[Presented at the 2021 Annual Meeting of the Society of Christian Ethics.]
Abridged version of the paper
Our world is made possible by cooperation. Day in and out, we cooperate with others around us, and our lives are the better for it. In the United States, we drive on the right side of the road. We expect that we will get correct change when we use cash to pay for our groceries. We live and work in buildings that were constructed by others, and are serviced by still others. We need each other.
The trouble is: cooperation is not something that we can always take for granted. We may be more confident that others will cooperate when it is in their interest to do so—as in the case of driving on the right side of the road, for example. But especially where there is risk involved, or where there is deficient social trust, we cannot always be certain that others will not defect from our common enterprises.
This paper introduces a theoretical tool that I believe will enable us to better understand how and when humans choose to cooperate with each other, and how to strategize when we are doubtful about others’ cooperation. That tool is game theory. It is my suspicion that thinking game theoretically can offer important insights that will help us to resolve problems that many of us in the discipline are preoccupied with regarding social and structural sin. I found it remarkable, in fact, that when I did a search of the last ten years of program books for this annual conference, not a single paper focused on the insights that game theory might offer to religious studies or theology. Finally, and perhaps most importantly, I think that thinking game theoretically would help us to move beyond certain contemporary interpretations of the doctrine which are preoccupied with the content of our deeds, rather than the content of our wills. We would see that what is totally depraved about human agency is not the content of human actions, but the deformed disposition of the human will, especially its temptation to doubt others’ commitments, and to focus on one’s own interests.
To make this case, I will spend the first few minutes of this presentation on a brief primer on game theory. Then, I will focus on one type of game, called an assurance game, to reflect on our ever-present temptation to defect, such that we might think about the doctrine of total depravity anew, and offer a number of present-day examples. Finally, I will explore what the reformed tradition might have to say about the state of affairs I discuss, and what our faith requires of us in that context today.
Game Theory: a Primer
To begin, I think it would be worth revisiting game theory. The approach centers around a simple but powerful insight, most famously advanced by the mathematician John Nash: that there are many circumstances in which the benefits a person gains as a result of a choice they make also depends on the choices others make.[1] That is, the outcomes of persons’ choices are often interdependent, even such that they can be mutually constitutive. Game theory shows us how each participants’ assumptions about all others’ participants motivations can shape the terrain of human action.
In its simplest form—a structure that you may have seen before—game theory models action in a matrix, in which the various choices available to different actors are laid out in columns and rows. The benefits available to each actor, as a consequence of each combination of choices, are identified in each cell. As a simple example, for instance, we could model the relative consequences for two different actors as they, let’s say, choose what side of the road to drive on.
For the sake of simplicity, we tend to combine these two tables into one, doing our best to make clear which consequence of the two in each cell pertains to which actor.
It’s very apparent here that interests converge: Blake and Amani are very likely going to decide to drive on the same side of the road, as it is in both of their interests to do so. Game theorists call this kind of matrix a “pure coordination game.” You can simply stipulate which side of the road to drive on—left or right—and everyone is likely to comply because it is in everyone’s individual interests to do so.
Most human interaction, of course, doesn’t look like that. There are, for example, zero sum games: if Amani and Blake only have so much pie to divide between them, however much Amani eats is exactly the amount that Blake cannot eat, and vice versa. Unlike in the pure coordination game, their interests—assuming they both want pie—conflict. Rock paper scissors is a great example of a zero-sum game, given that there are always winners and losers:
Usually, again for the sake of simplicity, game theorists will use numbers, rather than emojis, to identify the relative benefits and losses that each stands to earn:
You can tell here that it is a zero sum game, because the exact amount of gains one enjoys mirrors the exact amount of losses another suffers.
The fact is, though, zero sum games are not nearly as common as we often take them to be. (Some social psychologists call this “zero sum bias.”[2]) But there are loads of cases in which differing parties have competing interests, even in non-zero-sum games. In fact, I’d like to suggest that a great deal of the circumstances we find ourselves in are just like that: non-zero sum games that nevertheless include conflicting interests. Consider the following variation on the “which side of the road should I drive on?” game, unhappily referred to as the “battle of the sexes.”
