they make decisions when not maximizing? And (2) obviously, we know some rules are better than others, e.g., socialism precludes the possibility of economic calculation (Mises 1920; Hayek 1936, 1945; Lavoie 1985a, 1985b) and so people under socialist regimes will be poorer than those under capitalist regimes, ceteris paribus. How do we capture this knowledge if not through the apparatus of efficiency?

The second is less existential and thus easier to answer. Leeson himself points the way. We need to cease speaking of relative efficiencies and substitute discussion of relative wealth. People living under socialism are poorer than those who are not. It may be too costly to remove those constraints, and thus, it may be the case that, were the costs of socialism and the costs of privatizing fully known, socialism is occasionally an efficient system. We can always say that, since the relative costs of socialism and of replacing socialism are never fully known, it is impossible to say whether socialism is efficient. However, we can know that people under socialism will be poorer than they would be in a broadly capitalist society if switching away from socialism were costless. Our desire to reform socialist countries is thus, in a sense, an informed act of faith – the economic analysis of socialism groundlessly assumes costless transition.

The assumption of costless transition is baked into every level of economic analysis. Consider minimum wages. Econ 101 graphs show us that a binding price floor generates a surplus, with a measurable triangle of deadweight loss. We are tempted to describe the situation as inefficient because we think we can see a clear relevant alternative: the equilibrium without minimum wage. But Leeson, Demsetz, Barzel, Stigler, Coase, and that whole gang of thoughtful critics of the Pigouvian tradition remind us that it is not by any means costless to repeal the minimum wage. Thus, we cannot say the institution is inefficient. But what we can say is that, if it were costless to repeal, repealing it would make people less poor.

Clearly something is right about the 101 presentation, even if it lacks nuance. What I want to suggest is that it is legitimate, on occasion, to falsely assume costlessness of transition. Economists can be guided by their moral judgments: We know it is not costless to repeal a minimum wage, but we know that if Congress just knew a little more economics and was composed of marginally less immoral people, they would repeal the price control (assuming the 101 depiction accurately captures reality). We assume costlessness for the purpose of demonstrating that, if we did not confront the costs of evil and ignorant people making our rules, we would be less poor. And we also slip in a bit of moral judgment in our estimation of greater poverty being, ceteris paribus, bad, and less good. The reason we use the supply and demand analysis is to persuade: to show others why it is that the world we live in is not as good as it could be. And it is that act of persuasion that can on occasion improve the world (or at least, increase our wealth).

It is not inefficiency that justifies intervention or its absence, but our moral judgment about why putative inefficiency is perceived. It may be the case that the putative inefficiency is not at all inefficient, when positive transaction costs are accounted for, like the mall parking lot in Demsetz (1964) or the pre-fur-trade Montagne lands in Demsetz (1967); it may be the case that the only reason transaction costs are positive is on account of the wickedness or ignorance of some people. Welfare economics must, as Coase (1960) explained, resolve into ethics and aesthetics.

This fact is not a demerit. In fact, it sheds light on the first question: If people are not maximizers, then what are they doing when they make decisions? They are, I suspect, relying on ethical and aesthetic criteria which guide their beliefs. And to the extent that they are relying on such criteria, they are not maximizing. The islander must make a decision whether to sail or not to sail. His decision is arbitrary with respect to his beliefs. But suppose he can choose to believe something. I am describing something rather like what William James lays out in The Will to Believe. The conventional economic analysis goes something like: beliefs/information inform decisions. What I have shown is that there are, plausibly, decisions that have to be made without the advantage of prior beliefs/information. I want to now suggest that the way James articulates the capacity for choice among beliefs is relevant to economic analysis.

James makes his argument about religion. Belief in God, so says James, is forced (for on his account there is no middle ground, no suspension of judgment, only belief and disbelief), live for some (meaning that there are some people who, for whatever reason, consider Deity to be a plausible metaphysic), and momentous (the decision carries a great deal of weight). Since evidence is incapable of demonstrating either the nature or (non)existence of God, yet people must still either believe or disbelieve in God, then they must make a choice – a choice about what to believe. It is not at all clear what governs this choice, but James suggests it is a person’s “passional nature”. In other words, people choose to believe in God because they want to live in a reality governed by God (where James gets controversial and interesting is in his view that this choice is utterly legitimate).

