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.] Alternating offers bargaining with loss aversion (2009)
Bram Driesen, Andres Perea, Hans Peters
Abstract In this paper three different types of loss aversion equilibria in bimatrix games are studied. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points - points below which they consider payoffs to be losses - are endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000) under the name of `myopic loss aversion equilibrium'. There, the players' reference points depend on the beliefs about their opponents' strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference points are only based on the carriers of the strategies, not on the exact probabilities. In the third type, the safety level loss aversion equilibrium, the reference points depend on the values of the own payoff matrices. Finally, a comparative statics analysis is carried out of all three equilibrium concepts in 2 x 2 bimatrix games. It is established when a player benefits from his opponent falsely believing that he is loss averse.
[3.] On the manipulability of approval voting and related scoring rules (2009)
Hans Peters, Souvik Roy, Ton Storcken
Abstract We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of alternatives: by comparison of worst alternatives, best alternatives, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of alternatives. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable - has the smallest number of manipulable preference profiles - under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the k-approval rule with k around half the number of alternatives is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned.
[4.]
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.
[5.] 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.
[6.] A preference foundation for constant loss aversion (2010)
Hans Peters
Abstract
Following prospect theory we consider decision making under risk in which
the decision maker's preferences depend on a reference outcome. An outcome below
this reference outcome is regarded as resulting from a loss: a loss decreases
the decision maker's basic utility more than a comparable gain increases this
utility. An elegant and simple method to model this phenomenon was proposed by
Shalev (2002): the utility of an outcome below the reference outcome is obtained
from the basic utility by subtracting a multiple of the loss in basic utility:
this multiple, the loss aversion coefficient, is constant across different
reference outcomes. We provide a preference foundation for this loss aversion
model.
[7.]
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.