A. Gaunersdorfer, J.. Hofbauer and K. Sigmund, On the Dynamics of Asymmetric Games,
Theor. Pop. Biology 39 (1991), pp.345-357.

A game dynamical analysis of a simple asymmetric game (two roles with two alternatives each) shows that an interesting class of "semi-stable" heteroclinic cycles leading to a highly unpredictable behaviour can occur in a robust way. Biological examples related to conflicts over ownership and parental investment are analysed.

A. Gaunersdorfer, Time Averages for Heteroclinic Attractors,
SIAM J. Appl. Math. 52 (1992), pp.1476-1489.

In neighbourhoods of attracting heteroclinic cycles, the time averages fail to converge for almost all initial conditions, but spiral closer and closer to the boundary of a polygon. This is shown by using a Poincarée-section argument.

A. Gaunersdorfer and J. Hofbauer, Fictitious Play, Shapley Polygons, and the Replicator Equation,
Games and Economic Behavior 11 (1995), pp.279-303.

For many normal form games, the limiting behavior of fictitious play and the time-averaged replicator dynamics coincide. In particular, we show this for three examples, where this limit is not a Nash equilibrium, but a Shapley polygon.

E.J. Dockner und A. Gaunersdorfer, Die Bedeutung der Chaostheorie für die empirische Kapitalmarktforschung,
Österreichisches Bankarchiv 6/95, S.427-439.

Chaostheorie hat in den letzten Jahren im Bereich der Kapitalmarktforschung rege Diskussionen ausgelöst. Wir stellen in diesem Artikel einige grundlegende Konzepte dieser "Theorie" vor und diskutieren deren Bedeutung für die empirische Kapitalmarktforschung sowohl aus praktischer als auch aus theoretischer Sicht. Weiters vergleichen wir neue, mittels der Chaostheorie entwickelte Methoden, mit traditionellen Modellansätzen.

E.J. Dockner and A. Gaunersdorfer, Strategic New Product Pricing When Demand Obeys Saturation Effects,
European Journal of Operational Research 90 (1996), pp.589-598.

We analyze dynamic pricing strategies for durable goods over an infinite planning horizon in a duopolistic market. The sales dynamic is modelled as linear demand function with saturation effects, marginal costs are assumed to be constant. The optimal pricing strategies are obtained as (degenerate) closed-loop Nash solutions. It is shown that in the case of a strict positive discounting rate the optimal dynamic prices are greater than the static ones. In the case of no-discounting there is in addition to the constant solution also an equilibrium with monotonically increasing prices.

E.J. Dockner, A. Gaunersdorfer, and S. Jørgensen, Government Price Subsidies to Promote Fast Diffusion of a New Consumer Durable,
in: S. Jørgensen and G. Zaccour (eds.), Dynamic Competitive Analysis in Marketing, LN in Economics and Mathematical Systems 444, Springer, 1996, pp.101-110.

We consider a market in which a single supplier sells a new product characterized by diffusion effects on the demand side. In this setting we analyze the problem whether or not the government should subsidize the diffusion of this innovation. We assume that the government is a Stackelberg leader and decides about the subsidy (price or cost subsidy) before the supplier sets his optimal price. The objective of the government is to choose a subsidy policy such that the number of adopters at the horizon date is maximized. The firm chooses a pricing strategy so as to maximize the present value of profits.

A. Gaunersdorfer, Endogenous Fluctuations in a Simple Asset Pricing Model with Heterogeneous Agents,
Journal of Economic Dynamics and Control 24 (2001), pp.799-831.
(SFB-Report No.22, 1999)

In this paper we study the adaptive rational equilibrium dynamics in a simple asset pricing model introduced by Brock and Hommes (1997, 1998). Traders have heterogeneous expectations concerning future prices and update their beliefs according to a risk adjusted performance measure and to market conditions. Further, also their expectations about conditional variances of returns vary over time. We show that even for the simple case where agents can only choose between two different predictors complicated dynamics arise and we analyse the bifurcation routes to chaos.

R. Cressman, A. Gaunersdorfer, and J.F. Wen, Evolutionary and Dynamic Stability in Symmetric Evolutionary Games with Two Independent Decisions,
International Game Theory Review 2 (2000), pp.67-81.

A two-decision competition model is developed where players may choose different strategies at different decisions knowing that their payoff at one decision is not affected by their performance at the other. It is shown that both static solution concepts of Nash and evolutionarily stable equilibria for the two-decision model are directly related to those of the separate decisions. Furthermore, if there are at most two pure strategies at each decision, dynamic stability can also be characterized through a separate analysis of each decision. However, when there are more than two strategies, this last statement is not always true.

T. Dangl, E.J. Dockner, A. Gaunersdorfer, A. Pfister, L. Sögner G. Strobl, Adaptive Erwartungsbildung und Finanzmarktdynamik,
forthcoming in: Zeitschrift für betriebswirtschaftliche Forschung
(SFB-WP No.39, 1999).

