Optimum family size in progeny testing and the theory of games

In this paper, the optimum family size in a progeny test with limited testing facilities was determined for a scheme where several commercial companies were competing. Companies which determined family size in order to maximize the expected proportion of sires that will be selected from its stock were considered as competitive. On the other hand, companies that determined family size in order to maximize the expected genetic progress were considered as altruist. Using the theory of games, it was shown that competitive companies obtain better commercial results than altruist companies. When competing against competitive companies, altruist companies obtained worse commercial results than they expected. When all companies were competitive, the commercial results equalled those when all were altruist, but the total genetic progress decreased. A numerical procedure is described to calculate the family size to optimize the commercial results. The result of this algorithm showed that this commercial equilibrium depends only on the heritability and the ratio between the total testing facilities of the population and 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.  2000 Elsevier Science B.V. All rights reserved.