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1 2018

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

Ramsey D. M.

Mathematica Applicanda

2018

Vol. 46, no. 2

171--195

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 nondecreasing in the proportion of players still searching. Nash equilibria are derived which satisfy a refinement based on the following optimality criterion: each searcher accepts a prospective partner if and only if the reward that would be gained from such a partnership (given that it formed) is greater or equal to the expected reward obtained by that searcher from future search. So called "completely symmetric" versions of this game are considered, where the two types of player are equally frequent. In this class of games, there exists a unique Nash equilibrium satisfying the optimality criterion, regardless of the precise rule determining the rate at chich prospective partners are found. This equilibrium is given by a threshold time t0, such that before time t0 individuals only mate with prospective partners of the same type and from time t0 onwards each searcher accepts any prospective partner. Two examples are given. One example considers the so called "singles bar" model, according to which prospective partners are found at a constant rate. The secondo example considers the "mixing population" model, according to which the rate at which prospective partners are found is proportional to the fraction of individuals who are still searching for a partner.

Rozważane będą modele matematyczne, w których zmiana parametru jest przedmiotem badań statystycznych. Specjalizowanym narzędziem do tego celu są karty kontrolne. Celem pracy jest konstrukcja kart kontrolnych do badania zmian parametru rozkładu obserwowanej cechy w oparciu o dokładne rozkłady różnych estymatorów parametrów kontrolowanych wielkości i ich porównanie.