<p>This paper considers the design of robust control strategies for a discrete-time descriptor system influenced by multiple players with their own disturbance attenuation levels. Assuming players use linear feedback strategies, the Nash equilibrium strategies are derived for a non-cooperative setting. In a simulation study on water extraction from a common resource, it is demonstrated what the potential effects are if players use different attenuation levels. Also, the impact of the number of players and divergent preferences on results are investigated. To derive the equilibrium strategies, first, the solution of the zero-sum discrete-time dynamic game where one player is playing against nature is presented. Using this result, we present sufficient conditions for the existence of a soft-constrained linear feedback Nash equilibrium (SLFNE) for the multi-player soft-constrained linear quadratic regular dynamic game. From this result, we obtain then directly robust disturbance attenuation controllers for the system, where every player satisfies his own attenuation level.</p>