The article presents a management game with teams of players managing the activity of a non-life insurance company. Companies compete on the same market, therefore a strategy implemented by a single insurer influences the overall market situation, i.e. all other insurers. Companies operate in a given macroeconomic environment, modeling of which is also within the scope of the article. Theoretical game model underlies implementation of insurance management game. The described issues are treated as core, based on which the game can be developed by incorporating elements like adverse selection, catastrophic events, distribution channels, hedging instruments.