Table 9 The conditions that E₃ and E₈ are ESS points.

P_T < C_G + R_E + R_S + L_G, C_T < R_ZT + L_T + λδ²/2, R_GE > C_E

–

\({\it{\lambda }}_1^2 > 0\); \({\it{\lambda }}_3^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_7^3 > 0\); \({\it{\lambda }}_2^{\it{i}}\left( {{\it{i}} = 1,3} \right)\) and \({\it{\lambda }}_6^{\it{i}}\left( {{\it{i}} = 1,2,3} \right)\) are uncertain

E₃ is an ESS point

P_E + P_T > R_S + C_G

P_T + R_T > C_T

\({\it{\lambda }}_1^2 > 0\); \({\it{\lambda }}_3^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_{\it{j}}^3 > 0\left( {{\it{j}} = 2,6,7} \right)\)

E₃ is the unique ESS point

R_GE > C_E + λδ²/2

P_T < C_G + R_E + R_S + L_G, C_T < P_T + R_T + R_ZT + C_T + λδ²/2, R_E + P_E + R_GE > C_E

–

\({\it{\lambda }}_8^1 > 0\)

E₈ is not an ESS point

P_T < C_G + R_E + R_S + L_G, C_T < R_ZT + L_T + λδ²/2, R_GE > C_E

–

\({\it{\lambda }}_1^2 > 0\); \({\it{\lambda }}_3^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_7^3 > 0\); \({\it{\lambda }}_{\it{j}}^1 > 0\left( {{\it{j}} = 5,8} \right)\); \({\it{\lambda }}_2^{\it{i}}\left( {{\it{i}} = 1,3} \right)\) and \({\it{\lambda }}_6^{\it{i}}\left( {{\it{i}} = 1,2,3} \right)\) are uncertain

E₃ is an ESS point

P_E + P_T > R_S + C_G

P_T + R_T > C_T

\({\it{\lambda }}_1^2 > 0\); \({\it{\lambda }}_3^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_{\it{j}}^3 > 0\left( {{\it{j}} = 2,6,7} \right)\); \({\it{\lambda }}_{\it{j}}^1 > 0\left( {{\it{j}} = 5,8} \right)\)

E₃ is the unique ESS point

R_GE > C_E + λδ²/2

P_T > C_G + R_E + R_S + L_G, C_T < P_T + R_T + R_ZT + C_T + λδ²/2, R_E + P_E + R_GE > C_E

–

\({\it{\lambda }}_1^{\it{i}} > 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_5^2 > 0\); \({\it{\lambda }}_6^{\it{i}}\left( {{\it{i}} = 2,3} \right)\) are uncertain;\({\it{\lambda }}_7^3 > 0\); \({\it{\lambda }}_8^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\)

E₈ is an ESS point

P_T + R_T > C_T

\({\it{\lambda }}_1^{\it{i}} > 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_{\it{j}}^2 > 0\left( {{\it{j}} = 5,6} \right)\); \({\it{\lambda }}_7^3 > 0\); \({\it{\lambda }}_8^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\)

E₈ is the unique ESS point

R_E + P_E + R_GE > C_E + λδ²/2

\({\it{\lambda }}_1^{\it{i}} > 0\left( {{\it{i}} = 1,2,3} \right)\); \({\it{\lambda }}_5^2 > 0\); \({\it{\lambda }}_{\it{j}}^3 > 0\left( {{\it{j}} = 6,7} \right)\); \({\it{\lambda }}_8^{\it{i}} < 0\left( {{\it{i}} = 1,2,3} \right)\)