Denote a sequence of situations [mathematical expression not reproducible] by an
n-tuple of strategies [mathematical expression not reproducible], where [mathematical expression not reproducible].
by abusing notation, whenever J is a distinct-integer
N-tuple ([j.sub.1], ..., [j.sub.N]) of (11.4).
An
n-tuple of operators acting on H is a finite sequence of length n of commuting continuous linear operators [T.sub.1], [T.sub.2], ..., [T.sub.n] on H, and is written as T = ([T.sub.1], [T.sub.2], ..., [T.sub.n]).
Many will be mystified by the following quote from Nash: "An equilibrium point is an
n-tuple such that each player's mixed strategy maximizes his payoff if the strategies of the others are held fixed.
A burst of length b(fixed) is an
n-tuple whose only non-zero components are confined to b consecutive positions, the first of which is non-zero and the number of its starting positions in an
n-tuple is the first n - b + 1 positions.
More generally for n [greater than or equal to] 2 one has the notion of
n-tuple complex.
An
n-tuple ([a.sub.1], [a.sub.2], ..., [a.sub.n]) is symmetric, if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the set of all symmetric
n-tuples.
If [lambda] is a weight and we use the symbol [lambda] in a context where it has to be interpreted as an
n-tuple [lambda] = ([[lambda].sub.1], ..., [[lambda].sub.n]), we use the convention that a representative has been chosen implicitly.
where m = ([m.sub.1], ..., [m.sub.n] is an
n-tuple of integers (positive, negative or zero), x > y, h = 3 or 4, n [greater than or equal to] h, and the different linear factors are not proportional.
A time point t in H is an
n-tuple ([v.sub.1], ..., [v.sub.n]) such that for all 1 [less than or equal to] i [less than or equal to] n, [v.sub.i] is a time-value in the time-value set of [T.sub.i].