A Sequential-Arrivals Model of Territory Acquisition

Birds arrive sequentially at their breeding ground where the nest sites vary in value (measured by reproductive success). Each bird must either choose a vacant site or challenge an occupier for its site. In the latter case we assume the occupier to be the more likely winner. The loser of the contest incurs a cost and must go to a vacant site. The rational strategy for such a contest is found. There is a threshold phenomenon; early arrivals occupy vacant sites, late arrivals fight. This result is intuitively reasonable, but the sequence of sites chosen is complex. A recursive method for specifying the solution is described and applied explicitly to some illustrative cases.