From Game Theory to Group Action

In a recent thought experiment, I argued that institutions—including government institutions—are just the cost we pay for better outcomes. Specifically:

We want things—food, shelter, entertainment, whatever it may be—and in order to get those things, we need specialization and trade. In order to get specialization, we need the institutions that make it possible. These institutions, in theory, minimize certain costs—transaction costs, as well as the risk of violence or arson which tend to limit the extent of trade.

And:

Put more plainly, our institutions are the cost we’re willing to pay in order to offset other costs; they’re a net gain in the sense of providing more benefits for less than we would have in their absence (though there may be better alternatives).

This simplifies matters rather drastically. It is basically a social contract model, which means that it implies we have chosen these institutions so that we can pursue certain specified ends. The ends in the model are basically utility maximization, something I have trouble with but that certainly has its uses in terms of simplification.

Moreover, it’s not quite clear who we’re talking about here. Who pays the costs in this model? Who benefits?

In what follows I’m going to start from a bit of game theory and attempt to walk my way to a richer model of group action.

 

Adding Options to the Prisoner’s Dilemma

In “Governance as a strategy in state-of-nature games,” Jason Briggeman suggests an alternative to the most popular method of modeling Hobbesian state of nature scenarios in game theory.

It starts with a simple prisoner’s dilemma.  Each player can either defect or cooperate. If one defects and the other cooperates, the cooperator gets the worst possible payoff (possibly a negative one) while the defector gets the most. If they both cooperate, neither gets as much as the defector would in the previous scenario but the overall “pie” of payoffs is maximized. If they both defect, they each receive a punishment lower than the cooperator in the first scenario, but the overall “pie” is minimized. The payoff structure is such that defect/defect is the equilibrium outcome.

Game-Theory-prisoners-dilemma

 

The specific versions that Jason looked at were couched in Hobbesian terms; in place of cooperation is “lay aside natural right” and in place of defection is “retain natural right”. The typical addition to this in the literature was apparently to include an “install a sovereign” option, which is basically a stand-in for Leviathan.

installsovereign

 

This is some serious hand-waving. I mean, it’s game theory, so you can set it up however you like with whatever payoffs you like, if that’s how you get your kicks. But it doesn’t seem very useful to speak of an “install a sovereign” option. Rather…rex ex machina.

Jason certainly thinks so, and he offers an excellent alternative. These are the choices on his matrix:

1. Cooperate (and do not coerce other player)
2. Cooperate/Impose (i.e., cooperate while coercing other player to cooperate)
3. Defect/Impose (i.e., defect while coercing other player to cooperate)
4. Defect (and do not coerce other player)

Resulting in:

impose

 

You should check out the paper to get the full take on the math. The bottom line is that changes in the relative costs of coercion will change the outcome of the game.

I think this is a great, useful model with a wide range of applications. I’m going to add on top of it here for my purposes (and as a result it’ll get too unwieldy to put into a matrix).

First, being as we are at Sweet Talk, it seems to me that it would make sense to add a persuasion element. Following Jason, this would add two options for each players: Cooperate/Persuade and Defect/Persuade. Assuming persuasion isn’t a free lunch, there would be some cost to figuring out how to persuade someone, and probably some disutility to the one being persuaded, since there must be some reason they didn’t want to do it in the first place.

Given the commensurability of values in game theory models, it normally wouldn’t make much sense to add this in addition to the impose element. The reason is that even if we understand, conceptually, that one involves coercion and the other doesn’t, the big addition is really the inclusion of any option for a player to control the choice of the other player. You could say that the persuasion option has a lower relative disutility for the one being persuaded, or differentiate it in some other way. But you’re just going to be sacrificing elegance without really adding anything useful. But I’m going somewhere with this.

On top of adding persuasion, we can add some risk into the model, beyond the risk of choosing the wrong strategy relative to the other player’s strategy. Perhaps no amount of cost will guarantee that impose or persuade work every time; they just have some underlying probability that they will work.

Again, this mostly complicates the model rather than makes it more useful; expected utility is a pretty straightforward calculation that doesn’t really change the character of the model other than overcomplicating it further.

But I want to introduce the idea that some things are not guaranteed.

I introduce it in order to take my first step away from game theory: let’s now say that we’re not talking about risk, which is quantifiable, but uncertainty, which is not. All we know for sure is that our attempt to impose or persuade may not be successful, we cannot quantify the probability of failure.

We know how this sort of uncertainty is dealt with in practice, of course; a lot of heuristics learned from others and from experience.

Now say that we do not have commensurable utility. Say there’s a great deal of uncertainty about what other players will do, so that we need heuristics and experience there as well. Say knowledge is not flat, but requires interpretative frameworks—such that we can be persuaded, or persuade others, to change their interpretative framework in order to influence their choices. And there are obvious scenarios that would change relative costs of coercion—if one player had a gun and the other did not.

