Irreducibility and Solutions of the Odd-Order Reduced Games

Abstract

In Chapter 6, pages 99–117, we showed how certain classes of semi-reduced discrete games reduce further to odd-order games falling into four types, which we asserted to be not further reducible. In this chapter we shall make use of some Fibonacci-like sequences of polynomials to prove nonsingularity of certain matrices closely related to the payoff matrices, and the asserted irreducibility for all odd-order cases follows. We then obtain the unique optimal mixed strategies and the game values. The material in this chapter is adapted from [12]. In the next chapter we shall do the same for the even-order cases.