Examining Marital Infidelity via Game Theory

Abstract

Objective: Marital infidelity significantly impacts both the community and the institution of marriage. This study aims to develop a theoretical framework for analyzing marital infidelity through a game-theoretic lens. Methodology/Design/Approach: This research employs a game-theoretic model to predict the decision-making processes of unfaithful partners. Static game models are utilized to explore the interactions between spouses, focusing on identifying Nash equilibria that encapsulate the complexities and uncertainties inherent in infidelity-related decisions, whether through pure or mixed strategies. Results: The analysis reveals strategic dynamics in marital infidelity, where Nash equilibria indicate scenarios where one or both partners may engage in extramarital affairs. A Nash equilibrium is established when both partners perceive the benefits of infidelity as outweighing the costs, leading to diminished trust and communication. The Mixed-Strategy Nash Equilibrium (MSNE) hypothesis suggests that spouses may oscillate between fidelity and infidelity based on probabilistic strategies. Research Implications: This study provides a game-theoretic perspective on marital infidelity, whose findings may be used to inform legal frameworks and social policies addressing the consequences of infidelity, potentially impacting family counseling and legal services. Value/Originality: This research introduces a game-theoretic approach to understanding trust and transgression in marriages, identifying two primary categories of Nash equilibria. It fills a theoretical gap while providing practical insights into marital behavior.

1. Introduction

Trust is a fundamental aspect of interpersonal and economic connections in several domains, including sociology, psychology, economics, and law. Trust promotes collaboration, upholds societal structure, and increases the reliability of behaviors in complex relationships [1,2]. Hence, violations of trust, or acts of betrayal, lead to significant disruptions to established standards and anticipated outcomes. These violations can take place in situations ranging from personal relationships and corporate transactions to international diplomacy, all having significant repercussions [3,4]. Behavioral economics, game theory, psychology, and legal systems have all been extensively applied to the study of trust and its breach [5,6]. These studies have generated significant findings on the mechanisms of trust formation, the consequences of transgression, and various approaches to re-establish trust and achieve reconciliation [7,8]. The literature shows how trust changes over time and provides guidance for developing strategies and actions that promote resilience and honesty within and across communities [2]. Understanding these dynamics is essential for dealing with the complexities in situations such as marital infidelity, when the breach of trust can result in severe personal and societal consequences.

This paper is an extension of the theoretical framework presented in Batabyal’s (2018) [9] article “Marital Infidelity: A Game-Theoretic Analysis.” Building upon this framework, our ongoing study integrates the propensity for unfaithfulness in both spouses and their mutual efforts to monitor each other. This expansion aligns with one of the proposed research directions outlined in Batabyal’s report, which advocates a more inclusive framework that accounts for deceit by both parties and the associated expenses of surveillance. Our research investigates in depth the interactions and strategies utilized by both spouses, thereby offering a balanced and thorough analysis of the dynamics within a marriage.

Marital infidelity remains a major problem in many nations, challenging partnerships’ moral foundations and upending traditional family structures [10,11]. Nonetheless, the academic literature has frequently been slow in offering an in-depth theoretical analysis of the fundamental dynamics of marital infidelity. The discrepancy becomes even more apparent upon closer examination of the ongoing strategic exchanges, which may profoundly impact the psychological and monetary well-being of the participants.

Numerous studies have demonstrated the prevalence of infidelity, highlighting the importance of a thorough examination of its underlying root causes [12]. While empirical research has provided insightful information about how socioeconomic and demographic factors affect infidelity, the strategic aspects of this problem have received less attention. This covers the procedures spouses use to make decisions when they have knowledge or suspicion of infidelity, the emotions they feel when they discover the affair, and the responses they give.

To address this lacuna, the current study offers a novel approach that uses game theory to investigate the complex dynamics involved in cases of marital infidelity. It introduces a new paradigm for understanding marital infidelity by seeing the interactions between cheating spouses as a strategic game. The study goes beyond basic behavioral analysis and places it inside a larger economic and strategic framework. The research aim is to create a game model that examines the actions of one spouse in relation to the possible reactions of the other spouse. The model employs basic principles from game theory, such as mixed-strategy solutions and Nash equilibria, to identify the conditions that may encourage cheating. Moreover, it predicts the probable responses of both parties to deception, considering their common objective of maximizing utility. This new technique not only addresses a theoretical gap but also has practical ramifications. For example, the knowledge obtained from the model could have some impact on the methods used in marital counselling, by giving therapists a deeper understanding of the dynamics within marriages.

The present paper thus contributes significantly by clarifying and expanding the strategic understanding of marital infidelity, delineating clearly how both spouses’ decisions interact within a comprehensive and balanced model.

Our model extends previous game-theoretic frameworks in three key ways. First, it incorporates bilateral monitoring efforts by both spouses, whereas most prior models assume unilateral monitoring or infidelity. Second, it allows for mixed-strategy equilibria, capturing the probabilistic nature of decision-making in marital dynamics. Third, the model introduces a quadratic monitoring cost function that theoretically reflects increasing psychological burdens of surveillance. While this utility specification is motivated by empirical findings from psychology and behavioral economics regarding emotional and cognitive costs of monitoring, we emphasize that our analysis remains entirely theoretical and does not incorporate empirical calibration or estimation. Nonetheless, this functional choice allows us to approximate relevant psychological dynamics within a formal economic framework.

2. Literature Review and Theoretical Framework

2.1. Empirical Mechanisms and Motivations

Understanding the causes, patterns, and consequences of marital infidelity has been a central concern in the interdisciplinary study of intimate relationships. A substantial body of the empirical literature has emerged in recent decades, aiming to identify the psychological, social, and economic predictors of infidelity and to explore the strategic behaviors that individuals employ in navigating extramarital relationships.

Empirical studies have provided us with more information about what leads to infidelity in marriage and how it affects the victim. Researchers have identified critical components that influence the likelihood of adultery, and the strategic moves associated with extramarital encounters via the use of behavioral modelling, extensive surveys, and experiments. And although survey-based research provides rich insights, it frequently entails self-report biases, mainly because of the shame associated with infidelity [13].

Longitudinal Evidence: Relationship dissatisfaction is a strong predictor of adultery, according to longitudinal evidence. People who report being unhappy in their marriages are more likely to engage in extramarital affairs in the future [14]. Dissatisfaction may arise from several factors, such as unfulfilled emotional needs, sexual discontent, and interpersonal conflict within the partnership. Those who view their spouses as emotionally inattentive are more inclined to pursue intimacy outside of their marriage [15]. In addition, economic conditions influence infidelity rates; individuals in financially stable relationships may be less inclined to cheat due to higher opportunity costs, whereas those in economically disadvantaged circumstances may pursue affairs in order to acquire additional resources [10]. The link between social roles and economic difficulties was highlighted in research finding that male infidelity rates were higher when traditional masculine identity was challenged [16]. Research indicates that persons with a history of infidelity are more predisposed to participate in subsequent affairs, implying that prior cheating activity is a significant predictor of future infidelity [12]. This phenomenon may be attributed to variables, including less commitment to monogamy, decreased guilt over infidelity, or a propensity to perceive adultery as a viable coping strategy for marital discontent.

