Convexity and the Shapley value of Bertrand oligopoly TU-games in $$\beta$$ β -characteristic function form

Dongshuang Hou, Aymeric Lardon () and Theo Driessen
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Dongshuang Hou: Northwestern Polytechnical University
Aymeric Lardon: Université Jean Monnet
Theo Driessen: University of Twente

Theory and Decision, 2025, vol. 98, issue 4, No 3, 519-536

Abstract: Abstract The Bertrand oligopoly situation with Shubik’s demand functions is modeled as a cooperative transferable utility game in $$\beta$$ β -characteristic function form. To achieve this, two sequential optimization problems are solved to describe the worth of each coalition in the associated Bertrand oligopoly transferable utility game. First, we show that these games are convex, indicating strong incentives for large-scale cooperation between firms. Second, the Shapley value of these games is fully determined by applying the linearity to a decomposition that involves the difference between two convex games and two non-essential games.

Keywords: Bertrand oligopoly; Transferable utility game; Convexity; Shapley value (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11238-024-10022-y

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