Consumers strategies

I) Pro-GE SIG “always signal negative messages”; Consumer’s beliefs (p = ρ; q)

II) Pro-GE SIG “always signal positive messages”; Consumer’s beliefs (p; q = ρ)

1) “Always inspect”

1I): No PBNE

1II): No PBNE

2) “Inspect negative, not inspect positive”

2I):

$e\left(1-\rho \right)-\left(e-e\rho -d\rho \right)y<c_i<d\rho +\left(e-e\rho -d\rho \right)x$ ,

${c^{″}}_s>by$ , and $0<{\overline{c}}_s<b\left(1-y\right)$

2II): $e\left(1-\rho \right)-\left(e-e\rho -d\rho \right)y<c_i<d\rho +\left(e-e\rho -d\rho \right)x$ ,

$0<{c^{″}}_s<by$ , and ${\overline{c}}_s>b\left(1-y\right)$

3) “Not inspect negative, inspect positive”

3I): No PBNE

3II): No PBNE

4) “Always not inspect”

4I): No PBNE

4II): $c_i>\max \left[e\left(1-\rho \right)-\left(e-e\rho -d\rho \right)y,d\rho +\left(e-e\rho -d\rho \right)x\right]$

$0<{c^{″}}_s<b\left(x+y-1\right)$ where $1<\left(x+y\right)\le 2$

III) Pro-GE SIG “always signal facts from Nature”; Consumer’s beliefs (p = 1; q = 0)

IV) Pro-GE SIG “always signal messages opposite to the fact from Nature”; Consumer’s beliefs (p = 0; q = 1)

1III): $c_i<\min \left(d\left(1-x\right),e\left(1-y\right)\right)$

1IV): No PBNE

2III): $e\left(1-y\right)<c_i<d\left(1-x\right)$ ;

${c^{″}}_s>by$ , and ${\overline{\overline{c}}}_s>b\left(1-y\right)$

2IV): $dy<c_i<ex$

$0<{c^{″}}_s<by$ and $0<{\overline{\overline{c}}}_s<b\left(1-y\right)$

3III): $d\left(1-x\right)<c_i<e\left(1-y\right)$ ;

3IV): No PBNE

4III): $c_i>\max \left(d\left(1-x\right),e\left(1-y\right)\right)$ ;

${\overline{\overline{c}}}_s>b\left(1-x-y\right)$ when $0<\left(x+y\right)\le 1$ or

${c^{″}}_s>b\left(x+y-1\right)$ when $1<\left(x+y\right)\le 2$

4IV): No PBNE