Estate Division Problems

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• 研討會日期 : 2013-03-01
• 時間 : 14:30
• 主講人 : Professor Hans Peters
• 地點 : Conference Room B110
• 演講者簡介 : Hans Peters received his Ph.D. in Mathematics from University of Nijmegen in 1986. He is currently serving as Professor of Quantitative Economics at Maastricht University. His research field is in game theory and social choice theory.
• 演講摘要 : In the classical estate division problem or bankruptcy problem, an estate has to be divided among a number of claimants, whose total entitlements to the estate exceed its size. This problem, with its extensions, has many applications and interpretations beyond mere estate division or bankruptcy: taxation problems, in which the estate is the total tax amount to be collected and the entitlements are the incomes of the taxpayers; investment problems, where firms with different marketing budgets invest in consumer segments; political campaigning, where political parties with different campaign budgets aim at certain voter segments; Colonel Blotto games; etc. Most of the literature on this problem focuses on developing specific rules, backed up axiomatically, to handle estate division problems. Seminal papers are O’Neill (1982) and Aumann and Maschler (1985) – an overview of this literature is presented in Thomson (2003). In this presentation we take a noncooperative, strategic approach to the problem. Such an approach, apart from supporting cooperative axiomatic models, has the advantage of decentralizing the outcome in cases where players (claimants) may not accept a central rule, and – perhaps more importantly – can be applied in cases where strategic behavior is the natural assumption, like for instance in the marketing or political campaigning example above. Specifically, we formulate a so-called claim game associated with an estate division problem. Basically, in such a claim game each player may put claims on parts of the estate – as many as his entitlement allows – and then a specified sharing rule is invoked to divide each part among the players. The sharing rules used correspond to well-known rules from the classical approach: the proportional rule, the constrained equal awards rule, the constrained equal losses rule, the Talmud rule, and a whole family of rules generalizing the latter three. We then study Nash equilibria of these games, and the associated payoffs, and compare these with payoffs obtained by applying the classical rules to these problems. The presentation is based on three papers. In the first one (Atlamaz et al., 2011) we study claim games based on the proportional sharing rule – in fact, such games were already proposed by O’Neill (1982), but we extend them and offer a complete analysis. In the second paper (P´alv¨olgyi et al., 2012) we consider inhomogenous preferences (e.g., land division problems, where claimants may have different preferences for different parcels of land). In the third paper (Peters et al., 2013) we return to the homogenous case but study sharing rules other than the proportional rule. A special role turns out to be played by the Talmud rule (Aumann and Maschler, 1985).