Game theory of hookups

11 min read

Women and men have, on average, equal desire for sex. However, society makes it rationally necessary for women to hide that desire — and to play a defensive role in the context of casual hookups. Such disconnect between normative behavior and natural preference causes existential friction.  Stress and discontent is the price women pay to protect reputations and feel safe.

Let’s analyze a standardized male-female interaction using game theory:  as a simultaneous, non-cooperative, non-repeated two-player game.

Explanation of the game structure:

In this framework, the woman’s strategy alternatives are a “Defensive” or a “Proactive” posture.  The man’s strategy alternatives are a “Polite” or “Aggressive” approach.  The game objective is “Immediate Sex”.  Payoffs are unit-less utility measures, measured relatively such that a “10” for one player is equally motivating as a “10” for the other player (similar to a physical pain assessment scale).

 
Game #1:  Payoffs from immediate sex

Payoffs from immediate sex
  Man
  Polite Aggressive
Woman Defensive   9   10
5   4  
Proactive   9   10
6   5  

Mutual interests are not always equal interests.  Payoff from immediate sex with a new partner is asymmetric for women and men:

  • Quality of immediate sex is lower for women than for men. Whereas, mediocre sex for men is still pretty darn good for them (i.e., has a high utility), mediocre sex for women may not compare favorably with avoiding the interaction altogether.  Women’s enjoyment of sex generally increases with clearly established safety, time to develop partner familiarity, pacing to include extended seduction, genuine interest in her as an individual (vs as an interchangeable “masturbation sleeve”) and repetition.
  • STD risk is higher for women than for men in the same physical interaction
  • Pregnancy risk for women is not only a physical risk, but a stressful uncertainty that affects a woman for weeks after the hookup night is no longer a second thought to the man

Payoffs are also affected by the strategies deployed:  Men get slightly less utility out of sex obtained via the lower-testosterone Polite approach.  Women get slightly less utility out of sex capitulated to via an inauthentic Defensive approach, and usually less enjoyment when the guy is being Aggressive.

(Disagree? Play these games yourself further below, inputting your own assumptions about payoffs!)

Given those payoffs, a rational woman prefers to be Proactive, no matter what the man’s strategy is.  And, a rational man prefers to be Aggressive, no matter what the woman’s strategy is.

The self-enforcing equilibrium (Nash equilibrium) outcome of this game is Proactive-Aggressive.  Each player is doing the best it can, given the other player’s strategy.  After both play their strategies, both can say, “Given what other person did, I’m happy with my choice.”  (By definition, there can be 0, 1 or >1 Nash equilibria in a game.  Here we have 1.)  This outcome is a stable point, provided everyone understands the game parameters.

Moreover, in this game, each player’s strategy is “dominant”, in that it maximizes personal payoff no matter what the other player chooses to do.  We have a Nash equilibrium in dominant strategies – a very strong, sticky outcome that should occur in every game iteration.

Next, let’s take into account probabilities of sex occurring in each outcome:

Probability of immediate sex
  Man
  Polite Aggressive
Woman Defensive   5%   10%
       
Proactive   25%   50%
       
Probability-weighted payoffs
  Man
  Polite Aggressive
Woman Defensive   .45   1.00
.25   .40  
Proactive   2.25   5.00
1.50   2.50  

We see that the Proactive-Aggressive strategy combination is a very strong equilibrium. The expected (i.e., probability-weighted) value to both women and men in the Proactive-Aggressive outcome is many times greater than any of the alternative outcome states.  Maximizing individual self-interest yields the socially efficient result of maximum collective interest.

Why doesn’t this correspond to observed behavior and outcomes in the real world?

Game #2:  Payoffs from immediate sex + Social penalty

Social penalties of immediate sex
  Man
  Polite Aggressive
Woman Defensive   0   0
-2   -2  
Proactive   0   0
-5   -5  
Net payoffs
  Man
  Polite Aggressive
Woman Defensive   9   10
5   2  
Proactive   9   10
1   0  

Men impose a social cost on women that decreases women’s net payoff from immediate sex.  More often than not, men despise women to some degree for capitulating to the very thing they so desperately want from us. Women adopting an authentically Proactive posture are slut-shamed viciously to our faces and behind our backs to friends and strangers.  And, men’s vocal devaluation of women they’ve hooked up with foments a dangerous attitude of physical entitlement among their friends. Even men using the Polite approach disdain the woman for saying yes, and even if the woman adopts a Defensive posture.

Example:  A gentlemanly guy friend is flirting with me.  He enthusiastically relays the tale of a girl who did something with him that he had asked for and enjoyed.  Now, years later, he still remembers the exciting hookup vividly enough to detail it (preposterously and inappropriately) to me…  but not without ridiculing and dehumanizing the girl he once cared for, saying “she was such a slut.”  My rational incentive is now clearly to never become physical with this guy, lest he later punish and disparage me too.

Even if no sex occurs, the woman can still be slut-shamed aggressively for being hit on by a man.  (This is outside the framework of our example game.)

