Game analysis of merchants and consumers confronting fakes on e-commerce platforms

Figures & data

Table 1. Main parameters' symbols and implications of the three-party evolutionary game model.

Symbol	Implication
P	the price of a genuine commodity
α	the ratio of the price of a fake commodity to the price of a genuine one ($\alpha \in (0,1)$)
$C_m$	the cost of purchasing a genuine commodity by the merchant
β	the ratio of the cost of purchasing a fake commodity by the merchant to the cost of purchasing a genuine one ($\beta \in (0,1)$)
B	the loss of the merchant due to returning
$W_m$	the potential loss of the merchant brought by negative online word of mouth
$C_p$	the strict supervision cost of the e-commerce platform
$R_p$	the e-commerce platform's revenue after the merchant successfully selling a commodity
F	economic penalty that the e-commerce platform imposes on the merchant after finding a fake commodity
$R_c$	the utility of the consumer brought by a genuine commodity
γ	the ratio of the utility of the consumer brought by a fake commodity to the utility by a genuine one ($\gamma \in (0,1)$)
I	the economic compensation paid by the merchant to the consumer
$C_c$	returning cost of the consumer

Table 2. Payoff matrix of the mixed strategy game model among the merchant, e-commerce platform, and consumer.

		Consumer
Merchant	E-commerce platform	Accepting $(z)$	Returning $(1-z)$
	Strict supervision $(y)$	$P-C_m,R_p-C_p,R_c$	$-B,-C_p,-C_c$
Selling genuine commodities$(x)$	Slack supervision $(1-y)$	$P-C_m,R_p,R_c$	$-B,-C_p,-C_c$
	Strict supervision $(y)$	$\alpha P-C_m-F$,$F-2C_p+R_p,R_c$	$-F-B$,$F-2C_p,-C_c$
Selling fake commodities$(1-x)$	Slack supervision $(1-y)$	$\alpha P-\beta C_m-W_m$,$R_p,\gamma R_c$	$-B-F-I,F-C_p,I-C_c$

Note: Take $P-C_m,R_p-C_p,R_c$ as an example, these three payoffs are of the merchant, e-commerce platform, and consumer in turn. Their strategies are selling genuine commodities, strict supervision, and accepting commodities, respectively.

Figure 1. Phase diagram of the merchant's strategy evolution. It shows the relationship between the merchant's ESS and the probability z. Arrows represent the merchant's strategy choice.

Figure 2. Phase diagram of the e-commerce platform's strategy evolution. It shows the relationship between the e-commerce platform's ESS and the probability x. Arrows represent the e-commerce platform's strategy choice.

Figure 3. Phase diagram of the consumer's strategy evolution. It shows the relationship between the consumer's ESS and the probability y. Arrows represent the consumer's strategy choice.

Table 3. Stability analysis of equilibrium points.

Equilibrium points	${\lambda }_1$	${\lambda }_2$	${\lambda }_3$	Symbols of real parts
$E_1(0,0,0)$	F + I	$-C_p$	$\gamma R_c+C_c-I$	($+,-,?$)
$E_2(1,0,0)$	$-(F+I)$	0	$R_c+C_c$	($-,0,+$)
$E_3(0,0,1)$	$P-C_m-\alpha P+\beta C_m+W_m$	$F-2C_p$	$-(\gamma R_c+C_c-I)$	($?,?,?$)
$E_4(1,0,1)$	$-(P-C_m-\alpha P+\beta C_m+W_m)$	$-C_p$	$-(R_c+C_c)$	($?,-,-$)
$E_5(0,1,0)$	$F+\beta C_m$	$C_p$	$R_c+C_c$	(+, + , +)
$E_6(1,1,0)$	$-(F+\beta C_m)$	0	$R_c+C_c$	($-,0,+$)
$E_7(0,1,1)$	$\beta C_m+F+P-\alpha P$	$-(F-2C_p)$	$-(R_c+C_c)$	($+,?,-$)
$E_8(1,1,1)$	$-(F+P-aP)$	$C_p$	$-(R_c+C_c)$	(−, + , −)

Note: “+” represents that its real part is positive; “−” represents that it is negative; “$?$” represents that it is uncertain and needs to be discussed further; and “0” represents that it equals zero.

Figure 4. Influence of economic penalty F's changes on x, y, and z. (a) Influence of F's changes on x, y, and z and (b) influence of F's changes on x and y.

Figure 5. Influence of supervision cost $C_p$'s changes on probabilities x, y, and z. (a) Influence of $C_p$'s changes on x, y and z and (b) influence of $C_p$'s changes on y with time t.

Figure 6. Influence of economic losses $W_m$'s changes brought by negative online word of mouth on x, y, and z. (a) Influence of $W_m$'s changes on x, y, and z and (b) influence of $W_m$'s changes on x with time t.

Figure 7. Influence of economic compensation I's changes on probabilities x, y, z. (a) Influence of I's changes on x, y, and z and (b) influence of I's changes on x and z.

Figure 8. Influence of economic penalty F's changes on probabilities x and y with time t. (a) Influence of F's changes on x with time and (b) influence of F's changes on y with time.

Figure 9. Influence of supervision cost $C_p$'s changes on the probability y with time t.

Figure 10. Influence of loss $W_m$'s changes brought by negative online word of mouth on the probability x with time t.