Mein Doktorvater war J. Duistermaat. Jede Person in der unterstehenden Liste hat als Doktorvater der nachfolgenden Person; Platz und Jahreszahl beziehen sich auf die Doktorarbeit. Zur Erstellung dieser Liste habe ich Mathematics Genealogy Project benutzt.

- Pierre von Mouche (1959--), Utrecht 1988.
- Johannes Duistermaat (1942--2010), Utrecht 1968.
- Hans Freudenthal (1905--1990), Berlin 1930.
- Heinz Hopf (1894--1971) und Ludwig Bieberbach, Berlin 1925.
- David Hilbert (1862--1943), Königsberg 1885.
- Ferdinand von Lindemann (1852--1939), Erlangen-Nürnberg 1873.
- Felix Klein (1849--1925) und Julius Plücker (1801-1868), Bonn 1868.
- Rudolf Lipschitz (1832-1903), Berlin 1853.
- Gustav Dirichlet (1805-1859) und Martin Ohm, Bonn 1827.
- Siméon Poisson (1781-1840) und Jean-Baptiste Fourier, Paris 1800.
- Joseph Lagrange (1736--1813) und Pierre-Simon Laplace,
- Leonard Euler(1707--1783).
- Johann Bernoulli (1667--1748).

Komplette Publikationsliste.

- 2021
*Shock-independency of the Periodic Samuelson-Hicks Model.*

- 2021 (mit W. Pijnappel).
*Das Newton-Polygon Verfahren für Polynome die in Linearfaktoren zerfallen.*

Wir geben einen sehr elementaren Beweis für das Newton-Polygon Verfahren für Polynome die in Linearfaktoren zerfallen. Der Beweis beruht hauptsächlich auf allgemeinen Eigenschaften der unteren konvexen Hülle. Aus der Algebra benutzen wir eigentlich nur den Wurzelsatz von Vieta.

- 2021 (mit T. Iimura).
*Discrete Hotelling Pure Location Games: Potentials and Equilibria.*ESAIM: Proceedings and Surveys, Vol. 71, pp. 163--174. Kopie.

We study two-player one-dimensional discrete Hotelling pure location games assuming that demand f(d) as a function of distance d is constant or strictly decreasing. We show that this game admits a best-reply potential. This result holds in particular for f(d) = w^{d}with 0 < w ≤ 1. For this case special attention will be given to the structure of the equilibrium set and a conjecture about the increasingness of best-response correspondences will be made. -
2021 (mit J.-i. Itaya).
*Equilibrium Uniqueness in Aggregative Games: Very Practical Conditions.*Optimization Letters. Kopie. Pfl ege.

Various Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has ℝ_{+}as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions are completely in terms of marginal reductions which may be considered as primitives of the game. For many games in the literature they can easily be checked. They automatically imply that conditional payoff functions are strictly quasi-concave. The results are proved by means of the Szidarovszky variant of the Selten-Szidarovszky technique. Their power is illustrated by reproducing quickly and improving upon various results for economic games. - 2020.
*The Continuous Hotelling Pure Location Game with Elastic Demand Revisited.*In: MOTOR 2020, LNCS 12095, 246--262. Editors: A. Kononov et al. Springer Nature Switzerland AG. Kopie. Pfl ege.

The Hotelling pure location game is revisited. It is assumed that there there are two identical players, strategy sets are one-dimensional and demand as a function of distance is constant or strictly decreasing. Besides qualitative properties of conditional payoff functions, attention is given to the structure of the equilibrium set, best-response correspondences and existence of potentials. - 2020 (mit R. Haagsma).
*Securing Land Rights under Rapid Population Growth: the Feasibility of Institutional Land Rights Protection in Africa.*Journal of Institutional and Theoretical Economics 176, 2, 312--350. Kopie.

The paper examines the claim that a virtuous cycle of more secure land rights, more land-saving investments, and denser populations requires the development of institutions that regulate competition over land. We construct a contest model that links the tenure security-investment relationship to the efforts of land users to enhance land rights themselves and the role of institutional protection. We study the impact of population growth on a close-to-subsistence economy, including the possibility that it weakens institutional protection. We derive sufficient conditions for a positive effect on land investment, but also show that population growth can push the economy into a low-productivity trap. - 2020 (mit A. Hagen und H.-P. Weikard).
*The Two-Stage Game Approach to Coalition Formation: Where we Stand and Ways to Go.*Games, 11(1), 3. Kopie.

