Eye for Eye

“You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also. And if anyone wants to sue you and take your shirt, hand over your coat as well. If anyone forces you to go one mile, go with them two miles. Give to the one who asks you, and do not turn away from the one who wants to borrow from you.” Matthew 5:38-42 New International Version.

Introduction¶

Matthew 5:38-42 is part of Jesus’ Sermon on the Mount. Here, Jesus calls for non-retaliation and radical generosity.

It’s easy to grasp on the surface, but hard to live out. Turning the other cheek sounds noble. However, it becomes much harder when someone actually hits you.

The argument¶

In this article, I rigorously examine and stress-test Jesus’s teaching in Matthew 5:38-42. I apply game theory concepts, particularly the Prisoner’s Dilemma. My thesis is that this lens reveals Jesus’s ethic of non-retaliation. I explain the underlying logic of retaliation versus non-retaliation. I explore how cooperation can emerge in self-interested environments.

I consider why certain strategies are both crucial and rational. They begin with non-retaliation. They include retaliating when necessary, practicing forgiveness, showing generosity, and clearly signaling intentions.

Tit-for-Tat illustrates this. So does Matthew 5:27: “All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one.”

I also examine how homophily, such as church communities, sustains cooperation. I also discuss why weak ties are vital and rational for spreading cooperation. Matthew 5:23-24 illustrates this:

“Therefore, if you are offering your gift at the altar and there remember that your brother or sister has something against you, leave your gift there in front of the altar. First go and be reconciled to them; then come and offer your gift.”

Ultimately, Jesus’s teaching challenges our instincts and tests our resolve. I argue that game theory can sometimes provide insight into the effectiveness of cooperative or forgiving strategies under certain real-world conditions. However, it does not mathematically prove the universal rationality of non-retaliation. Many game-theoretic strategies still involve retaliation.

I conclude by examining the practical and ethical implications of these strategies for relationships and communities today. I also acknowledge the limitations and potential blind spots in my own analysis. In doing so, I aim to provoke deeper reflection on the intersection of faith, rationality, and human behavior.

Game theory¶

On the surface, Matthew 5:38-42 makes sense in theory, but it tests every instinct in practice.

A stylized game¶

Let me give a stylized example of interaction, which mathematicians and economists call a game. This example models the tension between individual rationality and collective well-being. It shows how rational self-interest can lead to irrational but valid outcomes. We see this paradox in economics, politics, relationships, and even evolution. Though we call it a game, it has real-life implications.

Imagine a simple scenario, given in the table below, where two people must each choose whether to cooperate or to defect.

The top-left cell is socially optimal cooperation. When both people cooperate, each gets 5 points. The off-diagonal cells show unilateral defection. If one defects while the other cooperates, the defector gets 10 points and the cooperator gets 0. The bottom-right cell is mutual defection. If both defect, each gets minus 5 points. In this one-shot game, the rational strategy is to defect.

The Prisoner’s Dilemma¶

Merrill Flood and Melvin Dresher first formulated this game, known as the Prisoner’s Dilemma, at RAND Corporation in 1950. In a one-shot Prisoner’s Dilemma, the interaction occurs only once. Hence, the rational strategy is to defect.

Such a Prisoner’s Dilemma plays out everywhere in real life, from business to politics to personal relationships. In 1994, John Nash, John Harsanyi, and Reinhard Selten won the Nobel Prize in Economic Sciences for their pioneering work in game theory. They are known especially for the concept of the Nash Equilibrium.

Nash Equilibrium is illustrated nicely in the clip from the movie, “A Beautiful Mind”. I highly recommend that readers watch it.^[1]

In the bar scene, John Nash, played by Russell Crowe, and his four friends see a group of five women enter. One of them is a blonde who is very attractive. The other four are her friends.

The men first think they should all compete for the most attractive woman. They quote Adam Smith, the father of modern economics. In competition, individual ambition serves the common good. After a pause, Nash realizes that Adam Smith needs revision.

Nash says: if we all go for the blonde, we block each other. Not a single one of us is going to get her. Then we go for her friends. They give us the cold shoulder, because nobody wants to be second choice.

What if no one goes for the blonde? We don’t get in each other’s way, and we don’t insult the other women. That’s the only way we all win.

Adam Smith said the best social result comes from everyone in the group doing what is best for himself. Nash says the best result comes from everyone in the group doing what is best for himself and for the group. This bar scene is the intuitive picture of what would later be formalized as Nash Equilibrium.

Nash Equilibrium underpins the logic of the Prisoner’s Dilemma. Individually rational actions can, paradoxically, lead to outcomes that are collectively irrational.

