Consumers strategies

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

ii) Anti-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): No PBNE

2ii): No PBNE

3) “Not inspect negative, inspect positive”

3i): $d\rho +\left(e-e\rho -d\rho \right)x<c_i<e\left(1-\rho \right)-\left(e-e\rho -d\rho \right)y$ ,

${c^{\prime }}_s>a\left(1-x\right)$ , and $0<{\overline{c}}_s<ax$

3ii): No PBNE

4) “Always not inspect”

4i):

$c_i>\text{max}\left[d\rho +\left(e-e\rho -d\rho \right)x,e\left(1-\rho \right)-\left(e-e\rho -d\rho \right)y\right]$

and $0<{\overline{c}}_s<a\left(x+y-1\right)$ where $1<\left(x+y\right)\le 2$

4ii):

$c_i>\text{max}\left[d\rho +\left(e-e\rho -d\rho \right)x,e\left(1-\rho \right)-\left(e-e\rho -d\rho \right)y\right]$ ,

$0<{c^{\prime }}_s<a\left(1-x\right)$ , and ${\overline{c}}_s>ax$

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

iv) Anti-GE SIG “always signaling 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): $e\left(1-y\right)<c_i<d\left(1-x\right)$

2iv): No PBNE

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

${c^{\prime }}_s>a\left(1-x\right)$ , and ${\overline{c}}_s>ax$

3iv): $ex<c_i<dy$ ;

$0<{c^{\prime }}_s<a\left(1-x\right)$ , and $0<{\overline{c}}_s<ax$

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

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

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

4iv): No PBNE