Job Allocation and Profits in Service Production

Abstract

We consider a decision situation in which a buyer's non-recurring allocation of two heterogeneous and independent service jobs to three different types of suppliers – two specialists and one generalist – depends on different profits (payments) of the parties (players) involved. The decision situation is modelled as a non-cooperative game with simultaneous one-shot moves. The optimal decisions assigning and accepting the jobs are derived by determining Nash-equilibria in pure and mixed strategies.In our approach, for the first time, the payments of the players are explicitly specified by quantities of production, costs, and sales. In addition, the necessary conditions for the existence of Nash-equilibria in mixed strategies for this case of service production are analysed. Strategic effects may become evident, since the probability of choosing an action by a player depends on the expected values of the outcome for the opponents’ strategies. In contrast to existing literature, we show under common assumptions made about the payment quantities that Nash-equilibria allocate jobs to the specialists or to the generalist but never in a mixed way to a specialist and a generalist.