Self-interest and the common good¶

The Nash Equilibrium is the outcome of the prisoner’s dilemma game. Rational individual choices produce poor collective results. That outcome challenges Adam Smith’s major claim.

In his seminal 1776 work, “An Inquiry into the Nature and Causes of the Wealth of Nations,” Smith argued that, in a competitive market, pursuing self-interest ultimately promotes the common good. He described this as if guided by an “invisible hand.”^[2]

Yet the prisoner’s dilemma shows that, without mechanisms for cooperation, self-interest can undermine collective well-being.

Real-life examples¶

Gas stations¶

For example, if two competing gas stations both keep prices fair, they each make a good profit. If one lowers prices sharply (defects) while the other keeps prices steady, the discounter grabs all the customers.

If both lowering prices are rational responses in the pursuit of higher sales, they start a price war. Everyone’s profit collapses.

Climate change¶

Nations face the same logic with climate change. If all nations cooperate by cutting emissions, everyone thrives. If one nation defects and keeps polluting while others reduce emissions, the defector gains a short-term economic advantage.

If all nations defect as the rational response, we will all face disaster sooner.

The Cold War¶

During the Cold War, both the United States and the Soviet Union faced a choice. They could build more nuclear weapons (defect). Or they could limit their arsenals through disarmament (cooperate).

If both cooperated, they could reduce military spending and live more securely. But if one disarmed while the other continued building, the defector would gain military dominance. Each feared being the weaker side.

So, both kept expanding their nuclear stockpiles. This led to massive costs, constant tension, and the ever-present risk of annihilation.

Individually, each nation acted “rationally” to protect itself. Collectively, they created the most dangerous standoff in human history.

The Iterated Prisoner’s Dilemma¶

In real life, we may need to play these games, similar to the Prisoner’s Dilemma, continuously and not just one time. This is known as the Iterated Prisoner’s Dilemma.

Imagine a workplace where one employee avoids duties, but colleagues always cover for them. The slacking continues. Or think of a friend who repeatedly borrows money, never pays it back, yet you keep lending without question.

In school, one student might rely on group members to do all the work, knowing the group will never complain. In relationships, a person might repeatedly break promises and be forgiven each time. The pattern continues.

In each of these stories, constant forgiveness without boundaries encourages others to take advantage. This shows how pure non-retaliation can lead to ongoing exploitation.

Solutions when non-cooperation is rational¶

If we never retaliate, we make ourselves vulnerable to exploitation. Others may realize they can take advantage of us without consequences.

Matthew 5:38-42 fundamentally boils down to the following question:

▶ If Jesus’s way of non-retaliation is not sustainable, how can we deal with this? “Eye for eye, and tooth-for-tooth” retaliation leads to a sub-optimal equilibrium of worse and irrational outcomes. More specifically, how does cooperation emerge in a population of self-interested players?

Tit-for-Tat¶

Robert Axelrod’s 1984 paper titled “The Evolution of Cooperation” provides empirical and simulation work on the solution to the Prisoner’s Dilemma.

Axelrod found something very, very surprising. The Tit-for-Tat strategy works best. It is almost like “eye for eye, a tooth for a tooth,” but with a crucial moral refinement.^[3]

Axelrod’s Tit-for-Tat strategy is remarkably simple. Be nice, forgiving, retaliatory, and clear. I highly encourage readers to watch this praiseworthy video by Veritasium that explains Axelrod’s Tit-for-Tat strategy.^[6]

Tit-for-Tat strategy, though counterintuitive, tends to break the vicious cycle of the Prisoner’s Dilemma. It enables cooperation to emerge even within a population of self-interested players. Below is an explanation of the Tit-for-Tat strategy.

Start by being nice or cooperating. If the other player defects, you respond in retaliation to signal that exploitation will not go unpunished, like “eye for eye, tooth for tooth”. However, if they return to cooperation, you immediately forgive and resume cooperating without any grudges.

Random forgiveness¶

But what if the other player keeps defecting? Axelrod found that pure Tit-for-Tat can lead to endless retaliation loops. To avoid this, he proposed adding a touch of random forgiveness. You occasionally cooperate, 10% or so, even after being wronged. This small chance of unexpected kindness breaks cycles of mutual defection and allows trust to re-emerge.

Furthermore, he found that Tit-for-Tat works best when it is transparent and straightforward. It does not rely on hidden or overly complex tactics. Other players can then recognize the pattern more easily. That builds trust and speeds up cooperation, because they see that cooperation will be returned and defection will get a proportional response.

As in Matthew 5:27, “All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one.” The simplicity and clarity are the spice of this game.

When everyone defects¶

However, they also find another striking fact. The Tit-for-Tat strategy cannot succeed in an environment where everyone always defects, no matter what you do. In such a population, cooperation has no opportunity to be reciprocated. Tit-for-Tat has no foothold to encourage mutual trust or positive cycles.

