Abstract
How does one achieve success in the game of life within a community? The Sermon on the Mount can be viewed as a set of strategies based on Christian principles. These strategies appear to be counterintuitive tactics for social dominance, but is such dominance a legitimate form of triumph in life’s game, and how do we quantify this? Can the strategies outlined in the sermon lead to sustainable victory?
Suppose victory is measured by the extent to which individuals balance social acceptance and moral goodness. The Sermon on the Mount proposes strategies that seem painful since they suggest that self-denial can lead to sustainable success. Analysing these strategies requires quantitative research through game theory, a mathematical approach to strategic decision-making with various applications in human interaction. In this article, we integrate the principles of the Sermon on the Mount into a game-theoretical framework to provide insights for a peaceful, communal, and victorious life. The challenge lies in quantifying rewards and victories to make such an approach feasible.
Game theory, a significant field in mathematics and economics, originated in 1944 through the work of John von Neumann and Oskar Morgenstern (Myerson 1999). It was further developed by John Nash in 1950 with the Nash equilibrium concept. The essence of game theory is the systematic study of strategic interactions among various entities, aiming to deepen our understanding of the world, similar to other theories.
In game theory, individuals are expected to behave in certain ways, with specific goals and strategies to achieve these goals, allowing for prediction in given situations. It focuses on interactions within a group where each individual’s actions affect the collective outcome. The theory involves scenarios where entities (players) interact in different contexts, influencing each player’s strategy and outcomes. It distinguishes between cooperative games, where players can communicate and collaborate, and non-cooperative games, where such collaboration is absent.
Key components of a game include a finite number of players, a set of rules, a finite set of moves or choices, and a numerical payoff. Players can be humans, groups, or impersonal entities like computer programs. Each game concludes with a set number of moves, leading to a final outcome and associated rewards for participants. The theory entails analysing players’ actions and their effects on others’ rewards. Strategies can be pure (unaffected by opponents’ strategies) or mixed (including probabilities regarding pure strategies). In two-person zero-sum games, one player’s gain is equal to the other’s loss, while non-zero-sum games do not have such constraints. Players’ strategies can vary based on their profiles, including personality, beliefs, circumstances, and available rewards.
Game theory offers a unique perspective for analysing the conflict between an individual’s selfish ego and the desire for social relationships. The Sermon on the Mount is found in Chapters 5 to 7 of the Gospel according to Matthew. We identify five specific commands or tasks for a life lived according to the Sermon. As a first attempt to interpret the text, the most prominent and diverse tasks are chosen. We assume that the Sermon on the Mount can be summarised as a call to perform five specific tasks. These five tasks are generosity, trust, judgement, prayer, and forgiveness. Each task is modelled as a subgame where the strategy for each game is to reward, punish, or defect from the opponent.
We quantify the game of the Sermon on the Mount for ego depletion and prosocial gain, identify and quantify five tasks accordingly and calculate the Nash equilibrium to determine the best strategy for each player. Solving the two-person non-zero-sum game with the Nash equilibrium shows the best strategy for both players is to defect for all five tasks in the game of living according to the Sermon on the Mount, quantified according to the loss of ego and the gain of relationship.
A sensitivity analysis is performed to determine the prosocial gain a player should receive to consider the reward strategies in the game of the Sermon on the Mount. The analysis is done to determine how much more additional gain is required to change the best strategy from defecting to rewarding. Theologically these additional gains could be a proxy for a measure of faith in additional, for example metaphysical, rewards. We show that a player requires more faith in additional gain to play the reward strategy in the game of trust than to play the reward strategy in the other games. However, all games require at least some measure of faith in additional gain to entice the player to choose to reward their opponent.
The best strategy for each player without faith in additional reward is to defect, but with faith in approximately twice the original payoff it becomes lucrative to play the reward strategy on the various tasks. The question arises as to whether the best one-off strategy remains such in repeated interactions with players of various life approaches. Various repeated interactions may be simulated to determine the total payoff and the expected payoff of all five different tasks.
In the natural game both players play according to the Sermon on the Mount but without a measure of faith in increased gain. In the faith game one player plays according to the tenets in the Sermon with a measure of faith and automatically receives additional reward when choosing to play the reward strategy while the opponent plays according to the natural game. In the sustainability game a player plays according to the tenets in the Sermon with a measure of faith greater than the lower bound calculated to entice the player to choose a reward strategy, while the opponent plays according to the natural game.
Two players have rounds of seven interactions each for different scenarios. Each scenario is categorised according to a combination of strategies chosen for each player. The players can maintain one of the three strategies or change their strategy during each of the seven rounds of interaction. After the expected values for each player in each scenario have been determined, the payoffs are ranked according to descending order indicating the best to worst total expected payoffs.
We rank repeated interactions between two players according to their total payout values and we demonstrate that living according to the Sermon on the Mount is not an intuitive choice, but with faith, a player can benefit and be victorious. In cases where the opponent mirrors the player’s strategies, the best outcome for both players is achieved when they collaborate to reward their opponent. This study is an interdisciplinary investigation where a mathematical technique is applied within a theological context.
Keywords: behavioural economics; decision analysis; game theory; quantification; religious studies
- The artwork on this article’s featured image is by Carl Bloch (1877) and is in the public domain. Available on Wikimedia Commons: https://en.wikipedia.org/wiki/Sermon_on_the_Mount#/media/File:Bloch-SermonOnTheMount.jpg.