An

n-tuple of operators acting on H is a finite sequence of length n of commuting continuous linear operators [T.

Any

n-tuple of strategies, one for each player, may be regarded as a point in the product space obtained by multiplying the n strategy spaces of the players.

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.

bar] E (G) the

n-tuple [sigma] (A) is the product of the

n-tuples on the edges of A.

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].

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.

Next, enumerate the elements of S and then, in the usual way, identify each subset of S with an

n-tuple of 0's and l's.

A voting pattern is an assignment of a strategy to each participant, in the form of an

n-tuple.

n] = (G, [sigma]), for any [subset or equal to] E (G) the

n-tuple [sigma](A) is the product of the

n-tuples on the edges of A.

Notice that the

n-tuple that represents the synthesized attributes has two distinct parts: tuples [l.