Machine Learning Methodologies: These have been used to ascertain the most significant determinants of extramarital relationships. Major predictors of infidelity, according to research that analyzed a dataset of more than 1200 individuals, include marital discontent, prior infidelity, and the effect of social networks [12]. Additionally, the same research proved that game-theoretic strategies, which include lying and misrepresentation, are critical factors in whether an affair goes undiscovered.

Experimental Methodologies and Behavioral Economics: Experiments in behavioral economics have shown that individuals modify their cheating behavior when they anticipate a higher likelihood of being discovered. Laboratory games and simulations offer regulated environments for observing such tendencies. Financial stability was shown to increase the opportunity cost of adultery, thereby reducing the probability of cheating [15]. Laboratory studies indicate that individuals are less inclined to engage in infidelity-like activities when their spouses use monitoring technologies, such as social media surveillance or financial tracking applications [17].

Cross-Cultural Perspectives: There is a strong correlation between infidelity and social and demographic variables. The attitudes towards extramarital relationships vary greatly between cultures, with some societies showing a higher tolerance for adultery than others. Greater acceptance of extramarital affairs was observed in societies where women had more economic opportunities outside of marriage and in places where there were fewer social or legal repercussions for such encounters [10].

Notwithstanding this research, the relative importance of individual and contextual factors in explaining infidelity remains unclear. While some researchers have pointed to logical cost–benefit assessments as the primary motivator for adultery, others have highlighted the role of emotional discontent and impulsive actions. The literature reflects the ongoing debate on the relationship between these factors.

The growing availability of digital technologies has added complexity to the analysis of infidelity. Digital communication platforms, dating applications, and social media have enabled novel types of extramarital relationships that deviate from conventional definitions of infidelity [18].

To enhance clarity,

Table 1. Empirical Mechanisms and Motivations.

	Effect on Infidelity	Mechanism/Motivation
McNulty et al. (2018) [14]; Fincham and May (2017) [10]	Increases likelihood due to unmet emotional/sexual needs	Relationship dissatisfaction
Vowels et al. (2022) [12]	Predicts future infidelity via reduced guilt or commitment	Prior infidelity
Munsch (2015) [16]; Adamopoulou (2013) [19]	Financial stress or opportunity costs affect cheating likelihood	Economic conditions
Vowels et al. (2022) [12]; Shackelford and Goetz (2006) [20]	Facilitates or discourages infidelity through peer dynamics	Social network influence
Hertlein and Piercy (2006) [18]; Vaterlaus and Frantz (2018) [21]	Enables new forms of infidelity (e.g., cyber-infidelity)	Digital technology usage

summarizes the key empirical mechanisms and motivations identified in the literature, along with their documented effects on infidelity and key references.

2.2. Theoretical Models, Methodologies, and Gaps

To learn more about cheating, scientists have used methods that include game-theoretic simulations, economic modelling, experimental designs, and self-report questionnaires. The validity and applicability of the findings are affected by the specific advantages and disadvantages of each method.

Self-Report Questionnaires: Infidelity research frequently makes use of self-report questionnaires. Researchers may learn a lot about people’s thoughts, feelings, and motivations concerning infidelity from these questionnaires. The General Social Survey (GSS) has been crucial in providing demographic data on extramarital partnerships. Self-report surveys indicate that marital discontent, prior infidelity, and emotional alienation are important predictors of the likelihood of engaging in an affair [13]. Despite being cost-effective and capable of capturing extensive samples, self-reports are susceptible to underreporting or social desirability bias due to apprehensions of judgment or consequences [20]. Moreover, memory bias may compromise the precision of self-reported infidelity activities, especially in retrospective investigations.

Experimental Methodologies: Researchers have increasingly used experimental procedures to overcome the limitations of self-report data. Laboratory studies and behavioral economic experiments enable researchers to examine decision-making processes in controlled settings [14]. Nonetheless, laboratory research frequently exhibits limited external validity since artificial environments may fail to mirror real-life interpersonal dynamics authentically and lack real-world complexity [17].

Longitudinal Studies: Researchers use longitudinal research to investigate the factors and ramifications of infidelity across time. Longitudinal study approaches monitor people and couples over several years to achieve a comprehensive knowledge of how relationship satisfaction, personality factors, and external stresses affect infidelity behavior [10]. A key advantage of longitudinal studies is their ability to show causal linkages, such as whether a decline in marital satisfaction leads to infidelity or if infidelity undermines relationship quality over time. Nonetheless, these investigations require substantial resources and encounter difficulties associated with participant attrition since participants may choose to withdraw from the study over time.

Game Theory Simulations: Game theory offers a systematic framework for examining the strategic interactions between partners surrounding infidelity. Researchers have created mathematical models replicating individual decision-making about secrecy, surveillance, and retribution in marital relationships [9,22]. These models help to identify the circumstances that increase the likelihood of adultery and predict behavioral patterns based on rational decision-making principles. Game-theoretic techniques offer insights into the strategic aspects of infidelity; nevertheless, they frequently depend on simplified assumptions, such as the idea that individuals behave purely rationally, which may not accurately reflect real-world conduct.

Extensive Data and Computational Learning: As digital communication channels proliferate, academics have investigated big data and machine learning methodologies to investigate infidelity. Machine learning methods may examine extensive datasets to discern trends and determinants of extramarital affairs [12]. Game-theoretic models may overly simplify emotional and psychological complexities, whereas purely psychological investigations could neglect the strategic and rational foundations of marital decision-making. Future improvements are anticipated from employing multidisciplinary frameworks that integrate complex psychological elements into formal economic and game-theoretic models. Although these technologies are highly analytical, they raise ethical concerns related to data protection and privacy.

Marital infidelity, defined as a breach of trust in a committed relationship through emotional or physical involvement with a third party [23], has been thoroughly studied in a wide range of disciplines, including psychology, sociology, philosophy, and economics. As a personal betrayal with major social, emotional, and financial consequences, infidelity is a complicated and weighty issue, warranting an interdisciplinary approach [11,24]. Estimates indicate that 20% to 50% of married adults engage in extramarital relationships at some stage in their lives, while prevalence estimates differ among cultural and demographic contexts [11]. Psychological and sociological approaches point to personality characteristics, attachment patterns, and societal influences as key predictors of infidelity [12].

Emotional dissatisfaction, the absence of intimacy, and personality characteristics like narcissism are often found in psychological research to be significant predictors of infidelity [10]. Sociological theories emphasize the impact of peer groups, cultural norms, and prevailing societal norms on marital fidelity [24].

