. 2021 Mar 10;20(3):102. doi: 10.1007/s11128-021-03054-8

Table 3.

Possible NE domains of the quantum model and the corresponding payoffs. In this table, $γ_{1} = arcsin (\sqrt{D_{r} / (1 + 2 D_{r} + △)})$ , $γ_{2} = arcsin (\sqrt{(D_{r} + △) / (1 + 2 D_{r} + △)})$ , $π_{D} = 1 + D_{r} + △ - (1 + 2 D_{r} + △) {sin}^{2} γ$ , $π_{Q} = - D_{r} + (1 + 2 D_{r} + △) {sin}^{2} γ$ , $p^{*} = q^{*} = [(1 + 2 D_{r} + △) {sin}^{2} γ - D_{r}] / △$ , ${\hat{Q}}^{*} = \hat{U} (p^{*})$ , and $π^{*} = - △ p^{* 2} + (1 + △) p^{*}$

Dilemma strength parameters	Entanglement	NE	Payoff
$D_{g} > D_{r}$	$\begin{matrix} 0 \leq γ \leq γ_{1} \\ γ_{1} \leq γ \leq γ_{2} \\ γ_{2} \leq γ \leq \frac{π}{2} \end{matrix}$	$\begin{matrix} \hat{D} \otimes \hat{D} \\ \hat{D} \otimes \hat{Q} \\ {\hat{Q}}^{} \otimes {\hat{Q}}^{} \\ \hat{Q} \otimes \hat{D} \\ \hat{Q} \otimes \hat{Q} \end{matrix}$	$\begin{matrix} (0, 0) \\ (π_{D}, π_{Q}) \\ (π^{}, π^{}) \\ (π_{Q}, π_{D}) \\ (1, 1) \end{matrix}$
$D_{g} = D_{r}$	$\begin{matrix} 0 \leq γ \leq γ_{1} \\ γ_{1} \leq γ \leq \frac{π}{2} \end{matrix}$	$\begin{matrix} \hat{D} \otimes \hat{D} \\ \hat{Q} \otimes \hat{Q} \end{matrix}$	$\begin{matrix} (0, 0) \\ (1, 1) \end{matrix}$
$D_{g} < D_{r}$	$\begin{matrix} 0 \leq γ \leq γ_{2} \\ γ_{2} \leq γ \leq γ_{1} \\ γ_{1} \leq γ \leq \frac{π}{2} \end{matrix}$	$\begin{matrix} \hat{D} \otimes \hat{D} \\ \hat{D} \otimes \hat{D} \\ \hat{Q} \otimes \hat{Q} \\ \hat{Q} \otimes \hat{Q} \end{matrix}$	$\begin{matrix} (0, 0) \\ (0, 0) \\ (1, 1) \\ (1, 1) \end{matrix}$