A model of partnership formation with friction and multiple criteria

We present a game theoretical sequential search problem modelling partnership formation based on two discrete character traits. There are two classes of individual. Each individual observes a sequence of potential partners from the other class. The traits are referred to as attractiveness and character, respectively. All individuals prefer partners of high attractiveness and similar character. Attractiveness can be measured instantly. However, in order to observe the character of an individual, a costly interview (or date) is required. On observing the attractiveness of a prospective partner, an individual must decide whether he/she wishes to proceed to the interview stage. During the interview phase, the prospective pair observe each other's character and then decide whether they wish to form a pair. Mutual acceptance is required for both an interview to occur and a pair to form. An individual stops searching on finding a partner. A set of criteria based on the concept of a trembling hand perfect equilibrium is used to define an equilibrium of this game. It is argued that under such a general formulation there may be multiple equilibria. For this reason, we define a specific formulation of the game, the so called symmetric version, which has a unique symmetric equilibrium. The form of this equilibrium has some similarities to the block separating equilibrium derived for classical models of two-sided mate choice and job search problems, but is essentially different.