More recent research has broadened the definition of infidelity to include economic and game-theoretic perspectives. Individuals weigh the benefits and drawbacks of having an affair, and these considerations portray adultery as a deliberate decision influenced by reasonable cost–benefit analyses. Economic models identify financial reliance, power dynamics in marriage, and the presence of alternative partners as critical determinants influencing such decisions [25]. Incorporating concepts like deceit, surveillance, and retribution into decision-making frameworks, game theory expands these models by examining how individuals make strategic decisions based on their partners’ anticipation of their actions [9].

The conceptualization of infidelity as a decision-making process aimed at maximizing individual benefit aligns with economic theories of human behavior, namely, rational choice theory. Rational choice theory posits that individuals assess the benefits and disadvantages of an activity when making decisions. Potential benefits, such as emotional satisfaction, sexual novelty, external affirmation, or enhanced self-esteem, are weighed as against potential drawbacks, including the risk of discovery, relationship termination, reputational harm, divorce-related costs, and other financial ramifications [26,27,28].

Initial theoretical research used time-allocation models to demonstrate how individuals allocate their time between their jobs, spouses, and extramarital companions [29]. Subsequent research broadened these concepts by integrating additional elements such as evolutionary forces [30,31], opportunity structures [32], and wealth accumulation [19].

Game-theoretic approaches consider infidelity as a strategic interaction between partners, focusing on the interdependence of choices, rather than individual agency. Whereas traditional economic models assume individuals make autonomous decisions, game theory emphasizes how choices are contingent upon each other, so that both partners plan their actions based on how their partner could react to infidelity. This creates a dynamic system where trust, deceit, and oversight play critical roles in decision-making.

The Prisoner’s Dilemma, a fundamental game-theoretic model for infidelity, illustrates that while both spouses ideally want mutual fidelity, they may resort to adultery if they suspect their spouse is also going to cheat. People in this situation may resort to anticipatory adultery as a defense mechanism or keep an increased focus on their partner’s actions out of fear of exploitation [7]. The Matching Pennies game illustrates how surveillance, suspicion, and dishonesty interact within marital relationships, leading to vicious cycles of retaliation and distrust [9].

The strategic interactions between participants are investigated with a focus on the interdependence between the actions of all participants. In this approach, one spouse’s decisions can somewhat or significantly impact the other’s decisions [22]. The Nash equilibrium model [33] is used to describe a situation where the strategies of both players are optimized based on their understanding of the other’s intentions. A Nash equilibrium may occur in cases of infidelity when both spouses decide whether to remain loyal or commit adultery by weighing the associated costs and rewards [5].

In addition to traditional game-theoretic models, evolutionary game theory has been employed to analyze the temporal development of infidelity behaviors. Evolutionary models indicate that adaptive factors such as reproductive success and resource acquisition influence human mating choices, including infidelity [34]. These models demonstrate that people modify their fidelity strategies in reaction to external circumstances, including imbalances in sex ratios in the population and fluctuations in economic stability.

To better understand marital infidelity, scientists have used varied methods that include game-theoretic simulations, economic modelling, experimental designs, and self-report questionnaires, methods whose advantages and disadvantages affect the validity and applicability of the findings. Despite being cost-effective and capable of capturing extensive samples, self-reports are susceptible to underreporting or social desirability bias due to fear of judgment or consequences. Experimental methods are more precise but lack external validity, and game theory provides strategic insights while abstracting away the complexities of human emotion.

Trust is fundamental to marital stability [1,2,6]. Whether betrayal is confirmed or just suspected, it can induce a spillover effect, undermining confidence in unrelated areas [2,3,4]. These dynamics are particularly prominent in adultery when the fear of exposure prompts deceit and subterfuge [7]. Furthermore, repeated or imagined betrayals may lead to continuous cycles of monitoring and secrecy, reflecting the complex feedback loops characteristic of repeated games [5].

Although unilateral infidelity theories are prevalent, studies on mutual infidelity—where both partners engage in extramarital affairs—are scarce [35]. According to Chiappori and Salanié (2016) [25], there is a need for more advanced game-theoretic models that can account for interactions where the reward structures, including emotional outcomes and reputational hazards, might be dynamically impacted by one spouse’s infidelity.

Contributing to the growing body of multidisciplinary work that uses mathematical modelling to shed light on the complexities of human relationships, this study applies game theory to the issue of marital infidelity.

A fundamental argument in the literature on marital infidelity pertains to the question of to what degree infidelity is influenced by logical decision-making instead of emotional impulsivity. Economic and game-theoretic models indicate that individuals commit adultery after thoroughly evaluating the costs and advantages, including the probability of detection and possible repercussions on their relationships [9]. Psychological research indicates that emotional dissatisfaction, attachment insecurity, and impulsive behavior are equally important factors [13]. Reconciling these perspectives poses a challenge for future study.

Gender Inequalities: Another question pertains to gender differences in infidelity behavior. Evolutionary psychology posits that men and women engage in extramarital affairs for different reasons—men tend towards opportunistic infidelity and the pursuit of sexual variety, whereas women tend to engage in affairs to secure better long-term partners [36]. Empirical evidence, however, remains contradictory, and developing social systems confound any simple gender-based dichotomy [16]. Recent studies indicate that social and economic transformations are modifying traditional gender-based patterns of infidelity: when women gain greater financial independence, their tendency to engage in extramarital relationships matches that of men, challenging longstanding beliefs regarding gender and infidelity [11]. To what extent genetic and sociocultural variables combine to affect gendered infidelity trends remains unresolved.

Advancements in Technology: Another subject of research is how contemporary technology has contributed to infidelity. Technological advancements in digital communication have significantly changed how people initiate, maintain, or hide their extramarital relationships. Online dating applications, social networking platforms, and encrypted messaging services have facilitated new avenues for extramarital affairs, resulting in the rise of cyber-infidelity [18,21]. Empirical research on the influence of digital technology on infidelity trends is still nascent.

Bilateral Infidelity with Dynamic Modelling: Current game-theoretic frameworks generally focus on unilateral decisions, highlighting the necessity to also represent how both couples could concurrently contemplate adulterous behaviors. Dynamic or evolutionary game models may include time-varying payoffs and emotionally influenced feedback loops [34,37].

The following section presents a formal model that builds on these theoretical and empirical foundations to better portray the strategic dynamics of infidelity through a game-theoretic lens.

Building on these observations, we provide below a comparative analysis of how our model advances the existing literature on marital infidelity.

This study significantly expands the existing game-theoretic literature on marital infidelity by addressing several critical limitations observed in prior models. Foundational research by Fair (1978) [29] introduced a utility-maximization approach to extramarital affairs, modeling infidelity as an individual decision based on a trade-off between the benefits of an affair and the risks of detection or moral costs. However, Fair’s model treats infidelity as an isolated, unilateral decision without incorporating the interactive strategic behavior of both spouses within the marital context. Our model, in contrast, introduces a novel approach that incorporates bilateral monitoring, psychological cost analysis, and comprehensive equilibrium analysis, offering a fresh perspective on the complex dynamics of marital infidelity.

