Table 3 Pure strategy points and their corresponding eigenvalues.
Equilibrium | The eigenvalues corresponding to the equilibrium point |
|---|---|
\(R_{1} (0,0,0)\) | \(G_{1} - C_{1} + \mu B_{2} - G_{2} + C_{2}\), \(S - L_{1}\),\(B_{1} - W_{1} - B_{2} + W_{2} + \mu B_{2}\) |
\(R_{2} (0,0,1)\) | \(G_{1} - C_{1} - F - \theta B_{1} - G_{2} + C_{2}\), \(S - L_{1} - \kappa W_{1}\),\(- (B_{1} - W_{1} - B_{2} + W_{2} + \mu B_{2} )\) |
\(R_{3} (0,1,0)\) | \(G_{1} - C_{1} - D + \mu B_{2} - G_{2} + C_{2}\), \(- (S - L_{1} )\),\(B_{1} + \beta S - W_{1} - B_{2} + W_{2} + \mu B_{2}\) |
\(R_{4} (1,0,0)\) | \(G_{1} - C_{1} - D - F - \theta B_{1} - G_{2} + C_{2}\), \(- (S - L_{1} - \kappa W_{1} )\),\(- (B_{1} + \beta S - W_{1} - B_{2} + W_{2} + \mu B_{2} )\) |
\(R_{5} (1,1,0)\) | \(- (G_{1} - C_{1} + \mu B_{2} - G_{2} + C_{2} )\), \(S - L_{1} + D\),\(B_{1} + [F - (\mu - \theta )B_{1} ] - W_{1} - B_{2} + W_{2} + \mu B_{2}\) |
\(R_{6} (1,0,1)\) | \(- (G_{1} - C_{1} - F - \theta B_{1} - G_{2} + C_{2} )\), \(S - L_{1} + D - \kappa W_{1}\),\(- \{ B_{1} + [F - (\mu - \theta )B_{1} ] - W_{1} - B_{2} + W_{2} + \mu B_{2} \}\) |
\(R_{7} (0,1,1)\) | \(- (G_{1} - C_{1} - D + \mu B_{2} - G_{2} + C_{2} )\), \(- (S - L_{1} + D)\),\(B_{1} + [F - (\mu - \theta )B_{1} ]{ + }\beta S - W_{1} - B_{2} + W_{2} + \mu B_{2}\) |
\(R_{8} (1,1,1)\) | \(- (G_{1} - C_{1} - D - F - \theta B_{1} - G_{2} + C_{2} )\), \(- (S - L_{1} + D - \kappa W_{1} )\),\(- \{ B_{1} + [F - (\mu - \theta )B_{1} ]+ \beta S - W_{1} - B_{2} + W_{2} + \mu B_{2} \}\) |
