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# Recent working papers

[1.] Claim games for estate division problems (2013)

Hans Peters, Marc Schröder, Dries Vermeulen

**Abstract** This paper studies the estate division problem from a non-cooperative perspective. The integer claim game initiated by O’Neill (1982) and extended by Atlamaz et al. (2011) is generalized by specifying a sharing rule to divide every interval among the claimants. We provide a condition under which a Nash equilibrium exists for a general class of sharing rules. Then we characterize the corresponding set of equilibrium payoffs in order to find division rules that always assign a payoff vector in this set. Well-known examples of such division rules are the adjusted proportional rule, the random arrival rule and the Talmud rule. Finally, we discuss the class of generalized estate division problems and a variation of the claim game.

[2.] The economic order decision with continuous dynamic pricing and batch supply (2014)

Anita van den Berg, Jean-Jacques Herings, Hans Peters

**Abstract ** In an infinite horizon inventory and sales model, we show that the seller’s unique strategy exhibits increasing prices under general conditions on the revenue function. An increasing discount rate leads to an increase of the time interval between order times, but an increase in batch size has an ambiguous effect.

[3.] Waiting in the queue on Hoteling’s main street (2015)

Hans Peters, Marc Schröder, Dries Vermeulen

**Abstract** We consider a variant of Hotelling’s location model that was proposed by Kohlberg (1983): when choosing a firm, consumers take travel time and also (expected) waiting time, which again depends on the number of consumers choosing that firm, into consideration. If we assume that firms are symmetric, then we show that a subgame perfect equilibrium exists if there is an even, but small, number of firms and no subgame perfect equilibrium exists if there is an odd, but small, number of firms. Further, we illustrate by means of examples what other subgame perfect equilibria exist if we allow for asymmetric firms.

[4.] An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains (2016)

Hans Peters, Souvik Roy, Soumyarup Sadukhan, Ton Storcken

**Abstract** We show that every strategy-proof and unanimous probabilistic rule on a binary restricted domain has binary support, and is a probabilistic mixture of strategy-proof and

unanimous deterministic rules. Examples of binary restricted domains are single-dipped domains, which are of interest when considering the location of public bads. We also provide an extension to infinitely many alternatives.

[5.] Linearity of the core correspondence (2016)

Denes Palvolgyi, Hans Peters, Vermeulen

**Abstract **We characterize the sets of balanced TU-games on which the core correspondence is Linear – first introduced by Bloch and de Clippel (2010) – by finitely many linear equalities and inequalities. Thus, the core is piecewise linear.