Building upon this foundational work, Cashel-Cordo and Friesner (2004) [38] developed a more intricate game-theoretic model that incorporates not only infidelity but also divorce and sexually transmitted disease risks. Their framework introduces a broader set of marital outcomes. Still, it does not explicitly address the psychological costs of monitoring nor the nuanced equilibrium conditions that emerge from continuous monitoring efforts.

Recent contributions by Batabyal and Beladi (2016) [7] and Batabyal (2018) [9] further advance the field by applying static game-theoretic approaches to model the strategic interactions between spouses. Batabyal and Beladi (2016) [7] conceptualize infidelity decisions as a binary game, identifying mixed-strategy equilibria. Yet, their binary structure limits the analysis by omitting gradations of monitoring intensity and neglecting psychological surveillance costs.

Batabyal (2018) [9] introduces continuous monitoring levels and provides insights into mixed-strategy equilibria, offering greater flexibility than prior models. Nonetheless, his framework remains unidirectional, focusing solely on one-sided monitoring and infidelity. It does not incorporate bilateral surveillance efforts, nor does it account for the escalating emotional costs associated with persistent monitoring behaviors.

In contrast to these models, our framework makes four pivotal contributions:

(1)

Bilateral and Continuous Monitoring: We explicitly model mutual surveillance by both spouses, allowing for continuous variation in monitoring efforts and thus reflecting more realistic relational dynamics.

(2)

Quadratic Psychological Cost Structure: Our model introduces a quadratic monitoring cost function, grounded in empirical psychological and behavioral research, to capture the increasing emotional burdens associated with intensified surveillance.

(3)

Comprehensive Equilibrium Analysis: By identifying both pure and mixed-strategy Nash equilibria, our model offers a nuanced and generalizable analysis of marital decision-making, applicable across a broad spectrum of relationship contexts.

(4)

Behaviorally Informed Theoretical Integration: While our model remains theoretical, its structural assumptions are explicitly informed by empirical findings regarding the psychological consequences of surveillance and betrayal within intimate relationships.

Through these innovations, our study offers the first unified, behaviorally grounded game-theoretic model of marital infidelity that simultaneously incorporates bilateral monitoring, continuous strategic choice, escalating psychological costs, and complete equilibrium characterization. This integrative approach offers a substantially richer and more realistic theoretical foundation for examining the strategic interplay between trust, suspicion, and infidelity within marital relationships.

3. General Model Framework

Traditional studies have focused on the empirical dimensions of marital infidelity or the unilateral decision-making processes, leaving a gap in the theoretical exploration of these complex interpersonal interactions. By providing a game-theoretic framework that captures the complexities of bilateral infidelity and monitoring decisions between spouses, the model presented here attempts to address this gap. Batabyal’s (2018) [9] model, which examined infidelity and monitoring in a marital relationship in detail, serves as the basis for our research. Our research expands upon Batabyal’s (2018) [9] model by incorporating the possibility of infidelity and the mutual monitoring efforts by both partners.

Our methodology aims to provide a more comprehensive understanding of the decision-making processes that impact marital fidelity and infidelity.

The decisions of two rational agents, the husband (H) and wife (W), who each face the dilemma of whether to remain faithful or commit infidelity, form the basis of this model. Additionally, each must determine the level of effort they should put into monitoring their spouse’s fidelity. The model incorporates key variables, such as the benefit of cheating without being detected, the penalty for being caught, and the cost associated with monitoring the spouse’s behavior. These variables have an impact on the utility functions of each participant, which in turn affect their decision-making process and can result in several alternative equilibria.

The model delineates the probabilities of infidelity, $p_H$ and $p_W$ as the likelihoods with which the husband and the wife, respectively, opt for cheating. The monitoring efforts, $m_H$ and $m_W$, represent the respective investments by the husband and wife in surveilling their spouse, where the effort is constrained within the interval [0, 1]. The benefit derived from successful, undetected infidelity is measured by γ > 0, representing the increase in utility caused by cheating. The cost of monitoring, on the other hand, is represented by a quadratic function of the effort, $\zeta {·m}_i^2$, highlighting the disutility or negative impact associated with the effort of monitoring, where $\zeta >0$ stands as the cost coefficient.

Formally, we define the monitoring cost as a quadratic function of effort:

$$C\left(m\right)=\zeta m^2$$

where $m\in \left[\mathrm{0,1}\right]$ represents the level of surveillance effort, and $\zeta >0$ is the monitoring cost coefficient. This functional form captures increasing marginal costs: the more a spouse monitors, the more disproportionately costly it becomes.

The marginal cost of surveillance, obtained by differentiating the cost function with respect to effort, is as follows:

$$MC={\displaystyle \frac{d\zeta m^2}{dm}} =2\zeta m$$

This convex structure is consistent with psychological and behavioral findings on the growing emotional and cognitive burden associated with sustained suspicion and control within a marital relationship.

To fully grasp the strategic underpinnings of the model, it is essential to elaborate on the fundamental assumptions regarding the utility structure and the psychological rationale for the chosen functional forms. Accordingly, we detail below the reasoning behind the cost function formulation and its consistency with established empirical findings. An essential modelling choice in this study is the specification of the utility function’s parameters, particularly the functional form of the monitoring cost. We adopt a quadratic form for the monitoring cost function, where the cost increases with the square of the monitoring effort. This structure captures the phenomenon of increasing marginal costs of surveillance, which is the idea that incremental monitoring becomes disproportionately more burdensome as surveillance efforts intensify.

This approach is consistent with empirical findings from psychology and behavioral economics, which document the emotional and cognitive strains associated with persistent surveillance and suspicion in intimate relationships [39,40,41]. These studies highlight that greater monitoring efforts may escalate anxiety, erode relationship satisfaction, and incur psychological costs beyond the immediate resource burden.

In our model:

• γ (gamma) represents the benefit derived from engaging in infidelity without detection. A higher γ implies a stronger incentive to cheat, as the utility from undetected infidelity rises.
• ζ (zeta) is the cost coefficient for monitoring effort. Higher values of ζ indicate more significant psychological and emotional costs associated with monitoring behaviors, thus deterring excessive surveillance.

Together, these parameters shape the strategic decisions of spouses by determining the trade-offs between fidelity, infidelity, and monitoring efforts within the game-theoretic framework. Their inclusion ensures that the model captures both the rational cost–benefit aspects and the psychological dynamics of marital interactions.

The utility function incorporates three distinct expressions, each reflecting aspects of the strategic dynamics within a marital relationship from a game-theoretic perspective. The first captures the disutility incurred from monitoring the spouse’s activities, scaled by the probability of the spouse’s infidelity. This term expresses the cost associated with vigilance efforts, highlighting how the anticipation of betrayal amplifies the psychological and resource-based burdens of surveillance. The second expression describes the conditional utility derived from marriage when the spouse remains faithful, adjusted for the costs of monitoring. It underscores the intrinsic value placed on marital fidelity, diminished by the expenditure involved in ensuring such faithfulness. This expression effectively balances the positive aspects of a trusting relationship against the drawbacks of maintaining oversight.

