The Game of Kissing
Kissing someone for the first time is an inherently risky act, as the wishes of the individuals are not typically vocalized…How then, do players wishing to engage in kissing navigate their fear of rejection and their lack of knowledge regarding the other player's wishes?
Most adult people have experienced the horrifying moment when a romantic advance goes unreturned. From either side of the interaction, eyes are averted, explanations are mumbled, and blossoming friendships are nipped in the bud.
Kissing someone for the first time is an inherently risky act, as the wishes of the individuals are not typically vocalized. These wishes tend to remain unspoken to both conserve the “romance” of the moment and to avoid the uncomfortable conversation in which the disparities between the desires of the individuals are revealed. However, this fear of rejection clearly does not hinder the kissing behavior of people everywhere. How then, do players wishing to engage in kissing manage to navigate their fear of rejection and their lack of knowledge regarding the other player’s wishes?
Using rudimentary game theory, I will attempt to build a model that describes the strategies of two players when both wish to kiss but neither is aware of the preferences of the other. After presenting a baseline model, I will examine how several factors can affect the outcome of the scenario. Through this, I strive to present a model that elucidates the mechanisms by which mutual cooperation occurs, and to describes those factors that maximize mutual cooperation.
In order to have a game, we must have both players and choices that the players must confront. In this scenario, the players can be defined as two individuals desiring to mutually cooperate in the act of kissing, but lacking knowledge regarding each other’s preferences. Cooperation in this game is defined as actively kissing the other player. Mutual cooperation requires both an initiating player and a complying player. Defection is defined as neither initiating the kiss, nor complying with the advances of another player. Unilateral defection therefore occurs when one player rejects the advances of the other. To simplify the model, we will assume that desire to cooperate is equal for both parties, or that both players have equal preference for mutual cooperation. However, each player in the game remains without knowledge of the other player’s preferences.
I will begin with a baseline model of two players, each with the preference to kiss. In order to make cooperation a reasonable option, we must assume familiarity of the two players. In general, increasing familiarity causes an increase in cooperation. As players get to know each other more intimately, they will likely feel more comfortable in each other’s presence and that they can better discern each other’s intentions. However, familiarity only increases cooperation to a point. As two players become very close friends or even “old friends,” increasing familiarity begins to decrease likelihood of cooperation. In the case of well-defined platonic friendship roles, players are less likely to break from these roles to pursue another type of relationship.
It is important to acknowledge that familiarity occurs on a spectrum. However, for the purposes of this model, we will define an arbitrary level of familiarity that is ideal for cooperation (an idealization used in future discussion). This ideal degree of familiarity in our model is fundamental in ensuring mutual cooperation. Making advances at a complete stranger is illegal, but attempting romance with an old friend could get the initiating player ridiculed by the entire friend group.
Figure 1: Payoff matrix assuming ideal familiarity
Figure 1 depicts the payoff matrix for two players, assuming an ideal level of familiarity. This is the baseline matrix for my model. It is immediately evident that neither player has a strictly dominant strategy in this game. In other words, the best action for Player 1, displayed on the Y-axis, changes based on the action of Player 2, whose payoffs are displayed on the X-axis. This leads to two distinct equilibria. As you can see, the highest payoff for each player (4) occurs with mutual cooperation. This is one of the equilibria, representing a situation in which neither player can be better off by unilateral movement (Elster 313). However, a second equilibrium can be achieved when mutual defection occurs. Although this equilibrium has a lower payoff (2) for each player than mutual cooperation, the same rules governing equilibria apply, and some games will also converge on this point. Finally, the situations in which one player cooperates (initiates) and the other defects lead to a payoff of 0 for the initiator and 3 for the defector. The larger payoff for the defector results from the perceived status that is gained from an unaccepted advance.
This dual-equilibrium result is less than ideal for an interested player, as it gives little assurance of mutual cooperation. What could shift the equilibrium towards mutual cooperation and reduce the risk of unilateral defection? One option is to account for possible hindrances to mutual cooperation by expanding the assumptions of the model. In other words, I will account for an additional factor that affects the scenario in order to ensure greater cooperation between the two players.
One factor to consider is the status of the two players. Disparities in status may be real or perceived and can impact likelihood of cooperation. In general, equal status is likely to increase payoff for the players, as neither player will feel uncomfortable as a result of disparity. Typical examples of status include age and socioeconomic class. In other cases, popularity or perceived differences in attractiveness could cause the same effect.
Figure 2: Payoff matrix assuming ideal familiarity and status equality
Figure 2 illustrates that increase in payoff from mutual cooperation (5,5) is achieved by assuming equal status along with familiarity. Despite this increase, equal status did not alter the payoff of mutual defection (2,2), and two equilibria remain. As before, players lacking knowledge of the other’s preferences will converge on the two distinct equilibria. Players desiring mutual cooperation are again unsatisfied by the results of this model. Perhaps further expanding the assumptions of the model by adding a new factor will provide more leverage over the situation.
The previous matrices dealt with characteristics of the relationship between the players. However, we can also attempt to increase cooperation by altering the environment in which the encounter occurs. One way this is done is by introducing a “romance” factor. This general factor includes any scenario that elicits romantic feelings or increases benefit derived from cooperation. Examples include a starry sky, a first snow, or a hanging piece of mistletoe during Christmas time.
