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Navigating Uncertainty with Bayesian Game Theory: A Strategic Pathway in the Auto Industry

Image Credit: Peter Kuo’s Creation (2023)


What is the Bayesian game?

The Bayesian games (Chen & Chen, 2021), characterized by asymmetric negotiation information, enable decision-makers to draw reliable conclusions amid private and secret information. Central to this theory is the concept of Bayesian probability, a mathematical approach that updates the likelihood of an event based on new evidence. Unlike traditional probability, which is based solely on the frequency of events, Bayesian probability combines prior knowledge (or beliefs) with new information to make more accurate predictions or decisions. This approach is particularly powerful in scenarios where information is incomplete or uncertain. It allows players to adjust their strategies based on evolving beliefs about the unknown factors or 'types' of other players. Hungarian economist John C. Harsanyi introduced Bayesian game theory in his three papers published between 1967 and 1968 (Harsanyi, 1967-8; Harsanyi, 1968; Harsanyi, 1968a), later receiving the Nobel Memorial Prize in Economic Sciences in 1994 for his contributions to game theory.


Why is it relevant to OEMs and suppliers’ negotiations?

(Patare & Venkataraman, 2023) Companies often try to protect their private information from competitors and customers, and it is very typical in the auto industry that firms have private information about their manufacturing know-how practices, technologies, and associated costs—the aspect of information asymmetry with respect to the cost associated with quality production among the supply chains. (Chen & Chen, 2021) consider OEMs facing uncertain demands that dictate suppliers’ production, and the OEMs' outsourcing budgets and the suppliers’ production costs are private information. The optimal pricing policies for achieving an agreement are derived from a Bayesian game accounting for asymmetric information. Take the lot sizes as an example, OEMs choose how much to order based solely on their profit structure, which is exclusive private information. Then, suppliers select the production quantity best suited to their cost structure, which is also exclusive private information. (Tayaran & Ghazanfari, 2020) point out when it comes to the information disclosure in the reverse auction, it can be divided into three categories: (1) the disclosure of seller’s information for other sellers, (2) the disclosure of seller’s information for the buyer, and (3) the disclosure of buyer’s information for sellers. The disclosure of seller’s information for other sellers mainly includes information about the bids and the rank of each seller. The reverse auction is sealed at most real auctions, meaning the sellers’ information is not disclosed, and the ranking result is privately announced to sellers. The Bayesian game rises as private and secret information is withheld among buyers and sellers.


How can Bayesian game theory help?

In Bayesian games, each player's "type" is crucial. It refers to their "state of mind" or their beliefs about the state of nature. The state of nature encompasses all data influencing a player's utility, such as actions taken and the outcomes of random variables. A player's type essentially characterizes their private information or uncertainty about various aspects of the game, like the actions of other players or external factors.

(Patare & Venkataraman, 2023) develop a Bayesian game between two competing manufacturers and determine their equilibrium strategies of product quality levels and retail price. The study compares the Bayesian game and the complete information game, showing that the manufacturer of the high type produces lower-quality products but sells them at higher prices in the Bayesian game with lower profits than in the case of games with complete information. Contrary to this, the manufacturer of low type produces better quality products and sells them at lower prices in the Bayesian game but achieves higher profits than the complete information game.

(Chen & Chen, 2021) point out that the information asymmetry is bilateral instead of unilateral—both the OEMs and suppliers own private price information. Compared with the traditional pricing decisions based on a Stackelberg game, the optimal prices were derived through a Bayesian game, such as the lot-sizing decisions. During the negotiation, both agents aim to maximize their own profits without knowing each other's exact costs. This situation is essentially a Bayesian game with incomplete information. In this scenario, the negotiators need to use limited information, such as historical cost structures, detailed cost breakdown of similar parts, industry benchmarks, prior performance of the suppliers, suppliers' reputations in the industry, etc., to define the type and Bayesian probability to calculate the potential outcomes.

(Gupta, 2021) proposes an effective way to negotiate with suppliers regarding new product development (NPD) by utilizing a combination of Game Theory (GT) and Multi-Criteria Decision Making (MCDM) tools to reach multiple Bayesian Nash Equilibrium strategies between the NPD team and the supplier, followed by weighting and ranking each of the objectives, both from the point of view of NPD team and the supplier. Traditional decision-making tools such as MCDM and GT may be limited if they are used individually to generate negotiation strategies, but their combination will create a robust framework. The research enables procurement professionals within Research and development organizations to better negotiate pricing variations by creating win-win scenarios with suppliers, which is essential in staying within the overall target budget for an effective product launch. It also addresses the level of uncertainty present during the NPD phase, where the information available to one party may not be disclosed to the other party due to dynamically evolving market conditions and the possible existence of more than one optimal strategy. The finding was validated via a real-world case study that was proven effective.


Conclusion – win/win

The application of Bayesian Game Theory offers a strategic lens for the US auto industry to navigate the complexities of asymmetric information, enhancing decision-making processes in critical areas such as negotiations, pricing, production, and strategic planning. By understanding and implementing the principles of Bayesian game theory, both OEMs and suppliers can more effectively anticipate and respond to the challenges posed by hidden or private information. This leads to more informed strategies, potentially transforming adversarial negotiations into collaborative opportunities for win-win situations. Ultimately, in an industry characterized by rapid technological advancements and competitive pressures, the ability to make optimal decisions under uncertainty is not only an academic exercise but also a practical necessity for sustained success and innovation. Embracing the insights offered by Bayesian game theory, the US auto industry can steer towards a future where 'win-win' scenarios are not just theoretical ideals but achievable realities. Let us all work together toward the bright, prosperous future of the US auto industry.


References:

Chen, Z., & Chen, C. (2021). Price negotiation and coordination in outsourcing supply chain under yield and demand uncertainties. RAIRO-Operations Research, 55(6), 3661-3675.

Gupta, S. (2021). Negotiating Change Orders with Suppliers during New Product Development using MCDM and Bayesian Game Theory. In IIE Annual Conference. Proceedings (pp. 608-613). Institute of Industrial and Systems Engineers (IISE).

Harsanyi, J. C. (1967-8). "Games with Incomplete Information Played by Bayesian Players, I-III." Management Science 14 (3): 159-183 (Part I), 14 (5): 320-334 (Part II), 14 (7): 486-502 (Part III).

Harsanyi, J. C. (1968). "Games with Incomplete Information Played by "Bayesian" Players, I-III. Part II. Bayesian Equilibrium Points". Management Science. 14 (5): 320–334. doi:10.1287/mnsc.14.5.320. ISSN 0025-1909. JSTOR 2628673.

Harsanyi, J. C. (1968a). "Games with Incomplete Information Played by "Bayesian" Players, I-III. Part III. The Basic Probability Distribution of the Game". Management Science. 14 (7): 486–502. doi:10.1287/mnsc.14.7.486. ISSN 0025-1909. JSTOR 2628894.

Patare, S., & Venkataraman, S. V. (2023). Strategies in supply chain competition: A game theoretic approach. Computers & Industrial Engineering, 180. https://doi-org.ezproxy.umgc.edu/10.1016/j.cie.2023.109242

Tayaran, H., & Ghazanfari, M. (2020). A framework for online reverse auction based on market maker learning with a risk-averse buyer. Mathematical Problems in Engineering, 2020, 1-13.

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