The third expression quantifies the utility derived from engaging in infidelity, moderated by the spouse’s monitoring efficacy. It evaluates the perceived benefits of cheating, based on the risk of being detected. This captures the calculated decision-making process regarding pursuing extramarital encounters while considering the potential for surveillance and discovery. Together, these expressions provide a framework for examining the interplay between trust, suspicion, and strategic decision-making in relationships, modeling the incentives and deterrents that influence the dynamics of marital fidelity and monitoring.

To summarize the key elements of the model,

Table 2. General model framework summary.

Interpretation	Mathematical Expression	Model Component
Net benefit from staying faithful under monitoring	Base utility—monitoring cost	Utility from infidelity
Expected gains from undetected infidelity	Benefit γ adjusted for detection risk	Utility from infidelity
Costs increase non-linearly with surveillance intensity	Quadratic cost function ζ·m2	Monitoring costs
Best response functions indicating equilibrium effort	Derived from FOCs of utility function	Optimal monitoring effort
Stable strategic outcomes in marital interactions	Pure or mixed-strategy Nash equilibrium	Nash equilibrium type

presents the mathematical formulation and interpretation of the main components.

The expected utility functions for the husband (H) and wife (W) are formulated as follows:

For the husband:

$${EU}_H=p_W\left(-\zeta m_H^2\right)+\left(1-p_W\right)\left(m_H-\zeta m_H^2\right)+p_H\left(1-m_W\right)\gamma$$

(1)

For the wife:

$${EU}_W=p_H\left(-\zeta m_W^2\right)+\left(1-p_H\right)\left(m_W-\zeta m_W^2\right)+p_W\left(1-m_H\right)\gamma$$

(2)

After simplification, the equations become:

$${EU}_H=-\zeta m_H^2+\left(1-p_W\right)m_H+p_H\left(1-m_W\right)\gamma$$

(3)

and

$${EU}_W=-\zeta m_W^2+\left(1-p_H\right)m_W+p_W\left(1-m_H\right)\gamma$$

(4)

The first-order necessary conditions (FONCs) for an optimum are derived by taking the partial derivatives of the utility functions with respect to the monitoring efforts, yielding the following:

For the husband:

$${\displaystyle \frac{d{EU}_H}{d{m}_H}}=-2\zeta m_H+\left(1-p_W\right)=0$$

(5)

For the wife:

$${\displaystyle \frac{d{EU}_W}{d{m}_W}}=-2\zeta m_W+\left(1-p_H\right)=0$$

(6)

Solving these equations for $m_H$ and $m_W$ gives the optimal monitoring efforts in terms of $p_W$ and $p_H$, respectively:

$$m_H={\displaystyle \frac{1-p_W}{2\zeta }}$$

(7)

and

$$m_W={\displaystyle \frac{1-p_H}{2\zeta }}$$

(8)

The optimal monitoring efforts for the husband and for the wife, derived from their respective expected utility functions, reveal a crucial aspect of marital strategy within a game-theoretic context. These expressions capture the equilibrium in monitoring behavior, showing that each spouse’s effort is finely tuned to the perceived probability of the other’s infidelity, inversely weighted by the costs of monitoring. This equilibrium highlights the strategic interplay between trust, surveillance, and the costs of such vigilance, illustrating the intricate calculus with which spouses navigate the dynamics of fidelity and mistrust.

Incorporating the derived optimal monitoring efforts, expressed as functions of $p_W$ and $p_H$, into the expected utility functions for the husband (H) and wife (W) yields the following refined formulations:

For the husband, the expected utility function becomes the following:

$${EU}_H={\displaystyle \frac{{\left(1-p_W\right)}^2}{4\zeta }}+p_H\left(1-{\displaystyle \frac{1-p_H}{2\zeta }}\right)\gamma$$

(9)

Similarly, for the wife, the expected utility function is expressed as follows:

$${EU}_W={\displaystyle \frac{{\left(1-p_H\right)}^2}{4\zeta }}+p_W\left(1-{\displaystyle \frac{1-p_W}{2\zeta }}\right)\gamma$$

(10)

Building upon the foundational analysis of the expected utility functions and incorporating optimal monitoring strategies, we identify subtle mechanisms that influence strategic decision-making regarding marital fidelity: the Direct Infidelity Impact (DII) and the Perceptual Fidelity Response (PFR). These mechanisms elucidate the multifaceted nature of decisions surrounding infidelity and their respective impacts on expected utility, as can be seen in Figure 1.

Figure 1 presents the expected utility functions over a continuous probability space ranging from 0 to 1, thus explicitly addressing the dynamic relationships between the Direct Infidelity Impact (DII), Perceived Fidelity Response (PFR), and infidelity probabilities.

The DII underscores a critical threshold in the individual’s propensity towards infidelity ($p_i$), revealing that an increase in $p_i$ above ${\displaystyle \frac{1}{2}}-\zeta$ correlates with a positive shift in expected utility $\left({\displaystyle \frac{d{EU}_i}{d{p}_i}}>0\right)$. This indicates that beyond this critical point, the anticipated benefits of engaging in extramarital affairs are perceived as greater than its drawbacks. Conversely, when $p_i$ falls below this threshold, there is a decrease in expected utility with an increased likelihood of infidelity. This underscores the inherent risk–reward calculation involved in the decision to cheat.

In contrast, the PFR addresses the impact of one spouse’s perception of the other’s fidelity ($p_j$, where i ≠ j), on their own utility. This effect demonstrates that for all $p_j<1$, an increase in the perceived probability of the partner’s infidelity leads to a decline in expected utility $\left({\displaystyle \frac{d{EU}_i}{d{p}_j}}<0\right)$. It underscores the negative impact of suspicion and mistrust on the individual’s well-being within the marriage and the need for adaptive behavior.

The theoretical model, including its structural assumptions, utility functions, and optimization framework, has now been fully specified. We proceed by systematically analyzing the derived solutions and exploring their implications for marital infidelity behavior within the context of strategic interactions.

To investigate the strategic interactions between spouses, we explore two forms of equilibrium: Pure-Strategy Nash Equilibrium (PSNE), in which players adopt deterministic strategies, and Mixed-Strategy Nash Equilibrium (MSNE), in which players randomize their choices probabilistically. The following subsections describe the conditions under which each equilibrium develops.

4. Results

In addition to the theoretical derivations, this section includes analytical sensitivity analysis to examine how equilibrium outcomes respond to parameter changes and assess model sensitivity.

4.1. Pure-Strategy Nash Equilibrium (PSNE)

This section examines the conditions that produce a stable Pure-Strategy Nash Equilibrium (PSNE) in the context of marital fidelity. Specifically, it aims to evaluate whether fidelity or infidelity can be sustained as a dominant strategy within the predicted utility framework. To achieve this, we incorporate previously defined optimal monitoring strategies, which are based on the probability of infidelity for both the husband and wife. This allows us to evaluate the strategic interactions represented by the expected utility functions of both spouses, as detailed in Equations (9) and (10). By methodically evaluating crucial strategic scenarios—where neither spouse cheats, both cheat, or just one cheats—we uncover stable strategies that meet the requirements of a Nash equilibrium. Using this method, we determine the decision-making circumstances under which couples’ preferences align to create an equilibrium.

