Supply Chain Bargaining with Flexible Disagreement Points: An Extension of the Kalai-Smorodinsky Solution

Abstract

This paper extends the supply chain bargaining framework of Feng et al. [1] by introducing flexible disagreement points — a departure from the classical assumption that negotiating parties maintain fixed reservation utilities throughout negotiations. Flexibility parameters τ_S ≥ 0 and τ_R ≥ 0, expressed as percentages of each party's walk-away value, enable meaningful cross-channel comparison. Analysing two canonical channel structures — a one-to-two channel (monopoly supplier, competing retailers) and a two-to-one channel (competing suppliers, monopoly retailer) — we compare the Kalai-Smorodinsky (KS) and Nash Bargaining (NB) solutions at the implied equivalence point θ = 0.6. Our key findings are: (1) both solutions produce identical outcomes at baseline, confirming Feng et al.’s characterisation; (2) under flexibility, NB is 1.2× more reactive than KS in the one-to-two channel and 8.5× more reactive in the two-to-one channel; and (3) NB’s hyper-reactivity destroys approximately 9% of total supply chain value in the two-to-one channel, while KS maintains near-baseline efficiency. These results demonstrate that the KS solution is not only “more reasonable” at baseline but also “more stable” under flexibility — and this stability has direct welfare consequences for supply chain performance.