Rewards and penalties in an evolutionary game theoretic model of international environmental agreements

Figures & data

Figure 1. Countries’ strategies for reward and penalty. Source: Author’s own calculation based on evolutionary game model assumptions.

Table 1. Stability analyses for equilibrium $X_i={(0,0,\dots \dots ,1,\dots \dots .0)}^T.$

Conditions	Stabilities	Equilibrium
$\forall {\lambda }_{im}=0:\mathrm{}\mathrm{i}.\mathrm{e},\mathrm{}{\overline{\pi }}_i={\overline{\pi }}_m,i\ne m$	Center
$\exists {\lambda }_{im}{\lambda }_{in}<0:\mathrm{}\mathrm{i}.\mathrm{e}\mathrm{}\exists {\overline{\pi }}_i>{\overline{\pi }}_m\wedge {\overline{\pi }}_i<{\overline{\pi }}_n$	Saddle
$\exists {\lambda }_{ij}>0:\mathrm{}\mathrm{i}.\mathrm{e},\mathrm{}{\overline{\pi }}_i<{\overline{\pi }}_j,i\ne j$	Unstable
$\forall {\lambda }_{ij}<0\mathrm{}\mathrm{i}.\mathrm{e},\mathrm{}{\overline{\pi }}_i>0,{\overline{\pi }}_i>{\overline{\pi }}_j,i\ne j$	Stable	$Y_i={(0,0,\dots \dots ,0,1,0,\dots \dots .,0)}^T$

Source: Authors own calculations based on proposed model conditions.