Scenario 1: Both Not Cheating ($p_H=0,p_W=0)$

When neither spouse cheats, the expected utilities for both are calculated as ${EU}_H={EU}_W={\displaystyle \frac{1}{4\zeta }}$. Considering the possibility of the husband’s deviation ($p_H=1$), his expected utility would increase to ${EU}_H={\displaystyle \frac{1}{4\zeta }}+\gamma$. Given γ > 0, this increase suggests that not cheating does not constitute a Nash equilibrium, as the husband benefits from deviating by choosing to cheat.

Scenario 2: Both Cheating ($p_H=1,p_W=1)$

In this scenario, both spouses’ utilities are equal to γ, indicating a potentially stable outcome. Checking for a deviation by the husband to $p_H=0$ results in ${EU}_H=0$, which is less than γ.

This lower utility confirms that there is no incentive to deviate, and hence this scenario represents a Nash equilibrium.

Scenario 3: One Cheats, the Other Does Not ($p_H=1,p_W=0$, and vice versa)

If the husband cheats while the wife does not ($p_H=1, p_W=0$), his utility becomes ${EU}_H={\displaystyle \frac{1}{4\zeta }}+\gamma$. Evaluating a deviation where the husband might stop cheating ($p_H=0$) results in a utility of ${EU}_H={\displaystyle \frac{1}{4\zeta }}$, which is less favorable than his utility when cheating. Thus, the husband has no incentive to deviate. Conversely, the wife’s initial utility in this scenario, when she does not cheat while her husband does, is ${EU}_W=0$. Should she consider deviating to cheating ($p_W=1$), her utility increases to ${EU}_W=\gamma$. Since γ > 0, this substantial increase indicates a clear incentive for the wife to deviate. This directional benefit, where the wife’s deviation leads to an increase in utility, underscores that this strategic configuration does not constitute a Nash equilibrium due to the unilateral advantage gained by changing strategies.

4.2. Mixed-Strategy Nash Equilibrium (MSNE)

When no stable Pure-Strategy Nash Equilibrium (PSNE) exists, strategic agents may resort to a Mixed-Strategy Nash Equilibrium (MSNE), which involves random decisions. Regarding marital fidelity, this means that spouses do not follow fixed patterns when it comes to monitoring each other for signs of infidelity but instead use probabilistic approaches. The expected benefits, detection risks, and costs of strategic choices determine the probability of infidelity or monitoring. By determining the probability of each spouse’s infidelity, we may analyze this behavior and derive the MSNE criteria. In this derivation, we consider how strategic incentives and monitoring costs influence equilibrium behavior. By calculating equilibrium probabilities, we learn how partners weigh the potential benefits and drawbacks of their marital relations.

In this section, we explore the Mixed-Strategy Nash Equilibrium (MSNE). Employing a game-theoretical approach, we analyze the conditions under which each spouse, within a theoretical framework, may choose to randomize their decision to cheat, thereby maintaining a strategic balance. Each partner’s predicted utility, according to the General Model Framework’s previously established utility functions, is conditional on the likelihood of infidelity, the benefits of cheating, and the costs of monitoring. By determining the first-order conditions (FOCs) of these utility functions, we may get the equilibrium probabilities, which assume that neither partner cares whether the other cheats or stays faithful.

The derivative of the husband’s expected utility function with respect to $p_H$ is calculated as follows:

$${\displaystyle \frac{{dEU}_H}{d{p}_H}}=\left(1-{\displaystyle \frac{1-{2p}_H}{2\zeta }}\right)\gamma =0$$

(11)

Solving for $p_H$ gives the following:

$$p_H={\displaystyle \frac{1-2\zeta }{2}}={\displaystyle \frac{1}{2}}-\zeta$$

(12)

Similarly, the derivative for the wife’s expected utility with respect to $p_W$ is as follows:

$${\displaystyle \frac{{dEU}_W}{d{p}_W}}=\left(1-{\displaystyle \frac{1-{2p}_W}{2\zeta }}\right)\gamma =0$$

(13)

Solving for $p_W$ results in the following:

$$p_W={\displaystyle \frac{1-2\zeta }{2}}={\displaystyle \frac{1}{2}}-\zeta$$

(14)

The cost of monitoring ($\zeta )$ influences each spouse’s decision to cheat, according to the equilibrium probability. When the costs required for monitoring are higher, adultery is more likely to occur, and conversely, infidelity is more likely to be detected when monitoring costs less, which is a deterrent to infidelity. This delicate equilibrium is a reflection of the dynamic nature of decision-making in marital relationships, where trust and surveillance interact to shape equilibrium behavior.

4.3. Interpretation of Equilibrium Dynamics

In contrast to deterministic models that posit that individuals either consistently cheat or are unwaveringly loyal, the mixed-strategy perspective highlights that spouses act probabilistically, modifying their likelihood of infidelity based on variables such as monitoring costs, risk assessments, and relational dynamics. This approach underscores the strategic complexities associated with trust and betrayal in long-standing partnerships.

A key implication of the Mixed-Strategy Nash Equilibrium (MSNE) is that there is no single optimal decision that applies universally. Each spouse evaluates the immediate short-term benefits associated with possible infidelity against the long-term benefits of fidelity [5,37]. The lack of a clear advantage for either “always cheating” or “always remaining faithful” leads each partner to adopt conditional strategies. Consequently, decisions involve balancing the payoffs [22]. These probability adjustments occur continually, highlighting the ongoing redefinition of marital roles as partners reassess the costs and benefits of infidelity [42].

The MSNE conclusion illustrates that even when both couples aspire to have a loyal marriage, uncertainty may compel them to employ randomized strategies. The probability of infidelity for each spouse is influenced by perceived surveillance, particularly the costs and reliability of discovery [8]. When surveillance is inexpensive and transparent, the danger of detection increases, and partners favor fidelity. If monitoring is challenging or costly (indicated by higher ζ), the probability of cheating increases, as individuals predict a lower risk of detection. This flexibility reflects the evolution of trust and suspicion within a relationship [43]. According to bounded rationality [44], certain spouses may depend on heuristics or “blind trust,” whilst others adjust their expectations more methodically.

From an economic perspective, game theory conceptualizes relationship stability as analogous to a contract enforcement issue [45]. Transparent communication, consistent involvement, and strong social norms are deterrents to opportunistic conduct. When these implicit enforcement mechanisms work effectively, cheating becomes riskier, thus discouraging infidelity. The MSNE framework further corresponds with Prospect Theory [46], indicating that spouses often exhibit heightened sensitivity to possible losses—such as reputational damage or relationship dissolution—compared to the transient gratifications of infidelity. Risk-averse partners may remain loyal if they believe that monitoring is effective.