Duncan J. Watts and Steven H. Strogatz have a solution to break this vicious cycle of continuous defections. They published it in their 1998 paper, Collective dynamics of ‘small-world’ networks. That paper has been cited more than 58,000 times, and the count is still growing.^[4]

In an environment where everyone always defects, no matter what you do, you need at least a small group of initial cooperators. That group lets strategies like Tit-for-Tat take hold and spread.

Homophily or church¶

If there is a small cluster of cooperators, what we might call a homophily or a church, that cluster can spread cooperation. Cooperation grows there because of familiarity and common belief. What is more striking is that cooperation can then spread into the wider community of non-cooperators. That happens especially when those outsiders start to interact with the closest weak ties of the cluster.

Think of weak ties as the closest defectors in or next to the cluster. They are loosely connected, and they are less committed to cooperative norms. These weak ties act as bridges. They connect the cooperative group to the wider population, which often defects more.

Nurturing weak ties appears to be almost what Matthew 5:23 suggests:

“Therefore, if you are offering your gift at the altar and you remember that your brother or sister has something against you, 24 leave your gift there in front of the altar. First go and be reconciled to them; then come and offer your gift.”

Weak ties¶

Please watch another praiseworthy video by Veratasim. It shows how nurturing weak ties spreads cooperation in a population where the majority are defectors.^[7]

According to Mark Granovetter’s theory of the strength of weak ties, it is often the weak links between clusters that allow ideas, behaviors, and innovations to reach new parts of a network. It is not the strong, close-knit bonds within them.^[5]

The weakest links within or between clusters of cooperators act as bridges. They connect groups that would otherwise stay separate. These bridges expose people in different clusters to new norms and behaviors, such as cooperation. Even one weak tie between a cooperative cluster and the wider population can be enough. Cooperative strategies can then flow outward, influence others, and help turn defectors into cooperators.

In this way, the strength of weak ties plays a critical role in spreading cooperation beyond isolated pockets. This makes transformation possible even in environments dominated by defection. This is probably why the Church Ministry has an important role in society.

Limitations¶

What this analysis cannot show¶

My analysis has significant limitations. In highly fragmented, distrustful, or violent environments, cooperation may be rare or even impossible. This exposes the risk of overgeneralization in game-theoretic optimism.

Moreover, Tit-for-Tat is effective for conditional cooperation. It fundamentally relies on proportional retaliation rather than unconditional forgiveness. This stands in clear distinction from the radical non-retaliation Jesus advocates in Matthew 5:38-42. Making this difference explicit is necessary for an honest analysis of the relationship between biblical ethics and game theory.

Additionally, weak ties can help spread cooperation. They can as easily transmit harmful behaviors or defection. This is especially true in toxic or adversarial networks, such as the spread of misinformation and hate on social media.

Stable cooperation on a societal scale often depends on institutions, enforcement, and shared norms that deter persistent exploitation. These factors are crucial for Jesus’s ethic to have transformative power beyond small communities.

Finally, the psychological and emotional costs of practicing non-retaliation should not be underestimated. This is especially true in the face of power imbalances or persistent harm. Mathematical models show cooperation can emerge. They do not guarantee success in every context. Recognizing these complexities deepens our understanding of both the promise and the challenge of living out the ethic found in Matthew 5:38-42.

However, Tit-for-Tat still involves retaliation. Jesus’s teaching is more radical. Matthew 5:39 says, “do not resist an evil person.” It calls for non-retaliation even in the face of harm.

This may create tension between the biblical ethic and the game-theoretic optimum. That tension also deserves an explicit acknowledgment.

Summary¶

Now circling back to Matthew 5:38-42. Jesus’s teaching about turning the other cheek is not simply a call to passive submission. It is a radical invitation to break cycles of retaliation. It creates the conditions for genuine cooperation.

The lessons from the Prisoner’s Dilemma and the evolution of cooperation show a trap. Pure self-interest and constant retaliation often trap individuals and communities in a downward spiral of mistrust and harm.

Yet even a small group can become the seedbed for cooperation to take root and spread. They choose forgiveness, transparency, and steadfast generosity. They live out the ethic of non-retaliation described by Jesus.

Clusters of cooperators can transform a hostile environment through their examples and weak ties. Followers of Jesus are called to model a new, transformative pattern of interaction. Rather than escalating conflict or responding to harm in kind, they extend unexpected grace. That grace can ripple outward and change the dynamics of the whole community.

In this way, Matthew 5:38-42 is not just an idealistic command. It is a practical strategy. In some contexts, it aligns with insights from mathematical models about how cooperation can sometimes emerge and be sustained.