Factors such as privacy and time of day also fall into this romance category. In regards to the former, people are more likely to kiss in a private place. This is mostly attributed to the fact that kissing is not considered an appropriate act in many public locations, but also because the humiliation that could accompany a rejected advance is better suffered away from the public eye. The latter occurs because of the romantic ideals associated with the nighttime hours, as well as the privacy granted by the cover of dark.
Figure 3: Payoff matrix assuming ideal familiarity, status equality, and romance factor.
Figure 3 shows that the payoff of mutual cooperation (6,6) is again increased by the presence of a romance factor. As before, the other payoffs remain the same. This demonstrates that even introduction of the romance factor cannot eliminate the second equilibrium that results from mutual defection. As before, the payoff matrix does not exhibit a dominant strategy for either player. This suggests that two players that have the same preferences and no knowledge regarding the preferences of others will converge on one of two equilibria, regardless of the factor introduced.
The model illustrated in Figure 3 is an example of the Stag Hunt game, where safety and social cooperation are in conflict (Elster 360). In this scenario, safety is avoiding the humiliation of an unreciprocated advance, and cooperation is the benefit derived from a shared kiss. This type of game is characterized by the existence of two Nash equilibria, which is the understanding that players will choose strategies that are best responses to each other. In other words, at an equilibrium point, no player has anything to gain by changing only his or her own strategy (Easley & Kingsburg 149).
However, individuals very often converge on the equilibria of mutual cooperation. How, despite lacking information and two distinct equilibria, is this so common? The model very clearly illustrates that the payoff from mutual cooperation is much higher than that of mutual defection. As conditions improve (through factors such as familiarity, status equality, and romance), the differential between the payoffs of the two equilibria becomes increasingly large. Eventually the sheer magnitude of payoff from mutual cooperation becomes an informal focal point. When this occurs, even if a player has no knowledge of the other’s preferences, the substantial payoff from potential cooperation is worth the risk of the other player’s unilateral defection. Although this model failed to define a strictly dominant strategy, it illustrates that by ensuring ideal familiarity and status equality, and by adding a dash of romance, two players are much more likely to converge on mutual cooperation.
Non-vocal actions, or signals, are as important as the informal focal point in shifting convergence towards the equilibrium of mutual cooperation. These signals, which express availability and interest in cooperation, could include intentionally remaining close to the other player, making eye contact, and providing ample opportunity for the other player to act. Such signals serve as encouragement for the initiating player, increasing likelihood of a player acting as the initiator. Increased familiarity with the other player will improve the ability to both detect and interpret these signals.
Similarly, the context of an encounter may set a framework that facilitates cooperation. For example, institutions such as “the date” serve to facilitate mutual cooperation in a variety of ways. For one, social norms dictate that asking and agreeing to a date conveys some romantic interest exists between two players. Therefore, a player wishing to mutually cooperate with another player could ask him or her on a date, establishing the context for this action.
Finally, knowledge gained from exogenous sources, such as mutual friends, could act as a powerful mechanism to alter convergence. In this case, however, an increase in knowledge can push convergence towards either equilibrium. For instance, if a player is told that his or her romantic interest has romantic ties elsewhere, the player is less likely to act on those feelings. This is different from actually knowing the preferences of the player, as informants could unintentionally disperse false information or otherwise have motives to misrepresent preferences of the player of interest.
It’s important to note that although the mechanisms concerning disparate equilibrium payoffs, signals, and external information are in place, they sometimes fail to provide players with the information required to make the best decision. This results in mutual defection despite preferences of both players to cooperate. Failure can be attributed in part to misread signals by either player. For example, a player who naturally exhibits very shy behavior may be read as disinterested regardless of true preference. However, failure can also result from the fact that, even with the mechanisms described above, a dual equilibrium is difficult to overcome, and some players will inevitably converge on the less-profitable equilibria.
In creating a model such as this one, making assumptions is an important part of gaining leverage over the situation. However, assumptions also inevitably weaken a model and make it less applicable to individual situations. Undoubtedly the most serious flaw in my model is the assumption of equal preferences of both players. In reality, preference for mutual cooperation occurs in a spectrum, and these preferences influence payoff. In other words, even if players with different preferences choose to cooperate, the payoff may be higher for one person than for the other depending on how much each player cares for the other. Take the example of disparate status. Depending on how disparate the status, this could decrease payoff for mutual cooperation of one player to the same level (or below) that player’s payoff for unilaterally defecting the advance of the other. In other words, a player may get more “benefit” from rejecting another player than from the mutual cooperation of kissing.
More than anything, this model illustrates why kissing is such a precarious endeavor. Lack of knowledge of preferences, fear of unilateral defection, and the presence of two distinct equilibria all cause failure of players to reach the most favorable equilibrium. However, this model also helped to illustrate the mechanisms by which mutual cooperation is enabled, such as signaling and exogenous information. Although I have not created a comprehensive model to ensure the cooperation of players everywhere, this model does provide insight into ways in which equilibrium can be shifted towards mutual cooperation, if not true love.
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Easley & Kingsley. 2010. Networks, Crowds, and Markets. New York City: Cambridge University Press.
Elster, Jon. 2007. Explaining Social Behavior. New York City: Cambridge University Press.