Trust in this context is relative, adapting to ongoing signals, perceived commitment, and the ease of detecting infidelity [42]. Inconsistent behavior or persistent ambiguity about a partner’s intentions can erode trust, creating a cycle where both spouses believe there is an increased likelihood of infidelity. As mistrust grows, each partner has a reasonable duty to adopt more defensive or self-protective measures [47]. This self-reinforcing cycle—where suspicion generates further distrust—can exacerbate mental suffering [48]. Isolated lifestyles, limited knowledge of each other’s whereabouts, or hidden financial matters can significantly increase surveillance costs, undermining confidence. In contrast, open communication and transparent daily routines reduce ambiguity, and with it, the strategic benefit of infidelity. Persistent distrust between partners may lead to marital tension, despair, and anxiety [49]. In contrast, couples who maintain transparency and share information easily reduce detection costs, therefore sustaining trust and lowering the incentives for infidelity [50].

An essential element is the perception each spouse has regarding the probability or costs of discovery. When individuals perceive that their spouse exerts less surveillance, they judge that their possible losses (such as divorce or reputational harm) decrease, hence increasing the likelihood of infidelity [51,52]. Partners demonstrate strategic adaptability by modifying their behaviors in response to observed signals, such as changes in schedule, unexpected secrecy, or abrupt shifts in emotional engagement [53]. This ongoing process of updating or learning can trigger dynamic responsiveness; an initial transgression, once discovered, may lead to heightened vigilance. Thus, the relationship fluctuates between phases of increased trust and heightened suspicion, depending on the efficacy of each spouse’s demonstrations of loyalty [54].

Economic limitations significantly influence decisions related to extramarital engagements. In marriages with substantial shared assets or financial interdependence, infidelity may incur severe legal or financial consequences [55]. Individuals in such relationships often face higher penalties if discovered, causing them to evaluate the cost–benefit ratio differently than they would in less interdependent circumstances. They might tend less to infidelity out of fear of losing financial security or child custody. In parallel, enforcement becomes more feasible if joint resources are transparent. On the other hand, when partners maintain financial and daily independence, the cost of monitoring increases, making surveillance less likely. As a result, the perceived risk of detection diminishes, thereby increasing the likelihood of infidelity [56].

When monitoring is too challenging or relationship constraints are weak, couples can slip into a cycle of “strategic withdrawal,” with each partner retreating from trust and expecting the other to act opportunistically [42]. Although the analysis presented above focuses largely on economic aspects, the literature indicates that clear communication and mutual goal setting can heighten the perceived cost of cheating, partly by lowering monitoring costs or highlighting the consequences [57,58]. In a sense, these relationship therapies or approaches function like external enforcement mechanisms that steer couples away from equilibrium states characterized by excessive mistrust.

A Nash equilibrium—whether mixed or pure—is stable if neither spouse can unilaterally improve outcomes by deviating, assuming the other partner’s strategy remains unchanged [59]. Yet that stability is susceptible to external changes, such as fluctuations in emotional well-being, economic factors [60], or cultural norms [61]. A spouse who experiences heightened stress or marital dissatisfaction might deviate if they see a potential advantage to cheating, thus reshaping the couple’s strategic profile. Similarly, a systematic improvement in communication or lowered surveillance costs can shift the equilibrium back toward fidelity.

4.4. Sensitivity Analysis

To better understand the strategic dynamics of our model, we conduct a comprehensive sensitivity analysis examining how the equilibrium outcomes respond to changes in the key parameters: the monitoring cost coefficient (ζ) and the benefit from undetected infidelity (γ).

4.4.1. Sensitivity of the Equilibrium Probability to Monitoring Costs

The Mixed-Strategy Nash Equilibrium yields an equilibrium probability of infidelity of $p={\displaystyle \frac{1}{2}}-\zeta$ for both spouses, taking the derivative with respect to the monitoring cost coefficient:

$${\displaystyle \frac{\partial p}{\partial \zeta }}=-1$$

This simple result reveals a one-to-one trade-off between monitoring costs and the probability of infidelity. For every unit increase in the monitoring cost coefficient, the equilibrium probability of infidelity decreases by exactly one unit. This direct relationship reflects a fundamental property of the strategic equilibrium: higher monitoring costs lead to a proportional reduction in the likelihood of extramarital affairs, demonstrating how cost considerations directly shape marital fidelity decisions.

4.4.2. Sensitivity of the Expected Utility to Infidelity Benefits

To understand how changes in the benefit from successful infidelity affect expected utility, we examine the partial derivative of expected utility with respect to γ. At the symmetric equilibrium, this sensitivity is given by the following:

$${\displaystyle \frac{\partial {EU}_i}{\partial \gamma }}=p_i\left(1-m_i\right)$$

where m represents the equilibrium monitoring effort; substituting the equilibrium values, we find that this sensitivity depends on both the probability of infidelity and the likelihood of avoiding detection. To explore how this relationship changes with monitoring costs, we compute the cross-partial derivative:

$${\displaystyle \frac{{\partial }^2{EU}_i}{\partial \gamma \partial \zeta }}=-{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{8{\zeta }^2}}$$

Given that our model requires ζ < 1/2 for valid probabilities, this cross-partial derivative is positive throughout the feasible parameter space. This reveals an essential strategic interaction: when monitoring costs are higher, each unit of infidelity benefit (γ) has a larger impact on expected utility. To understand this result, consider what happens at different monitoring cost levels. When monitoring is cheap (low ζ), spouses monitor intensively, making successful infidelity rare. Additional benefits from infidelity matter little because cheating is usually detected. However, when monitoring is expensive (high ζ), spouses monitor less intensively. In this environment, the same infidelity benefit becomes more valuable because successful cheating is more likely. Thus, while higher monitoring costs reduce how often people cheat, they increase how much the infidelity payoff matters to those who do consider cheating, creating a subtle but essential distinction between the frequency and value of infidelity.

4.4.3. Sensitivity of the Expected Utility to Monitoring Costs

The impact of monitoring costs on expected utility operates through multiple channels. After substituting the equilibrium values and differentiating, we obtain the following:

$${\displaystyle \frac{\partial EU}{\partial \zeta }}={\displaystyle \frac{\left[\left(\frac{1}{2}+\zeta \right)\left(\zeta -\frac{1}{2}\right)\right]}{4{\zeta }^2}}+{\displaystyle \frac{\gamma \left(\frac{1}{2}-\zeta \right)\left(2\zeta +1\right)}{4{\zeta }^2}}$$

This expression reveals two competing effects. The first term, which is negative for all valid parameter values (since ζ < 1/2), captures the direct cost burden of monitoring. Higher monitoring costs reduce utility by making surveillance more expensive for any given level of monitoring effort. The second term, which is positive when γ > 0, represents an indirect strategic benefit: as monitoring becomes more costly, equilibrium monitoring efforts decrease, making infidelity more likely to succeed when attempted. The net effect on utility depends critically on the magnitude of the infidelity benefit γ. When the benefits from successful infidelity are substantial, the strategic effect may partially offset the direct cost burden, leading to a more nuanced relationship between monitoring costs and marital welfare.

