I\'m having trouble understanding this block of definitions: Definition: Let A =

Question

I'm having trouble understanding this block of definitions: Definition: Let A = {(a1, ..., a_p)|a_1 elementof A_1 logicaland ... logicaland a_p elementof A_p} be a set of joint strategies over p players. Definition: For any p elementof P, a'_p elementof A_p, and a elementof A, let a||a'_p, denote the member of A obtained by replacing a_p with a'_p. This is called a unilateral defection from the joint strategy a by player p. It's really the first two definitions that I'm confused about. What is A supposed to represent, and what is the difference between A and A_p? I'm also not sure what unilateral defection is, or why it is called that. I think understanding the first definition will help clarify the other ones.

Explanation / Answer

Here A is the set of elements containing the list of players a1,a2,...ap( where p is no of players such that set A1 contains the details of a1(player1) and so on Ap contains details of player p.

now ap' is the replacement to player p so definition 2 says that if any member of A i.e, let us suppose player p is replaced by p' then ap is replaced by ap' and now a'p is contained in Ap where A is contained with set of all details of players A1,A2,....A'p now.

This is unilateral defection

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