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
2020 (mit J.-i. Itaya).
Equilibrium Uniqueness in Aggregative Games: Very Practical Conditions. Zur Publikation angeboten.
Sufficient conditions for a game in strategic form
aggregative structure to have a unique Nash equilibrium are presented.
The setting presupposes that each player has ℝ+
as strategy set, makes smoothness assumptions, but allows for a possible
discontinuity at the origin.
The conditions, in terms of marginal payoffs,
are in general easy to check.
In particular they imply the needed pseudo-concavity.
The results are proved by means of the Selten-Szidarovszky technique using
virtual backward reply functions.
Their power is illustrated by reproducing and improving
various results in the literature concerning Cournot oligopolies.
2020 (mit T. Iimura).
Discrete Hotelling Pure Location Games: Potentials and Equilibria.
Zur Publikation angeboten.
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) = wd 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 reply correspondences will be made.
2020 (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.
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.
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.
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.
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, 1--19.
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 correspondences. 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.
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.
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.
(mit W. Pijnappel). The Hotelling Bi-matrix Game.
Optimization Letters, 12, 1, 187--202, Kopie;
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,
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,
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.
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,
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.
A technique due to Selten and Szidarovszky for the analysis of Nash equilibria
of games with an aggregative structure
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.
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.
The recent results
in  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
2015 (mit W. Heijman).
Floquet Theory and Economic Dynamics II.
WASS Working Paper No. 15. DOI:10.13140/RG.2.1.1067.4009.
[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.
2015 (mit N. Abudaldah, W. Heijman und P. Heringa).
Return of the Icecream Men. A Discrete Hotelling Game.
Romanian Journal of Regional Science, 9, 2, 39-48.
[Verbesserung von: 2015
(mit W. Heijman, P. Heringa und N. Abudaldah).
Return of the Icecream Men. A Discrete Hotelling Game.
WASS Working Paper No. 11.
We consider a finite symmetric game in strategic form with
two players which can be interpreted as a discrete variant of the Hotelling game in a one or two-dimensional space.
As the analytical investigation of this game is tedious, we simulate with Maple and formulate some conjectures.
In addition we present a short literature overview.
2015 (mit H. Folmer).
Nash Equilibria of Transboundary Pollution Games.
In: Handbook of Research Methods and Applications in Environmental Studies, 504--524. Edward-Elgar. Editor: M. Ruth.
We reconsider the Nash equilibrium existence and uniqueness problem for transboundary pollution games.
There is special attention for the equilibrium set E for
effective compact transboundary pollution games with continuous strictly concave
production functions, continuous convex damage cost functions
and uniformly distributed transboundary pollution.
For this case we show that E is a non-empty polytope and that
for each country all equilibrium deposition levels are equal.
If in addition each damage cost function is differentiable, then there is a unique equilibrium.
The results are obtained by exploiting the aggregative structure of transboundary pollution games.
2015 (mit F. Quartieri).
Cournot Equilibrium Uniqueness in Case of Concave Industry Revenue: a Simple Proof.
Economics Bulletin, 35, 2, 1299-1305.
We provide a simple proof of an equilibrium uniqueness result by Murphy, Sherali and Soyster
for homogeneous Cournot oligopolies with concave industry revenue function and convex cost functions.
We show how to adapt this proof to obtain substantial improvements of this result concerning capacity constraints, non-differentiable cost functions and industry revenue functions that are discontinuous at 0.
2015 (mit T. Yamazaki).
Sufficient and Necessary Conditions for Equilibrium Uniqueness in Aggregative Games.
Journal of Nonlinear and Convex Analysis, 16, 2, 353-364.
We identify sufficient and necessary conditions for an aggregative game to have a unique Nash equilibrium.
In particular, an improvement of a result of Gaudet and Salant (1991) for
Cournot oligopolies is obtained. The results are obtained by exploiting the general relation between Nash equilibria
and fixed points of the (virtual) aggregate cumulative best reply correspondence.
2014 (mit M. Finus und B. Rundshagen).
On Uniqueness of Coalitional Equilibria.
In: Contributions to Game Theory and Management. Volume VII, 51-60.
Editors: L. Petrosjan, N. Zenkevich.
St. Petersburg State University. ISSN 2310-2608.
