Would Homo Economicus Cheat on Their Partners? Rudimentary Game Theory in a Relationship

Remiel, Maverick

Understanding the dynamics of commitment and cheating in relationships can be done by combining certain psychological insights and economic analytical frameworks like game theory. Rudimentary game theory offers a lens through which we can explore the choices individuals make when faced with the dilemma of fidelity versus infidelity. By constructing simple payoff matrices based on differing preference profiles, we can glean insights into the rational decision-making processes underlying relationship dynamics. Despite its simplifications, game theory can provide a valuable framework for understanding the delicate balance between commitment and temptation in romantic relationships.

            To illustrate this choice between committing and cheating in a relationship, we construct a rudimentary game theory payoff matrix seen in figure 1. Noticeably, we haven’t set the payoffs for either the husband or the wife and thus can’t yet determine whether a nash equilibrium exists. To do so, we need to have at least a vague picture of the parties’ preferences (i.e., their utility curves). Firstly, we need to set the assumption that each agents’ choices are revealed to each other before the payoffs are actualised. This means that anyone who cheats is eventually caught by their partner. Realistically, not everyone derives the exact same utility from cheating on their partner. Some would derive a great amount of positive utility from having the novelty of cheating on their partners. However, some would experience a great deal of guilt upon cheating on their partner that actually outweighs any initial pleasure from cheating and results in an overall negative utility being derived from the action. Thus, the long-run utility derived from cheating on one’s partner varies from person to person on a spectrum ranging from extremely positive to extremely negative. For simplicity’s sake, this article would only look at two contrasting preference profiles: Committed - Preference (derives negative utility from cheating on their partners) and Cheating - Preference (derives positive utility from cheating on their partners). Firstly we will look at the nash equilibria when these both parties in the relationship have the same preference profiles

            On both payoff matrices set above, both parties have the same preference profile. Firstly, we are going to look at the committed-preference couple composed of a husband and wife who both derive a great positive utility from committing to their partner and a negative utility from cheating on their partner. Notably, we also assume that getting cheated on is an undesirable situation and subtracts from their utility payoff regardless of their preference profile. As seen, the nash equilibrium from a committed-preference couple is for both parties to commit. This is considered to be the ideal condition for a healthy relationship. On the other hand, the second payoff matrix occurs when both parties have cheating-preference (i.e., they derive greatly positive overall utility from cheating on their partner). Generally, this relationship is considered to be highly toxic. As we can see, the nash equilibrium ends with both players cheating on each other. Comparing the two payoff matrices and their eventual nash equilibrium, we notice that each players’ choice in the nash equilibrium depends upon their preference profile: players who derive great utility from cheating would always cheat and players who derive great utility from committing would always commit. 

 

It is not fair however to take this conclusion without noting the specific assumptions of this rudimentary game theory model which causes it to falter in the real world. Firstly, this basic model assumes that preference profiles are static and that each agent is completely rational. As we know in the real world, preference profiles for committing and cheating on a relationship can be highly dynamic. One unfortunate example is the stories we sometimes hear of a married man/woman who suffers from mid-life crisis and ends up cheating on their partner despite a history of being very committed to their partner(s). This shows a shift in their temporary preference profiles from committing to cheating. Furthermore, the assumption that each agent is rational assumes that they will maximise their overall well-being over the long-term. However, in real life, we know that cheaters often regret their actions, this can occur either due to their aforementioned dynamic preference profiles shifting from cheating-preference to committed-preference or simply an irrationality in part of the cheater. The cheater may have a static committed-preference all along but acted irrationally in the short-term as they make their decision based on the immediate utility of cheating (i.e., short-term pleasure and novelty) despite that choice being the wrong one in maximising your utility in the long-run. Even with those assumptions in mind, now we will look at an unfortunate case whereby the two agents in a couple have mismatched preference profiles (i.e., one has a committed-preference profile and the other has a cheating-preference profile).

            When the two parties are mismatched, their choice in the nash equilibrium still reflects their preference profiles as seen above. The party which prefers to commit still commits and the party that prefers to cheat still cheats. Unfortunately, the nash equilibrium in this situation is very unfair towards one party (the one who gets cheated on) while being very advantageous to the other (the one who cheats). Naturally, the real-life payoff of a similar situation would not be exactly this. Furthermore their nash equilibrium in the mid to long term may change. For example, someone who got cheated on may be more willing to cheat on their current partner for “revenge”. However, even with all the assumptions involved in this rudimentary game theory model, we can illustrate very simply why it is important to be highly selective when choosing a partner so as to avoid getting emotionally hurt.

 

            In essence, we can use rudimentary game theory to illustrate a simple snapshot as to the decision-making someone may go through when they cheat on their partners. Although we did not delve deep into why someone may have a strong preference towards cheating on their partner, the model effectively depicts why for some people, it is an economically rational decision to cheat on their partner.

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