Optimum family size in progeny testing and the theory of games

In this paper, the optimum family size in a progeny test with limited testi ng facilities was determined for a scheme where several commercial companie s were competing. Companies which determined family size in order to maximi ze the expected proportion of sires that will be selected from its stock we re considered as competitive. On the other hand, companies that determined family size in order to maximize the expected genetic progress were conside red as altruist. Using the theory of games, it was shown that competitive c ompanies obtain better commercial results than altruist companies. When com peting against competitive companies, altruist companies obtained worse com mercial results than they expected. When all companies were competitive, th e commercial results equalled those when all were altruist, but the total g enetic progress decreased. A numerical procedure is described to calculate the family size to optimize the commercial results. The result of this algo rithm showed that this commercial equilibrium depends only on the heritabil ity and the ratio between the total testing facilities of the population an d the number of sires required for the market. This commercial equilibrium did not depend on the number of companies or the size of each company. (C) 2000 Elsevier Science B.V. All rights reserved.