Feel free to set aside the philosophy of religion, but keep the Jamesian framework. The islander confronts a forced, live, momentous decision, for which evidence is incapable of discrimination. What governs his choice? Perhaps it is some kind of ethical or aesthetic judgment about what kind of world would be a good one to live in.

Economists have a model that captures and explains some kinds of non-maximizing behavior: the coordination game. In the coordination game, there are obvious mistakes to be avoided (left-right and vice versa) but there are two equilibria where the payoff is equal, and thus between which the players should be perfectly indifferent. Is the player’s decision thus completely arbitrary? Perhaps in the pure case, but certainly not in most identifiable real-world cases of coordination games.

Focal points (Schelling 1960) often arise as a result of the use of ethical and aesthetic heuristics. Focal points guide players to an equilibrium neither deterministically nor randomly. They are not deterministic since they arise on account of mutual expectations, and expectations about another’s expectations about one’s own expectations about another’s expectations about one’s own expectations (etc.) cannot, ultimately, be determined by decision-theory. That is, the set of mutual expectations that generates a Schelling point is not a linearly defined relationship of cause and effect, but is instead a spiral process without clear beginning. It is of course possible that people hold expectations deterministically on account of some physico-chemical or divine subordination of their psyche, but that possibility is irrelevant. The important fact is that an individual’s expectations about expectations about expectations (ad infinitum) is not determined by a strictly rational decision-making process.

And yet focal points are clearly non-arbitrary, and people can and do coordinate around them. They are not arbitrary for two reasons. First, they are apparently constrained by the possibility of discoordination: Left-Right and vice versa cannot be focal points. Another way of putting the idea is that not every point can be focal. From the outset, the hard constraint on focal points is that they only occur at equilibria. Second, they are constrained by ethical and aesthetic judgments. The clock at Grand Central Terminal at 12 noon is not the meeting place because it satisfies our preferences uniquely (other places and times satisfy our preferences equally well) nor because it is the place of highest probability of meeting (it is meaningless to speak of probabilities, since expectations of others’ behavior cannot have a probability attached to them on account of their circularity), but because the clock at Grand Central at noon has a kind of aesthetic significance that lends itself to coordination. Maybe that significance can be explained — but not in terms of maximization.

In other words, coordination games are not maximization problems. And yet, coordination games can be solved for Nash equilibria, in the real world, in such a way that behavior is not arbitrary. In general, I think institutions are (often, or at least sometimes) solutions to coordination games, and not the product of maximization. This means that institutions are of indeterminate efficiency: They are better than disequilibrium, but there might be an alternative point around which we could coordinate which would be just as good, or even better (Assurance), or better for some but worse for others (Battle of the Sexes).

The foregoing discussion does not and should not be taken to imply that I believe maximization is a useless apparatus. On the contrary, much behavior does seem to be maximizing. Even the creation of some institutions, like property rights in the Demsetz story, seem to be the result of maximizing behavior. However, not all behavior is maximizing, and those institutions which are the product of coordination games and not of maximization cannot be said to be efficient. Maximization implies efficiency; some behavior is maximizing; some institutions are thus efficient. However, some behavior is not maximizing but coordinating; some institutions are thus of indeterminate efficiency.

Recall the above discussion of minimum wage laws. Are they efficient? Suppose that American society has coordinated around minimum wages being a good solution to poverty — everyone expects everyone to be better off with a higher minimum wage. The efficiency of the law, strictly speaking, is indeterminate, since no one here is maximizing (there might be an equally appealing putative solution to poverty that is, for whatever reason, not focal). Efficiency analysis is nonetheless useful in illuminating our moral commitments and the moral state of the world. We may show by means of an efficiency analysis that, relative to other states of the world where people are less ignorant and politicians are less motivated to distribute rents, the minimum wage makes workers poorer. The key feature of this analysis that makes it acceptable is the fact that the appeal to efficiency does not assume costlessness of transition, but rather illustrates that the transition would be good to make if it were costless. In doing so, it highlights what the costs of transition are: the ignorance and immorality of the people who are coordinating. Thus, aesthetic and moral judgments are essential for guiding all non-maximizing behavior — including that of the welfare economist.