Coalition formation is often analysed in an almost non-cooperative way as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalise this widely used approach for the case where in each stage actions are simultaneous. There is special attention to the case of a symmetric physical game. Various theoretical results, in particular for cartel games, are provided. As they are crucial, also recent results on uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives. -
2019 (mit T. Sato).
*Cournot Equilibrium Uniqueness: at 0 Discontinuous Industry Revenue and Decreasing Price Flexibility.*International Game Theory Review, 21, 2. Kopie. [Also in: 2019, Game Theoretic Analysis, pp. 203-221 Chapter 10, https://doi.org/10.1142/9789811202018_0010] ]

We consider the equilibrium uniqueness problem for a large class of Cournot oligopolies with convex cost functions and a proper price function p̃ with decreasing price flexibility. This class allows for (at 0) discontinuous industry revenue and in particular for p̃(y) = y^{- α}. The paper illustrates in an exemplary way the Selten-Szidarovszky technique based on virtual backward reply cspondences. An algorithm for the calculation of the unique equilibrium is provided. - 2018 (mit T. Iimura und T. Watanabe).
*Binary Action Games: Deviation Properties, Semi-Strict Equilibria and Potentials*. Discrete Applied Mathematics, 251, 57--68. Kopie; Pflege.

For binary action games we present three properties which have in common that they are defined by conditions on marginal payoffs. The first two properties guarantee the existence of a special type of Nash equilibrium called semi-strict Nash equilibrium, for which we also show an algorithm to locate. The third one guarantees the existence of an exact potential, and can realize the aforementioned two properties in a class of exact potential games. The first one guarantees the existence of a generalized ordinal potential. Each symmetric binary action game possesses all the three properties. The results are illustrated by three applications. - 2018 (mit N. Kukushkin).
*Cournot Tatonnement and Nash Equilibrium in Binary Status Games.*Economics Bulletin, 38, 2, 1038--1044. Kopie.

We study a rather simplified game model of competition for status. Each player chooses a scalar variable (say, the level of conspicuous consumption), and then those who chose the highest level obtain the "high" status, while everybody else remains with the "low" status. Each player strictly prefers the high status, but they also have intrinsic preferences over their choices. The set of all feasible choices may be continuous or discrete, whereas the strategy sets of different players can only differ in their upper and lower bounds. The resulting strategic game with discontinuous utilities does not satisfy the assumptions of any general theorem known as of today. Nonetheless, the existence of a (pure strategy) Nash equilibrium, as well as the "finite best response improvement property," are established. - 2018
(mit W. Pijnappel).
*The Hotelling Bi-matrix Game.*Optimization Letters, 12, 1, 187--202, Kopie; Pflege.

We study the pure equilibrium set for a specific symmetric finite game in strategic form, referred to as the Hotelling bi-matrix game. General results that guarantee non-emptiness of this set (for all parametric values) do not seem to exist. We prove its non-emptiness by determining the pure equilibrium set. In this proof so-called demi-modality properties of the conditional payoff functions play an important role. - 2018 (mit F. Quartieri).
*Cournot Equilibrium Uniqueness via Demi-Concavity.*Optimization, 67, 4, 441--455, Kopie.

A family of oligopolies that possess a unique equilibrium was identified in the second authors doctoral dissertation. For such a family, it is therein specified a class of functions--economically related to the price function of a Cournot oligopoly---that satisfy a particular type of quasi-concavity. The first part of the present article (i) conceptualizes that type of quasi-concavity by introducing the notion of demi-concavity, (ii) considers two possible variants and (iii) provides some calculus properties. The second part, by relying on the results on demi-concavity, proves a Cournot equilibrium uniqueness theorem which is new for the journal literature and subsumes various results thereof. A third part shows an example that illustrates the novelty of the result. - 2017 (mit T. Iimura und T. Watanabe).
*Best-Response Potential for Hotelling Pure Location Games.*Economics Letters, Volume 160, 73--77, Kopie.

We revisit two-person one-dimensional pure location games à la Anderson et al. (1992) and show that they admit continuous best-response potential functions (Voorneveld, 2000) if demand is sufficiently elastic (to the extent that the Principle of Minimum Differentiation fails); if demand is not that elastic (or is completely inelastic) they still admit continuous quasi-potential functions (Schipper, 2004). We also show that, even if a continuous best-response potential function exists, a generalized ordinal potential function (Monderer and Shapley, 1996) need not exist. - 2017 (mit T. Iimura und T. Watanabe).
*Best-reply Potential for Two-Person One-Dimensional Pure Location Games.*Tokyo Metropolitan University Research Paper Series, No. 178. Kopie.

We study two-person one-dimensional non-price pure location games à la Anderson et al. (1992) under the setting that the strategy set is either a compact real interval or a finite integer interval and demand as a function of distance is constant (inelastic) or strictly decreasing (elastic). We show that on a finite integer interval, the game is a best- reply potential game (Voorneveld, 2000); on a compact real interval, it is a best-reply potential game if the demand is a sufficiently decreasing, strictly decreasing continuous function of distance; otherwise a quasi-potential game (Schipper, 2004). We also show that, even if a best-reply potential exists, a generalized ordinal potential (Monderer and Shapley, 1996) need not exist. Thus, on a finite integer interval, the game generally lacks the finite improvement property (Monderer and Shapley, 1996) but has the finite best-reply property (Milchtaich, 1996); on a compact real interval, the existence of a pure Nash equilibrium is secured by the existence of some continuous potential function, which, as we shall show, is indeed the case. - 2016 (mit R. Haagsma).
*On the Endowment Effect in `Apple-Mars' Experiments.*Apstract, 10, 2-3, 47--50, Kopie; Pflege.