[Verbesserung von: 2005 (mit M. Finus und B. Rundshagen)
Uniqueness of Coalitional Equilibria.
Fondazione Eni Enrico Mattei, Nota de Lavaro 23.2005.
In the so-called `new approach' of coalition formation it is important
that coalitional equilibria are unique.
Uniqueness comes down to existence and to semi-uniqueness,
i.e. that there exists at most one equilibrium.
Although conditions for existence are not problematic, conditions for semi-uniqueness are.
We provide semi-uniqueness conditions by deriving a new equilibrium
semi-uniqueness result for games in strategic form
with higher dimensional strategy sets. The result applies in particular to
2014 (mit P. Bertoletti). Inferior Factor in Cournot Oligopoly Revisited.
Journal of Economics, 112, 85-90.
We reconsider the recent work by
Okuguchi (2010) on (possibly asymmetric)
Cournotian firms with two production factors, one being inferior for
each firm. It is shown there that an increase in the price of the inferior
factor does raise the equilibrium industry output. In addition of providing
a simpler and more rigorous proof of that result, we generalize it to the
case of technologies with s ≥ 2 factors and also allow some firms not to use the inferior one.
2013 (mit F. Quartieri).
On the Uniqueness of Cournot Equilibrium in Case of Concave Integrated Price Flexibility.
Journal of Global Optimization, 57, 3, 707-718.
We consider a class of homogeneous Cournot oligopolies with concave
integrated price flexibility and convex cost functions. We provide new
results about the semi-uniqueness and uniqueness of (Cournot) equilibria for
the oligopolies that satisfy these conditions. The condition of concave
integrated price flexibility is implied by (but does not imply) the
log-concavity of a continuous decreasing price function. So, our results
generalize previous results for decreasing log-concave price functions and
convex cost functions. We also discuss the particular type of
quasi-concavity that characterizes the conditional revenue and profit
functions of the firms in these oligopolies and we point out an error of the
literature on the equilibrium uniqueness in oligopolies with log-concave
price functions. Finally, we explain how the condition of concave
integrated price flexibility relates to other conditions on the price and
revenue functions usually considered in the literature, e.g., the concavity
of the price function or the concavity of the aggregate revenue associated
to a price function.
2013 (mit H. Folmer). Analysing the Folk Theorem for Linked Repeated Games.
In: Contributions to Game Theory and Management. Volume VI, 146-164.
Editors: L. Petrosjan, N. Zenkevich. Graduate School of Management
[Verbesserung von: 2007 (mit H. Folmer)
Linking of Repeated Games: When does it Lead to More Cooperation
and Pareto Improvements? Fondazione Eni Enrico Mattei, Nota de Lavaro 60.2007.
We deal with the linkage of infinitely repeated games.
Results are obtained by analysing the relations of the feasible individually rational payoff regions
of the isolated games and the linked game.
In fact we have to handle two geometric
problems related to Minkowski sums, intersections and Pareto boundaries of convex sets.
2013 (mit F. Quartieri und F. Szidarovszky). On a Fixed Point Problem Transformation Method.
Proceedings of the 10th international conference on fixed point theory and its applications (ICFPTA),
179--190. ISBN 978-606-17-0420-0. ISSN 1661-7738.
We show how the fixed point problem for a special type of correspondence R
which satisfies a factorisation property can be handled
by considering an associated more simple fixed point problem for a correspondence B
with domain typically a subset of ℝ.
In addition we analyse the fixed point problem for B
under additional conditions on R
that guarantee that B is at most singleton-valued.
In fact we generalize, improve and make more conceptual a game theoretic technique developed by Selten and Szidarovszky.
(mit P. Moffatt).
On Concrete Giffen Utility Functions with Very Nice Theoretical Properties.
Nash Equilibrium Uniqueness in Asymmetric Rent-seeking Contests: a Short Proof.
Multi Objective Games: Separability, Tensor Sums and Permutations.
(mit W. Pijnappel).
On Fully Reducible Polynomials with Formal Power Series as Coefficients.
The Selten-Szidarovszky Technique: Backward
versus Virtual backward Reaction Correspondences.
The Nikaido-Isoda Theorem Revisited.
Shock-independency of the Periodic Samuelson-Hicks Model.
Transboundary Pollution Games.
On Equilibrium Existence for Ordinal Status Games with Finitely Many Players.
(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.
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.