Eye for Eye

38 “You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ 39 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. 40 And if anyone wants to sue you and take your shirt, hand over your coat as well. 41 If anyone forces you to go one mile, go with them two miles. 42 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 NIV.

1. Introduction¶

Matthew 5:38-42 is part of Jesus’ Sermon on the Mount. Here, Jesus calls for non-retaliation and radical generosity. My pastor, Ed Glazier, says many people struggle to understand this passage. I do too. 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.

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

I consider why certain strategies are both crucial and rational: beginning with non-retaliation, retaliating when necessary, practicing forgiveness, showing generosity, and clearly signaling intentions, as illustrated in Tit-for-Tat and 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. Additionally, I discuss why weak ties, as illustrated in Matthew 5:23-24 (“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.”), are vital and rational for spreading cooperation.

Ultimately, I argue that while Jesus’s teaching challenges our instincts and tests our resolve, 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, especially since many game-theoretic strategies still involve retaliation. I conclude by examining the practical and ethical implications of these strategies for relationships and communities today, while also acknowledging 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.

2. Game theory¶

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

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 (5, 5). The off-diagonal cells show unilateral defection: the defector gets 10, the cooperator gets 0. The bottom-right cell is mutual defection: each gets -5.

If both cooperate, each receives a socially optimal benefit, like 5 points (top-left cell). If one defects and the other cooperates, the defector gains 10 points while the other gets 0 (off-diagonal cells). Mutual defection results in both players receiving minus 5 points (bottom-right cell).

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, where the interaction occurs only once, the rational strategy is to defect, as there’s no chance to reward trust or punish betrayal.

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, especially the concept of the Nash Equilibrium. Nash Equilibrium is illustrated nicely in this clip from the “A Beautiful Mind” movie, which I highly recommend that readers watch: https://www.youtube.com/watch?v=LJS7Igvk6ZM.^[1] Nash Equilibrium underpins the logic of the Prisoner’s Dilemma: individually rational actions can, paradoxically, lead to outcomes that are collectively irrational.

The Nash Equilibrium, the outcome of the prisoner’s dilemma game, where rational individual choices produce poor collective results, 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, as if guided by an “invisible hand,” ultimately promotes the common good.^[2] Yet the prisoner’s dilemma shows that, without mechanisms for cooperation, self-interest can undermine collective well-being.

3. Real-life examples¶

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, and everyone’s profit collapses.

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.

During the Cold War, both the United States and the Soviet Union faced a choice: build more nuclear weapons (defect) or 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.

In real life, we may need to play these games, similar to the Prisoner’s Dilemma, continuously. This is known as the Iterated Prisoner’s Dilemma. Imagine a workplace where one employee avoids duties, but colleagues always cover for them, so 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, allowing the pattern to continue. 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.

4. Solutions when non-cooperation is rational¶

If we never retaliate, we make ourselves vulnerable to exploitation because 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, and “eye for eye, and tooth-for-tooth” retaliation leads to a sub-optimal equilibrium of worse and irrational outcomes, how can we deal with this? More specifically, how does cooperation emerge in a population of self-interested players?

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, which 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 https://www.youtube.com/watch?v=mScpHTIi-kM. Tit-for-Tat strategy, though counterintuitive, tends to break the vicious cycle of the Prisoner’s Dilemma and 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.

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, occasionally cooperating (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 when the Tit-for-Tat strategy is transparent and straightforward, and doesn’t rely on hidden or overly complex tactics, allowing other players to recognize the pattern more easily, builds trust and encourages faster cooperation, as opponents understand that cooperative behavior will be reciprocated and defections will be met with proportional responses. 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.

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, so Tit-for-Tat has no foothold to encourage mutual trust or positive cycles.

However, another researcher, Duncan J. Watts and Steven H. Strogatz, in their 1998 paper, Collective dynamics of ‘small-world’ networks, cited more than 58,000 times and growing, have a solution to break this vicious cycle of continuous defections.^[4]

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

If there is a small cluster or group of cooperators, what we might call a “homophily or church,” this cluster can foster the spread of cooperation, which emerges due to familiarity and common belief. However, what is more striking is that the cooperation can spread throughout the wider community of non-cooperators, especially when they begin to interact with the closest weak ties (cooperators) of the cluster. In a way, weak ties can be thought of as the closest defectors within or adjacent to the cluster, those who are loosely connected and less committed to cooperative norms. These weak ties act as bridges between the cooperative group and the wider, often more defecting, population.

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.”

For an intuitive visualization of how nurturing weak ties spreads cooperation in a population where the majority are defectors, please watch another praiseworthy video by Veratasim https://www.youtube.com/watch?v=CYlon2tvywA.

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

The weakest links within or between clusters of cooperators act as bridges, connecting otherwise separate groups. These bridges expose members of different clusters to new norms and behaviors, such as cooperation. Even a single weak tie between a cooperative cluster and the wider population can be enough for cooperative strategies to flow outward, gradually influencing others and helping to convert defectors into cooperators. In this way, the strength of weak ties plays a critical role in spreading cooperation beyond isolated pockets, making transformation possible even in environments dominated by defection. This is probably why the Church Ministry has an important role in society.

5. Limitations¶

My analysis has significant limitations. In highly fragmented, distrustful, or violent environments, cooperation may be rare or even impossible, exposing the risk of overgeneralization in game-theoretic optimism. Moreover, Tit-for-Tat, while effective for conditional cooperation, 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, while weak ties can help spread cooperation, they can as easily transmit harmful behaviors or defection, especially 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, especially in the face of power imbalances or persistent harm, should not be underestimated. While 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, while Jesus’s teaching (“do not resist an evil person,” Matthew 5:39) is more radical: it calls for non-retaliation even in the face of harm. This may create tension between the biblical ethic and the game-theoretic optimum, which also deserves an explicit acknowledgment.

6. Summary¶

Now circling back to Matthew 5:38-42, we can see that Jesus’s teaching about turning the other cheek is not simply a call to passive submission, but a radical invitation to break cycles of retaliation and create the conditions for genuine cooperation. The lessons from the Prisoner’s Dilemma and the evolution of cooperation show that pure self-interest and constant retaliation often trap individuals and communities in a downward spiral of mistrust and harm. Yet, when even a small group chooses forgiveness, transparency, and steadfast generosity, living out the ethic of non-retaliation described by Jesus, they can become the seedbed for cooperation to take root and spread.

Just as 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, which can ripple outward and change the dynamics of the whole community. In this way, Matthew 5:38-42 is not just an idealistic command, but a practical strategy that, in some contexts, aligns with insights from mathematical models about how cooperation can sometimes emerge and be sustained.