In this article we take a close look at a specific type of behavioural experiment that Antonides conducted to study the endowment effect. We argue that if such experiments ignore to test for the presence of persons in the sample who are indifferent between alternatives, the identification procedure for establishing an endowment effect is fallible. - 2016.
*The Selten-Szidarovszky Technique: the Transformation Part.*In: Recent Advances in Game Theory and Applications, 147--164. Editors: L. Petrosyan and V. Mazalov. Birkhauser. ISBN 9783319438382. Kopie; Pflege.

A technique due to Selten and Szidarovszky for the analysis of Nash equilibria of games with an aggregative structure is reconsidered. Among other things it is shown that the transformation part of this technique can be extended to abstract games with co-strategy mappings and that this part allows for a purely algebraic setting. - 2016 (mit F. Quartieri).
*Equilibrium Theory for Cournot Oligopolies and Related Games: Essays in Honour of Koji Okuguchi.*Springer Series in Game Theory. Editors: P. v. Mouche and F. Quartieri. ISBN 978-3-319-29253-3. Kopie.

This state-of-the-art collection of papers on the theory of Cournotian competition focuses on two main subjects: oligopolistic Cournot competition and contests. The contributors present various applications of the Cournotian Equilibrium Theory, addressing topics such as equilibrium existence and uniqueness, equilibrium structure, dynamic processes, coalitional behavior and welfare. Special emphasis is placed on the aggregative nature of the games that are relevant to such theory. This contributed volume was written to celebrate the 80th birthday of Prof. Koji Okuguchi, a pioneer in oligopoly theory. - 2016.
*On the Geometric Structure of the Cournot Equilibrium Set: the Case of Concave Industry Revenue and Convex Costs.*In:*Equilibrium Theory for Cournot Oligopolies and Related Games: Essays in Honour of Koji Okuguchi.*Springer Series in Game Theory, 63--88. Editors: P. v. Mouche and F. Quartieri. ISBN 978-3-319-29253-3. Kopie. Pfl ege.

The recent results in [14] on equilibrium (semi-)-uniqueness for homogeneous Cournot oligopolies with concave industry revenue and convex costs are refined and conceptualised. For this class of oligopolies also new results concerning the geometric structure of the equilibrium set E are provided. In particular, a subclass is identified for which E is a non-empty polytope on which the equilibrium aggregator is constant and a subclass for which E is a 1-dimensional polytope on which the equilibrium aggregator is injective. - 2015 (mit W. Heijman).
*Floquet Theory and Economic Dynamics II.*WASS Working Paper No. 15. DOI:10.13140/RG.2.1.1067.4009. Kopie.

[Verbesserung von: 1996 (mit W. Heijman).*Floquet Theory and Economic Dynamics (Extended Version).*Wageningen Economic Papers, 1996-5. Und Verbesserung von: 1993 (mit W. Heijman).*Floquet Theory and Economic Dynamics.*Wageningen Economic Papers, 1993-3.]

Floquet theory is an appropriate tool for studying ordinary linear recurrence and differential equations with periodic coefficients, and is a generalization of the theory for constant coefficients. Floquet theory has still not found its way into economics, although it seems to be relevant for economic dynamics. As well as a discussion of this relevance and an illustration of it in the context of the Samuelson-Hicks multiplier-accelerator model, this article contains an appendix that provides a quite complete exposition of Floquet theory for recurrence equations.

- (mit P. Moffatt).
*On Concrete Giffen Utility Functions with Very Nice Theoretical Properties.* -
*The Selten-Szidarovzsky Technique.* -
*Nash Equilibrium Uniqueness in Asymmetric Rent-seeking Contests: Three Short Proofs.* -
*On the Structure of the El-Farol Bar Game.* -
*Multi Objective Games: Separability, Tensor Sums and Permutations.* - (mit W. Pijnappel).
*On Fully Reducible Polynomials with Formal Power Series as Coefficients.* -
*Formal Transboundary Pollution Games: Pareto Efficiency.* - (mit W. Pijnappel.)
*Pi in the Mandelbrot Set Revisited.* -
*The Monopoly Profit Function.* - (mit W. Pijnappel).
*Vers une Théorie de Perturbation de Rayleigh-Schrödinger Algébrique.* -
*Micro-economie (Buch).* -
*Spectral Asymptotics of Periodic Discrete Schrödinger Operators. II.* -
*The Selten-Szidarovszky Technique (Buch).* -
*Matrices de Jacobi Périodiques (Buch).* -
*Nombre de Bandes de l'Opérateur Discret de Harper Triangulaire.*

Meine Erdöszahl ist 3 (Erdös - Totik - Simon - von Mouche). (Siehe auch Famous Trails to Paul Erd&246;.)