Recent working papers
[1.] Non-cooperative collusion and price wars with individual demand fluctuations (2009)
Erik Pot, Ronald Peeters, Hans Peters, Dries Vermeulen
Abstract In this paper attempt to reconcile the - at first sight different - views on the determinants of collusion and price wars expressed in Rotemberg and Saloner (1986), Green and Porter (1984), and Stigler (1964). We first argue that the logic of R&S presupposes two determinants for collusion, namely (1) market shares are publicly observable, and (2) volatility of market shares due to exogenous factors is limited. We make our arguments in a model in which firms repeatedly play a Bertrand type price competition game. Following R&S we show under the two conditions of public observability and limited volatility of market shares that within the model firms can collude using dynamic price adjustment strategies. We show that when the first condition (public observability) is violated, we revert to the logic of Green and Porter. When the second condition (limited volatility of market shares) is violated, for example when consumer loyalty has decreased, we also observe that collusion can no longer be sustained, in line with the arguments in Stigler (1964).
[2.]
Intentional price wars on the equilibrium path
(2010)
Erik Pot,
Ronald Peeters, Hans Peters, Dries Vermeulen
Abstract In this paper we study the effect of information on the
occurrence of intentional price wars on the equilibrium path. An episode of low
prices is an intentional price war if it follows a period of high prices which
was ended intentionally by one of the firms in the market (the price war
leader). We show that for intentional price wars to exist on the equilibrium
path, two elements are necessary regarding the information on which the firms
base their decisions: (1) interperiod dynamics and (2) informational
asymmetries. We illustrate this by means of a repeated price-setting game in
which market shares fluctuate. Firms learn about the market share realizations
at the beginning of each period. We show that intentional price wars on the
equilibrium path are possible when firms have private information about their
market share. When market shares are public information, we either see collusive
price adjustment or episodes of low prices that do not classify as an
intentional price war.
[3.] A strategic approach to estate division problems with non-homogenous preferences (2010)
Dénes Pálvölgyi, Hans Peters, Dries Vermeulen
Abstract The classical bankruptcy problem (O'Neill, 1982) is extended by assuming that the agents have non-homogenous preferences over several estates. A special case is the one in which there are finitely many estates and the agents have homogenous preferences, i.e., constant utilities, per estate. In the general case, i.e., the infinite estate problem, players have arbitrary preferences over an interval of real numbers each of which is regarded as an estate. A strategic game is formulated in which each agent/player distributes his legal entitlement over the estates, resulting in individual claims per estate: each estate is then divided proportionally according to these individual claims. The focus of the paper is on the study of Nash equilibria, in particular on their existence, in finite and infinite estate games. It is also shown that, generally speaking, Nash equilibria are not unique nor Pareto optimal but that they are Pareto optimal in a second best sense: they do not Pareto dominate each other. The paper concludes with a brief consideration of envy-freeness.
[4.]
Judgement aggregation in search for the truth
(2011)
Irem Bozbay, Franz Dietrich, Hans Peters
Abstract We analyse the problem of aggregating judgments over multiple issues from the perspective of efficient aggregation of voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives when voters' disagreements stem (fully or partly) from conflicts of information rather than interests. Combining the two literatures, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. We analyse the resulting strategic incentives and determine which voting rules lead to collective judgments that efficiently use all private information, assuming that voters share a preference for true collective judgments. We find that in many, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of `yes' votes exceeds a particular quota.
[5.] On extensions of the core and the anticore of transferable utility games (2012)
Jean Derks, Hans Peters, Peter Sudhölter
Abstract We consider several
related set extensions of the core and the anticore of games with transferable
utility. An efficient allocation is undominated if it cannot be improved,
in a specific way, by sidepayments changing the allocation or the game. The set
of all such allocations is called the undominated set, and we show that
it consists of finitely many polytopes with a core-like structure. One of these
polytopes is the L1-center, consisting of all efficient allocations that
minimize the sum of the absolute values of the excesses. The excess Pareto
optimal set contains the allocations that are Pareto optimal in the set
obtained by ordering the sums of the absolute values of the excesses of
coalitions and the absolute values of the excesses of their complements. The
L-1-center is contained in the excess Pareto optimal set, which in turn is
contained in the undominated set. For three-person games all these sets
coincide. These three sets also coincide with the core for balanced games and
with the anticore for antibalanced games. We
study properties of these sets and provide characterizations in terms of
balanced collections of coalitions. We also propose a single-valued selection
from the excess Pareto optimal set, the min-prenucleolus, which is
defined as the prenucleolus of the minimum of a game and its dual.