4.4.4. Implications for Model Dynamics

Our sensitivity analysis uncovers several crucial insights into the strategic nature of marital infidelity. First, the model’s parameters are deeply interconnected. Changes in monitoring costs not only impact the direct burden of surveillance but also on the strategic calculations that underline decisions about infidelity. This interconnectedness implies that policies or interventions targeting one aspect of marital behavior may have unintended consequences through these strategic channels. Second, the analysis brings to light a fundamental tension in the model. While higher monitoring costs discourage infidelity (reducing p), they simultaneously make successful infidelity more attractive by lowering equilibrium monitoring levels. This delicate balance hinges on the relative magnitudes of the cost coefficient and the benefit of infidelity, adding a layer of complexity to the model. Third, our findings underscore the intricate relationship between monitoring technology and marital fidelity. The model’s complexity is not immediately apparent, but it becomes clear that improvements in monitoring technology (reducing ζ) do not simply increase surveillance and reduce infidelity. They fundamentally reshape the strategic calculus of marriage, potentially leading to qualitatively different equilibrium outcomes. These sensitivity results offer profound insights into the mechanisms driving our model’s predictions and underscore the importance of considering strategic interactions when analyzing marital behavior. The interplay of monitoring costs, monitoring efforts, and infidelity probabilities creates a rich framework for understanding the complex dynamics of trust and betrayal in intimate relationships. The analytical relationships derived above fully characterize the model’s behavior across the parameter space.

To visualize the combined effects of monitoring costs and infidelity benefits on equilibrium welfare, Figure 2 presents the normalized expected utility surface. The normalization relative to the mutual fidelity baseline (EU₀ = 1/(4ζ)) allows for meaningful comparison across different parameter values. The surface reveals that the mixed-strategy equilibrium consistently yields lower utility than mutual fidelity (normalized values < 1) across all examined parameter combinations. The welfare loss varies systematically with the parameters: higher infidelity benefits combined with lower monitoring costs produce the greatest reduction in marital welfare, as these conditions foster an environment of active surveillance and strategic mistrust. In contrast, when monitoring becomes more costly, the equilibrium probability of infidelity decreases, leading to outcomes closer to mutual fidelity with correspondingly smaller welfare losses.

5. Conclusions

This study utilizes game-theoretic models to look at marital infidelity, specifically, how partners deal with the complexities of possible or actual adultery. Finding a Pure-Strategy Nash equilibrium (NE) where both couples choose infidelity and have no reason to deviate when they anticipate the other would cheat is one important consequence. This situation is in line with research showing that spouses who see more personal gain in cheating may engage in behaviors which undermine trust and communication, potentially leading to a cycle of mistrust [10,33,62,63].

The study also highlights a Mixed-Strategy Nash Equilibrium (MSNE), indicating that neither partner relies on a strictly uniform approach [22]. Instead, spouses seesaw between fidelity and infidelity according to probabilistic assessments of their partner’s likely actions, reflecting the inherent variability found in real-life relationships [43]. In such a setting, each decision is continuously shaped by evolving circumstances and by constant evaluation of the other spouse’s strategies [42]. Empirical work suggests the fluid nature of romantic needs and expectations, showing how couples must adapt to shifting dynamics if they are to maintain relational stability [61,64].

Each partner obtains a better grasp of strategic balance when they consider the pros and cons of cheating in light of the likelihood that the other may engage in similar behavior. Neither trust nor predictability is fixed; both continue to evolve as individuals perceive new advantages or encounter shifts in their circumstances [43,61]. Unlike a pure-strategy setting, which identifies a single optimum for both spouses to follow, the MSNE framework reveals that no single method is categorically superior, given the constant interplay of mutual decisions [22,65]. This reciprocal process underscores how the capacity for negotiating shifting incentives may be especially critical in relationships prone to infidelity.

Modelling infidelity and analyzing decisions within a strategic framework make it possible to see how each partner weighs potential gains from unfaithful behavior against the risks of detection and subsequent conflict. In reality, variables like power imbalances, economic limitations, and insufficient knowledge can significantly change conventional assumptions, even if these decisions are usually regarded as symmetrical.

The research also explores how open communication, and resilience can be critical to managing the uncertainties inherent in MSNE-driven interactions. Studies on marital processes show the crucial role of transparent dialogue in mitigating conflict and maintaining stability [53]. While implications for marital therapy and counselling lie beyond the study’s central economic framework, they illustrate how an understanding of strategic behavior might benefit practice areas that address the emotional toll of infidelity [33].

Counsellors and therapists can benefit from these insights by recognizing that infidelity may not arise solely from impulsive or emotional triggers but also from a cost–benefit logic that can be moderated through better communication, greater transparency, or conflict-resolution measures [57,66,67].

Furthermore, the strategic considerations outlined in this analysis may have consequences for legal and policy responses by identifying the multifaceted drivers of infidelity, which include both emotional dissatisfaction and the calculation of benefits derived from deception [68,69]. Practitioners and legislators addressing relationships issues could consider these factors for devising more targeted interventions or settlements in adultery cases.

Financial limitations also play an important part in whether spouses opt to cheat or stay loyal. Shared assets and childrearing costs raise the stakes of marital breakdown, meaning a partner in a financially dependent position might be far less inclined to risk the repercussions of infidelity [55]. The potential for difficult legal or monetary repercussions increases the value of maintaining trust.

Future research could benefit from studies that examine cultural contexts with differing norms and values [61,64] and incorporate direct empirical examination of actual cases of infidelity [10]. More explicit incorporation of asymmetric information would illuminate how individuals make decisions with only partial knowledge of each other’s intentions. A systematic exploration of financial interdependence is merited, since higher stakes often link the cost–benefit calculation of infidelity to legal and monetary consequences. Future models should potentially incorporate gender differences in risk assessment, which are influenced by social and psychological variables. Lastly, extensions of game theory models that describe the impact of coercive influence on strategic decision making may be necessary in analyzing relationships of unequal social, financial, or emotional power, which differ greatly from traditional equilibrium structures.

Additionally, the sensitivity analysis conducted in this study deepens our understanding of how equilibrium outcomes in marital infidelity dynamics respond to variations in key model parameters. By analytically examining the impacts of monitoring costs and infidelity benefits, we demonstrate that small changes in these variables can produce disproportionate shifts in both the probability of infidelity and the expected utility of the spouses. The derived cross-partial derivatives highlight critical strategic trade-offs and expose previously hidden interactions between surveillance efforts and the perceived value of cheating. These findings underscore the importance of considering parameter sensitivity when designing policy interventions or counseling strategies aimed at mitigating the risk of infidelity. This analytical extension further aligns our study with the quantitative and mathematical rigor expected in decision-theoretic and game-theoretic research.

On balance, this unified approach shows that marital infidelity involves not only emotional aspects but also strategic considerations, as part of a dynamic network of incentives, costs, and belief adjustments.