 

Social, Organizational, and Coercion Capital

We’ve now basically stepped outside of game theory and utility-based models. However, I hope we have done so in a way that has shown how they can serve as useful simplifying analogies.

I would now like to step away from the vacuum that individuals appear to be in within these models to the background of groups and group action which forms the basis of nearly all human decisionmaking.

Let us imagine that the biggest sources of variance in the relative costs of persuading, coercing, and coordinating are differences in capital stocks. Organizational capital provides the resources for efficiently accomplishing a task as a group. Social capital provides the resources for persuading certain people to a particular point of view. And coercion capital provides the resources for Jason’s “impose” option.

In the flat and commensurate world of game theory and utility economics, capital is numerical; more capital is better than less capital. On the other hand, the Austrian School has long emphasized the heterogeneous nature of real-world capital and the resulting illiquidity. A bread-slicer cannot be used to manufacture cars; stockpiling bread-slicers will not help you to compete with Toyota even if you’ve technically increased your capital stock. Details matter.

Consider the following: a police state that is heavily armed but widely distrusted and considered illegitimate by its citizens. Moreover, there is a high degree of trust—or social capital—among the civilian population. So black markets flourish; even though the state built up a great deal of coercion outcome it still has a hard time imposing specific behaviors on its citizenry.

What has been called “the authorizing magic of legitimacy” may be thought of as a regime that has an enormous amount of social capital, which allows it to more effectively economize on its coercion capital.

OK, we know what a bread-slicer looks like, and an assembly line robot arm. What do these more abstract forms of capital look like? How do they work?

I believe that all three categories can only be drawn upon by people who are members of particular groups. More than that, membership of the group is a crucial and embodied part of who they are, of their identity. I think the Catholics are correct that there are groups that can usefully be thought of as having their own existence.

Barack Obama is able to draw on some of the coercion capital of our nation because he has immersed himself in the machinery of modern politics, and committed himself to a role within a group (the federal government) that draws certain boundaries. Those boundaries are more indeterminate that people like to think (though not as toothless as others imagine). One of the hard constraints is that the shape of the coercion capital is, itself, the social capital that the role of President has built up in persuading everyone below him in the hierarchy to follow his lead in those areas where his lead is considered appropriate. As John Searle put it, most people think power comes from the barrel of a gun, but actually the one with the gun is the most at risk, while the one with power often sits behind a desk away from harm. But that is only possible because the bureaucrat’s power is “an institutional fact” created by “collective intentionality”. For our purposes here, it is because his role has considerable social capital.

Organizational capital is largely about developing skills and practical knowledge, and effectively transmitting them to new members as well as to those with a pressing need for them. Norms, ethics, and culture cut across this and social capital; in as much as they promote cooperation they act as the latter, in as much as they promote effectiveness they act as organizational capital. A culture of trust is largely a matter of social capital, a culture that promotes commitment to achieving the group’s goals is more a matter of organizational capital.

Practices that address uncertainty also fall into organizational capital. In the section above I spoke of heuristics and learning from experience, but often the best approaches are simply time-tested practices we don’t necessarily know the reasons for. In a famous case, what appeared to be completely superstitious agricultural practices based on priestly mandates turned out to be an extraordinarily effective system for coping with the challenges of a specific ecosystem.

 

Out Groups

It’s my belief that accessing these forms of capital means, in practice, that decisions are made at the level of the group rather than the individual more often than not. The very nature of the capital requires this, as I hope I made clear with the example of the President above. On the whole, I don’t think this is either good or bad; it’s human nature. Most arguments that it’s better to decide at the level of the individual simply miss out on how deeply individual context is set by groups. Individualism is a very important tradition of thought, but it is only possible when given shape by an enormous background established by groups, as caretakers of living traditions. Of the various forms of capital.

But there are definite fault lines created by this. The nature of human group membership unfortunately biases against those perceived to be outside of that group. And one of the classic ways we distinguish one another is by physical features; skin color but also other traits that signal difference in ethnicity. When the coercion capital especially is concentrated in the hands of a particular subset of the population, they may find they have freer hand to err on the side of tyranny for those groups who they do not much rely on for social or organizational capital. In short, minorities are inevitably harmed disproportionately by political systems.

When I say that good government is an ideal worth thinking seriously about, I don’t mean to deny this point, so emphasized by Sam and boatfloating. When I say that governance and coercion are necessary, I don’t mean to sweep injustice under the rug. And I certainly agree with both of them that we have invested far too much in our coercion capital, and drawn on it far too often, with reckless disregard for the people out of view who will be disproportionately harmed.

I do think that people who see harm these days are far too inclined towards outright negation; that their rhetoric and their actions recklessly drag us towards a future where we kill the goose who laid the golden egg. Such critiques, like game theory and mainstream economics, should instead serve as a kind of critical theory. It should serve to identify fault lines in what is a constructive, rather than destructive, project on the whole.

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  1. Pingback: Group Decisionmaking and Individual Responsibility - Front Porch Republic

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