A strategic justification of the constrained equal awards rule through a procedurally fair multilateral bargaining game
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A strategic justification of the constrained equal awards rule through a procedurally fair multilateral bargaining game Makoto Hagiwara1
•
Shunsuke Hanato2
Accepted: 7 October 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is ‘‘procedurally fair’’ (claimants are treated equally) and ‘‘multilateral’’ (all claimants negotiate simultaneously). In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game. Keywords Strategic justification Claims problem Constrained equal awards rule Nash program
An earlier version of this paper was titled ‘‘Strategic justification in claims problems: Procedurally fair and multilateral bargaining game.’’ We thank two anonymous reviewers, Ryo Kawasaki, William Thomson, and Takehiko Yamato for their helpful comments. This work was partially supported by JSPS KAKENHI Grant Nos. JP17J01520 (Hagiwara) and JP18J20162 (Hanato). & Makoto Hagiwara [email protected] Shunsuke Hanato [email protected] 1
Faculty of Economics, Osaka University of Economics, 2-2-8, Osumi, Higashiyodogawa-ku, Osaka 533-8533, Japan
2
Department of Industrial Engineering and Economics, School of Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
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M. Hagiwara, S. Hanato
1 Introduction In a claims problem, a group of agents have claims on the liquidation value of a bankrupt firm, which we call the ‘‘endowment.’’1 The endowment is not sufficient to honor the totality of the claims. How should it be allocated? A ‘‘rule’’ is a singlevalued mapping that associates with each claims problem an ‘‘awards vector.’’2 As a central rule for claims problems, we consider the so-called constrained equal awards (CEA) rule. The CEA rule satisfies a number of desirable properties, and it has been characterized in multiple ways, reviewed in Thomson (2019).3 Our purpose is to develop a strategic justification of the rule.4 Our game is as follows: at each period t, each claimant proposes a pair consisting of an awards vector and a permutation. If some awards vector is proposed by more than one claimant, then the awards vector which receives the highest number of votes is chosen as temporary awards vector. The components of this temporary awards vector are subject to the composition of the reported permutations, and the game ends.5 If no two claimants propose the same awards vector, the game proceeds to the period t þ 1 and we repeat the above process. The formal definition of the above game is proposed in Sect. 3. Our game is ‘‘procedurally fair’’ (claimants are treated equally) and ‘‘multilateral’’ (all claimants negotiate simultaneously). If a g
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