A Large Population Partnership Formation Game with Associative Preferences and Continuous Time

David Mark Ramsey

Mathematica Applicanda, Tome 46 (2018) no. 2, pp. 173-196.

Résumé

A model of partnership formation is considered in which there are two classes of player (called male and female). There is a continuum of players and two types of both sexes. These two types can be interpreted, e.g. as two subspecies, and each searcher prefers to pair with an individual of the same type. Players begin searching at time zero and search until they find a mutually acceptable prospective partner or the mating season ends. When a pair is formed, both individuals leave the pool of searchers. Hence, the proportion of players still searching and the distribution of types changes over time. Prospective partners are found at a rate which is non- decreasing the proportion of players still searching. Nash equilibria are derived which satisfy the following optimality criterion: each searcher accepts a prospective partner if and only if the reward from such a partnership is greater or equal to the expected reward obtained from future search. So called ”completely symmetric” versions of this game are considered, where the two types of player are equally frequent. A unique Nash equilibrium exists regardless of the precise rule determining the rate at which prospective partners are found. Two examples are given.

Détail

DOI : 10.14708/ma.v46i2.5128

Classification : 91A13, 60G40.
Mots-clés : partnership formation, dynamic game, Nash equilibrium, stopping problem