This model attempts to capture the dynamics of coupling (people, as in romantically). Agents, the strategies they employ, and market conditions in general are greatly simplified. However, I argue that the model is still useful in understanding certain dynamics in coupling/relationships.
Like any good model, we start with simplifying assumptions.
-All agents have the parameter, attractiveness. All agents have the same perception of attractiveness (ie there is an objective scale), and all agents have complete information regarding this parameter (knows his attractiveness, knows the attractiveness of all others).
-Agents try to maximize their utility, U(attractiveness of partner) = attractiveness of partner (ie they are rational).
-The attractiveness scale is continuous. The distribution of people on this attractiveness scale is continuous and differentiable (ie at any given attractiveness level, there are plenty of people).
-Markets are efficient. It is equally convenient for any two given sets of people to couple. There are no market frictions such as distance, time spent courting, etc. (at least, none that would skew an agent's preferences for one coupling scenario as opposed to another)
-Markets must clear. In other words, people will form couples. An agent will not employ a strategy if it results in him being alone. It will never be the case, in equilibrium, that everyone is alone. This follows from the assumption that agents are rational
To simplify the solving of this problem further, let us consider the case where all agents employ the same strategy.
Case: couple with only those of greater attractiveness
-Agents are acting rationally, trying to maximize their utility
- The problem with this is that markets will not clear. No-one will be able to couple with someone else; for any two people, one person is of equal or lesser attractiveness.
Case: agents only couple with those of greater or equal attractiveness
-Agents are still maximizing utility
-No agent will be able to couple with another of greater attractiveness, as the more attractive agent is employing the same strategy. Therefore, only agents of equal attractiveness will couple
Other cases: not maximizing utility
Implications: There is no such thing as a male-female friendship without any desire to form a couple. One agent in this relationship must be of equal or lesser attractiveness, and this agent will desire to form a couple with the other agent.
Further research: Consider relaxing assumptions, particularly those of market efficiency.