The Cardinality of the Sets Involved in Lattice Games - Search Theory: A Game Theoretic Perspective - page 109

on the lattice L and on the ring. In this game an

optimal strategy for both players is the uniform distribution over the set of their
pure strategies

= { 1 , 2 ,..., 14 }×{ 1 , 2 ,..., 8 }

Fig. 7.2 Strategy on the lattice and on the ring

1 1 1

F

m .
To obtain the value of the game we have to compute

α ( A )=

| = | = | X | Y

n

,

1
F

n , m A ∈ X M ( A , B )

M ( A , α )= M ( α , B )=

let X h the subset of X defined by
X h = {

A ∈ X : A ( i )= B ( i ) for i = 1 , 2 ,..., h , A ( h + 1 ) = B ( h + 1 ) }