Example:  Meet a male acquaintance one afternoon at a bar for a friendly chat. He steers the conversation toward sex and ultimately propositions me several times. I do my best to decline and change topics without creating conflict. Preserve reputation by declining, while not hurting reputation by appearing to overreact. When I relay this (frequent, exhausting) scenario to the (self-described feminist) guy I’m seeing, he explodes in anger…. at me!  I am diminished in his eyes for being targeted, being seen as attractive, for purportedly “inviting” and “enduring” the suggestion, despite the fact that I declined.

In our new payoff matrix that incorporates social costs, the woman rationally prefers a Defensive posture.  The man still prefers to be Aggressive.  The unilateral social punishment of women by men reduces payoffs to women, forcing players into a Nash equilibrium of Defensive-Aggressive strategies.  This is the behavior and outcome which we commonly observe in the real world.

Now factor in the probability of sex:

Probability-weighted net payoffs
  Man
  Polite Aggressive
Woman Defensive   .45   1.00
.15   .20  
Proactive   2.25   5.00
.25   0  

We now see that this Defensive-Aggressive Nash equilibrium causes a big expected value loss for men (compared to their expected value from the Proactive-Aggressive outcome, which as we saw above would occur in the absence of social punishment of women).

This Nash equilibrium is Pareto-inefficient.  The rational pursuit of self-interest leads the players to a stable equilibrium outcome that fails to maximize collective interest.  In our hookup game, collective interest would be maximized by a Proactive-Polite strategy combination.  (By definition, there can be 1 or >1 Pareto-optimal solutions in a game.  Here we have 1.)  But Proactive-Polite is not a Nash equilibrium, as the man’s dominant strategy is Aggressive.  Rational players in this simultaneous, non-cooperative, non-repeated game will (unfortunately for all involved) be Defensive-Aggressive.

The most famous formulation of a conflict between individual and collective interest is the “Prisoner’s Dilemma”.  Two isolated, guilty prisoners could maximize value if they could only co-operate.  Because they cannot, they both rationally choose to confess, and thus face longer prison sentences than if they both kept quiet.  Could men and women – who are not denied the possibility of cooperation by physical jail walls — find a Pareto-efficient Nash equilibrium?

How can we change the male-female hookup game so that it ends in a Pareto-efficient Nash equilibrium?  (maximum self-interest = maximum collective interest)

  1. Widespread social change. Eliminate the social penalty on women for sex.
  2. Bilateral co-operation. Use a “commitment device” to force the Nash equilibrium to also be socially optimal.
    • Credible promise to not slut-shame. As we have seen, if we remove the social penalty, a woman’s rational strategy is Proactive, and the players have a Pareto-efficient Nash equilibrium in dominant strategies of Proactive-Aggressive.  However, without a credible threat from women to enforce the man’s promise, men have no incentive to abide by it.  That risk means that the woman cannot actually switch her strategy to Proactive.  So, who can provide the credible threat to enforce such a promise?  Bystander men.  Bystander men are finally being named as a key force in ending rape culture, and they are the linchpin in eliminating the social cost to women of hookups.

Back to my friend who slut-shamed his past hookup:  He had made an upfront implicit promise to her to not penalize her for sex. (e.g., being attentive and flattering, referencing the idea of future interaction with her, behaving like a gentleman, being grateful for each incremental physical step that night, giving general social cues that he’s “one of the good guys”, etc.)  But, then he turned around and flippantly violated that promise. 

The only way to stop this deceit by men is to assertively shame and admonish men for slut-shaming women. Anyone (friend, bystander, stranger in a bar) hearing a man saying such things must immediately and vocally express disgust — and educate the man as to why his attitude is deplorable.  Men themselves must take the initiative to make it prohibitively costly for other men to penalize women for sex.

  • Credible choice of Polite strategy. Generally, as men age, their decreasing obsession with Immediate Sex relative to High-Quality Sex changes their payoffs in our matrix.  Their rational strategy shifts toward Polite, enabling women to shift toward Proactive.  (Suggesting that if men truly switch their focus to high-quality sex over immediate sex, they are paradoxically more likely to get immediate sex.) Simultaneously, women know that older men’s recognition of unfair social costs borne by women means a lower risk of slut-shaming. Thus, women’s payoffs in our matrix change, too.  Moreover, women’s utility from sex with a new, more mature partner are generally higher.  The entire matrix changes dramatically, making a Pareto-efficient Nash equilibrium more likely.

The behavioral economics revolution has taught us that what looks like irrationality may in fact be rationality… if one adequately considers the parameters of the game and true utility for each player.  Thus, in the male-female hookup framework:

  • Frustrated men perceive women as being irrationally defensive and skeptical towards their advances. (Preposterously, some men even attribute women’s defensiveness to a lesser inherent interest in sex.)  But, if men were to consider the social punishment women face, they would realize that a defensive posture is supremely rational.
  • Conversely, exasperated women perceive men as being irrationally and counter-productively aggressive. But, unfortunately, it is arguably rational for men to behave this way…  as long as the patriarchal culture men support imposes an asymmetric cost on women for engaging in the very sexual encounters men seek.

Input payoffs into this matrix to see where the Nash equilibrium is. (Each player’s best strategy is highlighted, given each of the other player’s possible strategies.  Nash equilibrium is the square(s) where payoffs from both players are highlighted.)

[interactive matrix forthcoming]

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2 Responses to Game theory of hookups

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