UCL
Université catholique de Louvain Louvain School of Management / CESCM
SUPPLY CHAIN MANAGEMENT
Cooperative Supply Chain Games
Per AGRELL
[email protected]
Outline Game theory applications in SCM – – – –
Cooperative games Concepts Alliances Applications
Allocation game General reference: – Ch 4 in Cachon G and S Netessine (2004) Game Theory in Supply Chain Analysis. Ch 6 in David Simchi-Levi, S. David Wu and ZuoJun (Max) Shen (Eds), Supply Chain Analysis in the eBusiness Era, Kluwer
Categories Cooperation – Cooperative games: players can make binding commitments – Non-cooperative: no coalitions
Information – Complete information: all players observe all draws – Asymmetric information
Stages: – Static games: simultaneous moves – Dynamic games: several games
Why collaborate with someone else? Obtaining needed skills or resources more quickly Reducing asset commitment and increase flexibility Learning from partner Sharing costs and risks Can build cooperation around a common standard
Risks in undertaking cooperative agreements or strategic alliances Adverse selection – Partners misrepresent skills, ability and other resources
Moral Hazard – Partners provide lower quality skills and abilities than they had promised
Holdup – Partners exploit the transaction specific investment made by others in the alliance
Cooperative games Already in Neumann and Morgenstern (1944) Cooperative: Focus at outcome of the game, not actions Non-cooperative: Focus at actions, not outcome
Assumptions Coalitions – Players N can form any coalitions S that are beneficial to them, no prior assignment of power (cf. Stackelberg) – Value of a coalition S, v(S), does not depend on non-coalition members’ actions
The Core of the game
The core may not exist (i.e. be empty) The core may not be unique The sharing rule of the core is not necessarily defined
Existence and uniqueness of the core Hartman et al. (2000) – newsvendor centralization game. – game has a non-empty core under certain restrictions on the demand distribution.
Muller et al. (2002) – show that the core for newsvendor centralization is always nonempty, certain conditions for uniqueness.
Muller et al. (2002) give a condition under which the core is a singleton.
Problems with independence in SCM Classical SCM formulation: v(S) = “SC surplus” = Π(S) = revenues – variable costs – fixed costs = p(S, N – S)q(S) – c(S)q(S) – K(S) v(S) is not independent of residual coalitions, standard formulations must assume competitive markets
Shapley value
The Shapley value is unique Logic = marginal gains from random coalition configuration
Shapley value: Example
Source: BIS Quarterly Review, September 2009, p. 77
Gains from alliances (ex. automotive) Product development – Synergies in systems – Common product platforms / modularity
Manufacturing – Common process development (if platforms/modular design) – Scale economies in sourcing (if platforms/modular design) – Learning effects
Distribution – Transport/Warehouse consolidation, scale effects – Spare-part logistics
Alliances in SCM: Example VAG Audi Lamborghini Bentley Bugatti Porsche SEAT Skoda Volkswagen
Scania (trucks) Volkswagen ComV
VAG product portfolio
Speech of B. Pischetsrieder at NAIAS Detroit January, 2001
VAG Platforms (Example) Platform
Cat
VW
Audi
SEAT
A0/A00
City cars
Lupo
A0
Supermini
Polo
A2
Ibiza Cordoba
A
Compact
A3 TT
Leon Toledo Altea
B
Mid-size
Golf Bora Jetta Eos Tiguan Passat
A4
Exeo
C
Executive
D
Luxury
Phaeton
T
Vans
Transporter
B-VX62
MPV
Sharan
PL71
SUV
Touareg
Skoda
Porsche
Bentley
Arosa Felicia Fabia Roomster Octavia
Superb
A6 A8 V8
Cont GT Cont FS Alhambra
Q7
Cayenne
(Ford Galaxy)
Shapley and SCM Shapley values are analytically attractive, but lack empirical support. Very little work in SCM
Rönnqvist et al. (2008, sev) – Cooperative transportation planning (routing) in forestry – Models + empirics – Shapley used as focal point
Biform games Brandenburger and Stuart (2003) – Two-stage game: – 1. Players make separate actions and incur costs – 2. Players play a cooperative game, characteristic form depends on choices in (1)
Example: Co-branding 1
A supplier can supply one retailer (R1 or R2) with a product at normalized marginal cost (zero). At time 0, the supplier can invest $1 in co-branding. At time 1, the supplier negotiates with R1 and R2. Values retail (no co-branding): {R1,R2} = {9,3} Values retail (co-branding): {R1,R2} = {9,7}
Source: Brandenburger and Stuart, 2003, p. 4
Example: Co-branding 1I Supplier profit (no co-branding) =[3,9] Contract {R1,R2} = {1,0} Value {R1,R2} = {9,0} Supplier profit (co-branding) = [7-1,9-1] = [6,8] Contract {R1,R2} = {1,0} Value {R1,R2} = {9,0} – Co-branding serves no value-added, only to improve supplier profit margin! – Thus: R1 can pre-empt the investment if pre-game commitment is possible for a contract of 6 (cancelling out the bargaining power of R2)
Example: Co-branding 1I The Intel-inside story – Intel invests 500 M$ 1990-93 in ad campaign for PC and laptops – IBM and Compaq opts out from cobranding 1994-96
Botticelli, Collis, and Pisano (1997)
Conclusion Cooperative game theory is an interesting tool for the collaborative or strategic phase prior to supply chain coordination, e.g. formation of alliances or the scope of joint operations. Shapley values or investigations of the existence of a nonempty core are only valid for certain applications. Biform games provide currently the base base for cooperative models and are widely used in literature.
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