Definition 4.4 (Strategies) A strategy for player \(i\) is a function \(s_i:V_i \rightarrow Act\) where for all \(v\in V_i\), \(s_i(v)\in Act(v)\). A strategy profile, denoted \({\mathbf{s}}\), is an element of \(\Pi_{i\in N} S_i\). Given a strategy profile \({\mathbf{s}}\), let \({\mathbf{s}}_i\) be player \(i\)’s component of \({\mathbf{s}}\) and \({\mathbf{s}}_{-i}\) the sequence of strategies form \({\mathbf{s}}\) for all players except \(i\).