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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2019, Vol. 14 Issue (1) : 85-101     https://doi.org/10.1007/s11465-019-0523-4
RESEARCH ARTICLE |
An application of game theory in distributed collaborative decision making
Angran XIAO()
Department Mechanical Engineering and Industrial Design Technology, New York City College of Technology, City University of New York, Brooklyn, NY 11201, USA
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Abstract

In a distributed product realization environment, new paradigms and accompanying software systems are necessary to support the collaborative work of geographically dispersed engineering teams from different disciplines who have different knowledge, experience, tools and resources. To verify the concept of collaboration by separation, we propose a generic information communication medium to enable knowledge representation and exchange between engineering teams, a digital interface. Across digital interfaces, each engineering team maintains its own perspective towards the product realization problem, and each controls a subset of design variables and seeks to maximize its own payoff function subject to individual constraints. Hence, we postulate the use of principles from game theory to model the relationships between engineering teams and facilitate collaborative decision making without causing unnecessary information exchange or iteration across digital interfaces. A product design and manufacturing scenario is introduced to demonstrate the efficacy of using game theory to maintain a clean interface between design and manufacturing teams.

Keywords collaboration      distributed product realization      game theory      digital interface     
Corresponding Authors: Angran XIAO   
Just Accepted Date: 13 June 2018   Online First Date: 26 July 2018    Issue Date: 30 November 2018
 Cite this article:   
Angran XIAO. An application of game theory in distributed collaborative decision making[J]. Front. Mech. Eng., 2019, 14(1): 85-101.
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http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0523-4
http://journal.hep.com.cn/fme/EN/Y2019/V14/I1/85
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Angran XIAO
Fig.1  Mathematical formulation of the compromise DSP [23]
Fig.2  Design-manufacturing interfaces
Fig.3  Solution of concurrent compromise DSPs
Fig.4  Solution of sequential compromise DSPs
Fig.5  Game solution of coupled compromise DSPs
Fig.6  Solving a leader/follower game
Fig.7  Light switch cover plate and the snap fit
Fig.8  The design player’s compromise DSP
Fig.9  Finite element analysis of cover plate
Fig.10  The manufacturing player’s Compromise DSP
Fig.11  Solution process for games (manuf.: Manufacturing)
Variable Value Deviation
System variable
a/mm 1.197 0.165136
t/mm 2.500
LT/mil 8.000
HOC/mil 2.649
FOC/mil 2.000
State variable
Force/N 2.946 d+ = 0.000539, d-= 0
Deformation/mm 4.680 d+ = 0, d-= 0.063965
Volume/mm3 24129.280 d+ = 0.003129, d- = 0
Time/h 24.630 d+ = 0.231500, d- = 0
Cost/USD 2500.900 d+ = 0.250449, d- = 0
Finish/mil 0.243 d+ = 0.215000, d- = 0
E/GPa 2.350 d+ = 0, d- = 0.338601
Y/MPa 46.380 d+ = 0, d- = 0.217904
Tab.1  Results from the Traditional Trial-and-Error Approach
Variable Value Deviation
System variable
a/mm 1.220 0.160609
t/mm 2.500
LT/mil 8.000
HOC/mil 1.600
FOC/mil 2.000
State variable
Force/N 2.943 d+ = 0, d- = 0
Deformation/mm 4.880 d+ = 0, d- = 0.023933
Volume/mm3 24131.760 d+ = 0.003233, d- = 0
Time/h 23.990 d+ = 0.199500, d- = 0
Cost/USD 2459.480 d+ = 0.229739, d- = 0
Finish/mil 0.243 d+ = 0.215000, d- = 0
E/GPa 2.186 d+ = 0, d- = 0.375343
Y/MPa 45.180 d+ = 0, d- = 0.238122
Tab.2  Results from fully cooperative protocol
Experiment Design player Manufacturing player
LT a t HOC a t HOC
1 2 1.367 2.714 1 0.5 2.5 2.651
2 2 1.173 2.500 4 0.5 4.0 1.897
3 2 1.110 2.500 7 0.5 5.5 0
4 4 1.319 2.637 1 1.5 2.5 2.649
5 4 1.177 2.500 4 1.5 4.0 1.896
6 4 1.140 2.500 7 1.5 5.5 0
7 8 1.239 2.508 1 2.5 2.5 2.647
8 8 1.183 2.500 4 2.5 4.0 1.894
9 8 1.210 2.500 7 2.5 5.5 0
Tab.3  Experimental Results of Noncooperative Games
Variable Value Deviation
System variable
a/mm 1.320 0.200169
t/mm 2.640
LT/mil 8.000
HOC/mil 1.900
FOC/mil 2.000
State variable
Force/N 3.798 d+ = 0.291831, d- = 0
Deformation/mm 4.990 d+ = 0, d- = 0.001693
Volume/mm3 24486.560 d+ = 0.059556, d- = 0
Time/h 24.100 d+ = 0.205000, d- = 0
Cost/USD 2466.790 d+ = 0.233394, d- = 0
Finish/mil 0.243 d+ = 0.215000, d- = 0
E/GPa 2.230 d+ = 0, d- = 0.363182
Y/MPa 45.560 d+ = 0, d- = 0.231694
Tab.4  Results from a non-cooperative protocol
Fig.12  Response surface model of HOC, a and t
Fig.13  Deviation values of goals
Fig.14  Deviation values of design and manufacturing
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