Nash equilibrium seeking (NES) scheme consists of a number of decentralized extremum-seeking (ES) "agents", each controlling an input such that an associated (selfish) cost is regulated to its steady-state Nash equilibrium. A non-local stability result for the NES scheme is provided which allows two agents to use the same dither signal if the effect of each agent on the other's steady-state cost function is sufficiently weak. Its application to plants with quadratic cost functions is presented as an example. It is then demonstrated in simulation that, by reducing the number of distinct dither signals, the proposed scheme still has acceptable convergence properties, while design effort is reduced.