Amani and Blake are married and are going to go on a date to see a movie this evening. They both would rather be together, but they disagree about which movie to go see. (Indulge me, if you can, and imagine this scenario is not happening at a time when they should both be suspect for going to the movies and endangering public health.) Amani wants to see Freaky, the new Kathryn Newton and Vince Vaughn horror flick; Blake wants to see Wonder Woman 1984. We might model their preferences thus:
It’s clearly the case that they ought to figure out, somehow, to make sure that they get to go to the same movie. But which one should do the sacrificing to ensure that they can go together? Their interests conflict and yet they would be better off coordinating. (Of course, I should also recognize here that it’s not as if all cooperation is good: humans also cooperate to accomplish evil. However, in this paper I am focused on cooperation toward good ends.)
I hope it has become clear by this point that modeling the variety of consequences that can follow from different combinations of choices can powerfully show us how the interdependence of many of our choices shapes the possibilities before us. I am convinced that religious studies, and theological ethics in particular, would benefit from integrating this methodological perspective into the discipline.
Assurance games
At this point I’d like to introduce the type of game for which this talk is named, often called an “assurance game.” Consider an arms race between two countries, in which both would prefer that neither build nuclear weapons, but if the other country were to build weapons, each country would also want to build weapons. We might create the following matrix to represent such a situation:
Imagine what might happen. If there were any possibility that the countries might be able to trust each other, they very well may be able to achieve their strongest preference: avoiding an arms race altogether. They may use treaties or other systems to enforce cooperation, but however they are to manage it, these countries accomplish the most desirable outcome by cooperating. (This, I should note as an aside, is what distinguishes assurance games from the most famous game in game theory, the “prisoner’s dilemma,” where the numbers in that upper left cell are not high enough to motivate cooperation.)
What is noteworthy here, however, is that neither wants to be duped. If either were to get a whiff of the other’s failure to cooperate, each country would get to work building nuclear weapons.
The point I am trying to make here echoes the work done by political theorist Brian Skyrms in his book The Stag Hunt and the Evolution of Social Structure, which is also named after Rousseau’s example of an assurance game. In that text, Skyrms argues that, assurance games deserve more of scholars’ attention.[3] It is impossible to even count the number of assurance games we encounter on a daily basis. Recall that in an assurance game, cooperation yields the ideal outcome, but such an outcome is inhibited by the fact of each participant’s uncertainty that the other will cooperate. Consider the following examples that feel all too real these days:
We would all be better off if we could depend on one another to buy no more than the toilet paper we need. But absent assurances that other people won’t hoard, we’re inclined to do some hoarding ourselves. Or consider a similar possibility:
Multi-state cooperation on mask ordinances is essential, in order to accomplish desirable effects—like keeping people alive and out of hospitals. Especially in the time of COVID, these kind of cases are everywhere you look. But they extend beyond the pandemic. Think of climate accords: no country wants to be the only ones to commit to stringent restrictions on carbon emissions if others will merely free-ride on their discipline. Or patriarchal standards of beauty: especially at in-person AAR gatherings, I find myself floored by how much more time and energy women are expected to invest in their appearance than men are. But few individual women are motivated to resist such standards, without the assurance of a collective commitment to do so; otherwise those few who do will merely be punished for not wearing lipstick, high heels, and well-coiffed hair.
Game Theory and Reformed Theology
In particular, I want to argue that thinking in game theoretical terms might help us to reconceive our approach to the doctrine of total depravity. In the assurance game, for example, it’s not that no one is ever willing to cooperate; instead, we are simply always tempted to defect. Game theory shows us that in so many cases, temptation lurks. Why? Because we are, as Luther says, incurvatus in se.[4] We are preoccupied by those numbers in our column, rather than with achieving good of all those whom God loves. Furthermore, in assurance games, we are each aware that our potential collaborators are, too, prone to temptation. When we lack the assurance of others’ collaboration, and we know that others might be as tempted to defect as we are, we are sensibly concerned that we might be duped. This rational suspicion makes us, in turn, even more prone to defect; the temptation doubles. The fact of our separateness, a reality precipitated by the fall, multiplies sin.[5]
Notice that here the focus is not on the acts of wrongdoing, but the widespread temptation to defect that impedes positive cooperation. This occasions a new interpretation of our common confession to God that “we have sinned against you in thought, word, and deed, by what we have done, and by what we have left undone.” Just as Jesus tells us that an adulterous heart alone makes an adulterer (Mt. 5:28), we can say that we have, just by the fact of our being tempted by our own private incentive structures, forsaken our neighbor.
