Relations among the central rules in bankruptcy problems: A strategic perspective

Strategic justifications of the TAL family of rules for bankruptcy problems

“…First, as a SPE is a NE, the above implies thatσ θ (c, E) is a NE of the game Γ θ 2 (c, E) with outcome T θ (c, E). Next, for each N ∈ N with |N | = 2, each (c, E) ∈ B N , and each θ ∈ [0, 1], it is clear that the sum of each possible outcome of Γ θ 2 (c, E) is always the endowment E. Thus, the proof can be completed in the same way as the proof of the uniqueness part at Proposition 1 in Tsay and Yeh (2019). Q.E .D.…”

“…Now, due to the nature of the game, the bilateral negotiation at Stage 3 plays the crucial role in our analysis. Stage 3 of our game closely relates to Stage 3 of Tsay and Yeh (2019) and Moreno-Ternero et al (2020). More precisely, Stage 3 of the game in Tsay and Yeh ( 2019) is based on Dagan's (1996) axiomatization of the Talmud rule as it exploits two operational properties known as "invariance under claims truncation" and "minimal rights first".…”

“…See, for instance,Serrano and Vohra (2002),Thomson (2005),Tsay and Yeh (2019),Moreno-Ternero et al (2020).8 This feature is also shared byTsay and Yeh (2019) andMoreno-Ternero et al (2020).9 See Serrano (1995),Dagan et al (1997), andChang and Hu (2017). In the case ofSerrano (1995), the exogenous bankruptcy rule is actually obtained as the equilibrium outcome of a random dictator bargaining game, which could be considered as an expected strategic justification of the Talmud rule.…”

Sixty-seven years of the Nash program: time for retirement?

“…Also in cost sharing problems, Hu et al (2018) offers an axiomatization and implementation of the nucleolus, inspired by the consistency principle. Tsay and Yeh (2019) proposes a class of strategic games where even bilateral renegotiations take place noncooperatively, in order to shed light on the differences among four of the most central rules in bankruptcy problems (the constrained equal-awards, the constrained equal-losses, the proportional, and the Talmud rules). Moreno-Ternero et al (2020) builds on a previous axiomatization of the Talmud rule to suggest a new procedure implementing it.…”

Sixty-Seven Years of the Nash Program: Time for Retirement?

“…Also in cost sharing problems, Hu et al (2018) offers an axiomatization and implementation of the nucleolus, inspired by the consistency principle. Tsay and Yeh (2019) proposes a class of strategic games where even bilateral renegotiations take place noncooperatively, in order to shed light on the differences among four of the most central rules in bankruptcy problems (the constrained equal-awards, the constrained equal-losses, the proportional, and the Talmud rules). Moreno-Ternero et al (2020) builds on a previous axiomatization of the Talmud rule to suggest a new procedure implementing it.…”