This study proposes a non-cooperative coalitional bargaining game model to analyse wage negotiations between one employer and two workers. Here, randomly selected workers choose whether to negotiate their wage contracts together or separately, considering wage contract externalities. We show...

This supplement provides proofs of all propositions in [Tomohiko Kawamori and Toshiji Miyakawa, "Equivalent conditions for the existence of an efficient equilibrium in coalitional bargaining with externalities and renegotiations," Operations Research Letters 45(5), 427-430, 2017]