 The idea is that if two outcomes \(w\) and \(w'\) are such that \((w,w')\in \succeq_i\) then player \(i\) considers outcome \(w\) at least as good as outcome \(w'\). The fact that \((w,w')\in \succeq_i\) will be abbreviated \(w \succeq_i w'\). Its inverse is the relation \(\preceq_i\),which holds for \((w,w')\) whenever \(w' \succeq_i w\). Its strict counterpart is the relation \(\succ_i\), which holds for \((w,w')\) whenever \(w \succeq_i w'\) and it is not the case that \(w' \succeq_i w\). Moreover \(w \sim_i w'\) denotes the fact that \(w \succeq_i w'\) and \(w' \succeq_i w\), meaning that \(i\) is indifferent between \(w\) and \(w'\).