This paper has investigated the extent to which differences as between players can resolve the indeterminate nature of many rent-seeking games. These differences might be limited to a generally accepted ordering amongst players so that in considering n person games all potential players will know which are the leading n players who should therefore participate. Within the Tullock model analysed here this still leaves as indeterminate those games with multiple equilibria. The number of equilibria is reduced when the differences between players, and the resulting ordering, are associated with differences in the effectiveness of rent-seeking activity. However, whilst we have shown that fairly modest differences can be guaranteed to lead to either a unique or dual equilibria, there is in general no way of ensuring a unique equilibria. Thus dual equilibria can exist even with substantial cost differences, and with smaller differences there may be more extensive multiple equilibria. Along with situations in which a single player might choose a 'pre-emptive' level of expenditure (which generally implies non Cournot-Nash equilibria, and which case has not been considered here), a satisfactory equilibrium solution to one of these multiple equilibria games would seem to require it to be reformulated as a multistagegame.