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job search problem is conceived of as a dynamic program which has to be solved
in finite time, so labour markets are best described by optimal control problems.
The literature here is vast and well studied.
Job search has also been modelled as a mating or network game, with
representative contributions being Albelda [ 1 ], Beller [ 6 ], Peterson et al. [ 30 ], Coles
and Francesconi [ 11 ], Fisman et al. [ 17 ], Pissarides [ 31 ]. In the biological literature,
mate choice is modelled as sequential observation of prospective mates. The model
presented here is a development of this strand. For models of mutual mate choice
based on common preferences see Johnstone [ 23 ], Alpern and Reyniers [ 4 ], and
Janetos [ 22 ].
For a model of mate choice based on homotypic preferences see Alpern and
Reyniers [ 3 ]. Their models assume that the distribution of the value of available
mates changes over time as partnerships form and individuals leave the mating pool.
Ramsey [ 32 ] considers a similar problem interpreted as a job search problem.
The general approach is presented in Sect. 17.2 . Section 17.3 compares the
approach used here and classical models of two-sided job search and mate choice
problems. It is intended that this section will give an intuitive feel for the approach
to solving such problems and the added complexity involved when common and
homotypic preferences are combined. Section 17.4 describes a model of partnership
formation in which character forms a 'circle' and neither the distributions of the
traits nor the search costs depend on the class of a searcher. This model is called
symmetric. Section 17.5 gives the set of criteria that we wish an equilibrium to
satisfy. These conditions are based on the concept of a trembling hand perfect equi-
librium (a refinement of the concept of Nash equilibrium). Section 17.6 describes
a general method for calculating the expected utilities of each individual under a
given strategy profile. Section 17.7 considers the dating subgame (when individuals
decide whether to form a partnership) and the soliciting subgame (when individuals
decide whether to go on to the dating subgame). Section 17.8 presents results on
the existence and uniqueness of a symmetric equilibrium in the symmetric game.
An algorithm for determining this equilibrium is presented, together with an exam-
ple. Section 17.9 illustrates the problems involved in adopting such an approach to
the more general formulation. Section 17.10 gives a brief conclusion and suggests
directions for further research.
17.2 General Formulation
We present a model of a sequential decision process leading to the formation of a
long term partnership. It is assumed that there are two classes of player and indi-
viduals in a partnership have to be of different classes (e.g. in job search problems
employees form partnerships with employers, in mate choice problems males form
partnerships with females). Individuals view a sequence of prospective partners.
It is assumed that costs are incurred during the search process, so in general an
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