The influence of mutations: an evolutionary inspection game with three strategic actors

Suboptimal business decisions lead to corporate cost increases. The basis of the following study is a game theoretical model of Fandel and Trockel (Eur J Oper Res 226:85–93, 2013a), which analyses the relationship between bonuses and financial penalties in a three-person inspection game and the measures that counteract suboptimal decisions. In the present article we investigate from evolutionary perspectives whether the strategic behaviour of the actors described in an inspection game can be invaded by mutants and what risks emerge as a result. In a first step each of the three decision variables of the players will be discussed. It will become apparent that corporate optimal behaviour is realised when the actions of the business management or the controlling department are fixed. In a second step it will be shown that in games with three strategic variables mutations can undermine the solutions. In a third step we will investigate the model in consideration of monotonic payment and monotonic positive payment functions and divide the area of the solutions into octants to which we will allocate the influence of the mutations and demonstrate the circumstances under which a solution tending towards optimal corporate behaviour can be generated.