Reduction by dominance

Abstract

In [6], it is shown that every discrete Silverman game with ν ≥ 1 reduces by dominance to a finite game, and in [7], it is shown that if S_i ∩ [a,b] = Φ, where a and b are elements of S_3-i, then b is dominated by a. In this section we shall discuss four types of dominance for Silverman games, including the above two. Through repeated reduction of the strategy sets S₁ and S₂ by means of these four types of dominance we obtain what we call pre-essential sets W̃₁ ⊂ S₁ and W̃₂ ⊂ S₂. These are minimal subsets in the sense that no further reduction is possible through the use of these four types of dominance.