Evolutionary game analysis of problem processing mechanism in new collaboration

doi:10.23919/JSEE.2021.000013

Abstract

Abstract:

This paper analyzes a problem processing mechanism in a new collaboration system between the main manufacturer and the supplier in the “main manufacturer-supplier” mode, which has been widely applied in the collaborative development management of the complex product. This paper adopts the collaboration theory, the evolutionary game theory and numerical simulation to analyze the decision-making mechanism where one upstream supplier and one downstream manufacturer must process an unpredicted problem without any advance contract in common. Results show that both players ’ decision-makings are in some correlation with the initial state, income impact coefficients, and dealing cost. It is worth noting that only the initial state influences the final decision, while income impact coefficients and dealing cost just influence the decision process. This paper shows reasonable and practical suggestions for the manufacturer and supplier in a new collaboration system for the first time and is dedicated to the managerial implications on reducing risks of processing problems.

Key words: collaborative development management, unpredicted problem, problem processing mechanism, evolutionary game theory

Ming ZHANG, Jianjun ZHU, Hehua WANG. Evolutionary game analysis of problem processing mechanism in new collaboration[J]. Journal of Systems Engineering and Electronics, 2021, 32(1): 136-150.

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Supplier	Main manufacturer
Supplier	Deal with the problem (D)	Not deal with the problem (N)
Deal with the problem (D)	${I}_{s}+\left(1+\alpha \right)\left(1+\beta \right){\pi }_{s}-{c}_{s}^{{\rm{DD}}}+{c}_{m}-{c}_{s}$ , ${I}_{m}+\left(1+\alpha \right)\left(1+\beta \right){\pi }_{m}-{c}_{m}^{{\rm{DD}}}-{c}_{m}+{c}_{s}$	${I}_{s}+\left(1+\beta \right){\pi }_{s}-{c}_{s}^{{\rm{DN}}}+{c}_{m}-{c}_{s}$ , $ {I}_{m}+\left(1+\beta \right){\pi }_{m}-{c}_{m} $
Not deal with the problem (N)	$ {I}_{s}+\left(1+\alpha \right){\pi }_{s}-{c}_{s} $ , ${I}_{m}+\left(1+\alpha \right){\pi }_{m}-{c}_{m}^{{\rm{ND}}}-{c}_{m}+{c}_{s}$	$ {\pi }_{s}-{c}_{s} $ , $ {\pi }_{m}-{c}_{m} $

Scenario	ESS
$ {a}_{x}^{}<0 $ and $ {a}_{y}^{}<0 $	$ \left({0,0}\right) $
$ {a}_{y}^{}<{b}_{y}^{} $ and $ {a}_{x}^{*}>0 $	$ \left({0,1}\right) $
$ {a}_{x}^{}<{b}_{x}^{} $ and $ {a}_{y}^{*}>0 $	$ \left({1,0}\right) $
$ {a}_{x}^{}>{b}_{x}^{} $ and $ {a}_{y}^{}>{b}_{y}^{} $	$ \left({1,1}\right) $

Number	Scenario	ESS	Figure
1	$ {b}_{x}^{}<{a}_{x}^{}<0 $ and $ {b}_{y}^{}<{a}_{y}^{}<0 $	$ \left({0,0}\right),\;\left({1,1}\right) $	Fig. 1(a)
2	$ 0<{a}_{x}^{}<{b}_{x}^{} $ and $ 0<{a}_{y}^{}<{b}_{y}^{} $	$ \left({0,1}\right), \left({1,0}\right) $	Fig. 1(b)
3	$ {b}_{x}^{}>{a}_{x}^{}>0 $ and $ {b}_{y}^{}<{a}_{y}^{}<0 $	No ESS exists	Fig. 1(c)
4	$ {b}_{x}^{}<{a}_{x}^{}<0 $ and $ {b}_{y}^{}>{a}_{y}^{}>0 $	No ESS exists	Fig. 1(d)

Number	Scenario	ESS	Figure
5	$ {a}_{x}^{}<0 $ , $ {a}_{y}^{}<0 $ , and $ {a}_{x}^{}<{b}_{x}^{} $ or $ {a}_{y}^{}<{b}_{y}^{} $	$ \left({0,0}\right) $	Fig. 2(a)
6	$ {a}_{y}^{}<{b}_{y}^{} $ , $ {a}_{x}^{}>0 $ , and $ {b}_{x}^{}<{a}_{x}^{} $ or $ {a}_{y}^{}<0 $	$ \left({0,1}\right) $	Fig. 2(b)
7	$ {a}_{x}^{}<{b}_{x}^{} $ , $ {a}_{y}^{}>0 $ , and $ {b}_{y}^{}<{a}_{y}^{} $ or $ {a}_{x}^{}<0 $	$ \left({1,0}\right) $	Fig. 2(c)
8	$ {a}_{x}^{}>{b}_{x}^{} $ , $ {a}_{y}^{}>{b}_{y}^{} $ , and $ {a}_{x}^{}>0 $ or $ {a}_{y}^{}>0 $	$ \left({1,1}\right) $	Fig. 2(d)

Number	$ {a}_{x}^{*} $	$ {b}_{x}^{*} $	$ {a}_{y}^{*} $	$ {b}_{y}^{*} $
1	?3	?7	?2.5	?5.5
2	1.5	7	1.5	5.5
6	5	?7	?3	4
8	5	?7	3	?4