Table 4. SPNE conditions using the parametrization of three different action-response games [4,25, 26].

Eq	SPNE conditions	JMS91	BL97	PS14	Differential cost model
	1. Equilibrium
5.	W h +rV h>0	S-1+r>0	-d+ra>0	1+r>0	1+r>0
6.	W l+rV l<0	S-1+r(1-V)<0	-d+rb<0	-1+r(a-b)<0	-1+r>0
7.	p(V h+rW h)>c h	p(1+r(S-1))>t	p(a-rd)>c	p(1+r)>c	p(1+r)>d
8.	q(V l+rW l)<C l	q(1-V+r(S-1))<t	q(b-rd)<c	q(a-b-r)<c	q(1-r)<c
9.	xp(1-α)(W h +rV h)>C r	xp(1-α)(S-1+r)>C r	xp(1-α)(-d+ra)>C r	xp(1-α)(1+r)>C r	xp(1-α)(1+r)>C r
10.	(p-q)(V h+rW h)>C ah.	(p-q)(1+r(S-1))>C ah	(p-q)(a-rd)>C ah	(p-q)(1+r)>C ah	(p-q)(1+r)>C ah
	SPNE conditions
	2. Equilibrium
12.	W l +rV l>0	S-1+r(1-V)>0	-d+rb>0	It is not possible.	It is not possible.
13.	W h +rV h>W l +rV l	S-1+r>S-1+r(1-V)	-d+ra>-d+rb	NA	NA
14.	$\begin{array}{l}p\left(1-\alpha \right)\\ \left[\begin{array}{l}x({{\displaystyle W}}_h+r{{\displaystyle V}}_h)+\\ (1-x)({{\displaystyle W}}_l+r{{\displaystyle V}}_l)\end{array}\right]>{{\displaystyle C}}_r\end{array}$	$\begin{array}{l}p\left(1-\alpha \right)\\ \left[\begin{array}{l}x(S-1+r)+\\ \left(1-x\right)\left(S-1r\left(1-V\right)\right)\end{array}\right]>{{\displaystyle C}}_r\end{array}$	$\begin{array}{l}p\left(1-\alpha \right)\\ \left[\begin{array}{l}x\left(-d+ra\right)+\\ \left(1-x\right)\left(-d+rb\right)\end{array}\right]>{{\displaystyle C}}_r\end{array}$	NA	NA
15.	(p-q)(V l+rW l)>C al	(p-q)(1-V+r(S-1))>C al	(p-q)(b-rd)>C al	NA	NA