Thinking about our total depravity in terms of our ever-present temptation to abandon our neighbors also allows us to make more conceptual space for the exercise of human agency. It’s not as if humans never accomplish good things together; no reformed theologian that I know of would ever make such a claim.[6] in fact, they tend to focus on the good humans can accomplish when they cooperate. Recognizing this dynamic not only opens up space for the exercise of agency, but also directs our attention to the structural arrangements that we can institute in order to guide our wills toward the common good. Indeed, Skyrms’ research on the assurance game shows that structural arrangements can actually create cultures of assurance game cooperators—or defectors. By means of social norms and legislation, communities can establish practices that facilitate cooperation. Moreover, cooperative behavior is contagious; encouraging it structurally can unleash a positive feedback loop that increases cooperation. This is surely one of the reformed tradition’s best contributions: that by means of covenants, communities can actually transform the world in which we live—even if we can never thereby completely eradicate sin. (I am thinking here of Calvin and Beza’s commitment to civil law in Geneva, John Winthrop’s “Model of Christian Charity,” and even the theological politics of Karl Barth.[7])
We need not only think about game theoretic models of human behavior descriptively, however. While these models may describe how humans interact, theologians have prescriptive claims to bring to the theory. (**) We are, after all, called by Paul to look not only to our own interest, but the interest of others. Calvin writes, in a commentary on the Beatitudes, that Christ blesses those “who are not only prepared to endure their own afflictions, but to take a share in the afflictions of others, who assist the wretched, who willingly take part with those who are in distress.”[8] Christians have important reasons to concede the fact of the human temptation to defect—and to exhort one another to withstand that temptation. The unassailable fact is that rational agents are often reasonably disincentivized from doing the right thing, which in many cases includes participating in collective action to better our world. Especially apart from the assurance of others’ cooperation, we can be reluctant to modify our own behavior. What is needed is a theological grounding for our commitment to cooperate, even absent such assurances, with the faith that benefiting our neighbors and future generations will not be in vain.
[1] It is worth noting that game theoretical insights appear long before the emergence of what we might call “game theory proper” in the twentieth century: Thomas Hobbes, John Locke, David Hume, and Jean-Jacques Rousseau were all proto-game theorists of a sort. But the approach was first pioneered in earnest by John von Neumann in the thirties and forties, and thereafter by John Nash—whose life was portrayed in the well-known film A Beautiful Mind. Game theorists are well-represented among Nobel Laureates: eleven have been granted Nobel Prizes.
[2] See, for example Daniel V. Meegan, “Zero-Sum Bias: Perceived Competition Despite Unlimited Resources,” Frontiers in Psychology 1 (November 5, 2010).
[3] Brian Skyrms, The Stag Hunt and the Evolution of Social Structure (Cambridge; New York: Cambridge University Press, 2003).
[4] For a discussion of the concept in Christian theology, see Matt Jenson, The Gravity of Sin: Augustine, Luther, and Barth on Homo Incurvatus in Se (New York: T&T Clark, 2006).
[5] In fact, I might even be inclined to offer an account of the fall that maps onto a game theoretical matrix, with our forebears acting as “player 1,” and God as “player 2.” As I see it—and as Luther saw it—the trouble entered not when a human ate of the fruit, but the very moment when a human entertained the possibility that God was not for her. Just the mere temptation to believe that God is not for us allows the temptation to defect to enter in. This, we might say, is why original sin is original: not because it is somehow genetic, but because once the suspicion of others’ defection enters in, it is impossible to eradicate it. I am grateful to Chelsea Williams for helping me to see this latter point.
I should also specify that it is not our separateness as such that is the source of sin; I do not, for example, believe that we will lose the integrity of our identities in the hereafter. If we are to confess, according to the Apostles’ Creed, our faith in the resurrection of the body, we cannot imagine that all separateness as such will be reversed. It is rather the inclination of humans to be incurvatus in se that will be remedied in God’s Kingdom. We simply won’t pay attention to the numbers in our column as we move through life in eternity.
[6] Not all games are “prisoner’s dilemmas,” in which we are structurally disinclined from cooperation. However, most common contemporary misunderstandings of reformed theology imagine the reformed position to be that human beings are never oriented toward the common good. In assurance games, we each do stand to benefit from cooperation.
[7] I am thinking of Haddorff’s introduction a 2004 collection of Barth’s writings on the state. David Haddorff, “Karl Barth’s Theological Politics,” in Community, State, and Church: Three Essays by Karl Barth, by Karl Barth (Eugene, Or.: Wipf and Stock, 2004).
[8] In Calvin’s commentary on Matthew 5:7.