Aufbauend auf einem klassischen Finanzmarktmodell behandeln wir drei Modellvarianten, die jeweils einen anderen Ansatz der (heterogenen) Erwartungsbildung von Investoren über künftige Wertpapierpreise in den Vordergrund der Betrachtungen rücken: das Konzept der konsistenten Erwartungen, das Konzept der "Adaptive Belief Systeme" und künstliche Finanzmärkte, wo die Modellierung der Erwartungsbildung mittels "Classifier Systemen" erfolgt. Wir untersuchen, welche Auswirkungen diese unterschiedlichen Mechanismen der Erwartungsbildung auf die Gleichgewichtsdynamik von Wertpapierkursen haben und vergleichen statistische Eigenschaften von Renditen der mittels dieser Modelle generierten Kurszeitreihen mit jenen realer Daten.

E.J. Dockner and A. Gaunersdorfer, On the Profitability of Horizontal Mergers in Industries with Dynamic Competition,
forthcoming in: Japan and the World Economy

The consequences of horizontal mergers on firms' profits are traditionally studied within a static Cournot framework. In such a setting the merger is modelled as an exogenous change in market structure. One of the key results in this literature is that if firms compete in a homogeneous product market, mergers will in general be unprofitable to the merging firms. In this paper we analyze horizontal mergers of firms that compete in a dynamic Cournot market. We find unlike in static Cournot models that mergers are always profitable independent of the number of merging firms. While firms have an incentive to merge, welfare in the economy, however, does not increase since the gain in producer surplus does not offset the loss in consumer surplus due to increased prices.


A. Gaunersdorfer and C.H. Hommes, A Nonlinear Structural Model for Volatility Clustering
SFB-WP No.63, 2000 and CeNDEF WP 00-02   (see also SSRN).

A simple nonlinear structural model of endogenous belief heterogeneity is proposed. News about fundamentals is an IID random process, but nevertheless volatility clustering occurs as an endogenous phenomenon caused by the interaction between different types of traders, fundamentalists and technical analysts. The belief types are driven by an adaptive, evolutionary dynamics according to the success of the prediction strategies in the recent past conditioned upon price deviations from the rational expectations fundamental price. Asset prices switch irregularly between two different regimes -- close to the fundamental price fluctuations with low volatility, and periods of persistent deviations from fundamentals where the market is dominated by technical trading -- thus, creating time varying volatility similar to that observed in real financial data.

(WP version: risk adjusted profits as performance measure; latest version: profits as perfomance measure)

[PDF-file (latest version)]

A. Gaunersdorfer, C.H. Hommes, and F.O.O. Wagener, Bifurcation Routes to Volatility Clustering under Evolutionary Learing
SFB-WP No.73, 2000 and CeNDEF WP 00-04.

A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically in nonlinear multi-agent evolutionary systems.

[PDF-file (version: June 2003)]     [older version: zipped PS-file (2.46 MB)]

A. Gaunersdorfer, Adaptive Beliefs and the Volatility of Asset Prices,
forthcoming in: Central European Journal of Operations Research 9 (2001), 5-30
(SFB-WP No.74, 2000).

I present a simple model of an evolutionary financial market with heterogeneous agents, based on the concept of adaptive belief systems introduced by Brock and Hommes (1997a). Agents choose between different forecast rules based on past performance, resulting in an evolutionary dynamics across predictor choice coupled to the equilibrium dynamics. The model generates endogenous price fluctuations with similar statistical properties as those observed in real return data, such as fat tails and volatility clustering. These similarities are demonstrated for data from the British, German, and Austrian stock market.


A. Gaunersdorfer, Nonlinear Adaptive Beliefs and the Dynamics of Financial Markets: The Role of the Evolutionary Fitness Measure
forthcoming in: Proceedings of the International Conference on Artificial Neural Networks 2001, Lecture Notes in Computer Science, Springer-Verlag.

We introduce a simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical traders. Traders update their beliefs according to past performance and to market conditions. The model generates endogenous price fluctuations and captures some stylized facts observed in real returns data, such as excess volatility, fat tails of returns distributions, volatility clustering, and long memory. We show that the results are quite robust w.r.t.\ to different choices for the performance measure.


E.J. Dockner and A. Gaunersdorfer, Dynamic Oligopolistic Competition and Quasi-Competitive Behavior,
in: G. Zaccour (ed.), Optimal Control and Differential Games - Essays in Honor of Steffen S. Jørgensen, Kluwer Academic Publishers, 2002.

Many real world markets exhibit features of imperfect competition, most likely oligopolistic structures. Since oligopolistic markets generate welfare losses to society, they are the focus of regulatory and/or procompetitive actions. One popular action against oligopolistic markets structures is the provision of free access into these markets. In this paper we study the implications of free market entry on the equilibrium price in the industry. In particular we demonstrate that independent of the corresponding market game (i.e. whether firms play an open-loop or a Markov game) the equilibrium price converges to the competitive level as the number of firms increases in the market. This quasi-competitive behavior holds irrespective of the time horizon of the game, i.e. whether firms have a finite or an infinite horizon.

S. Thurner, E.J. Dockner, A. Gaunersdorfer, Asset Price Dynamics in a Model of Investors Operating on Different Time Horizons, 2002

We present a dynamic asset pricing model based on a heterogenous class of traders. These traders are homogenous in the sense that they are fundamentalists who base their investment decisions on an exogenoulsy given fundamental value. They are heterogenous in the sense that each trader is working with a different frequency of the underlying price data. As a result we have a system of interacting investors who together influence the market price. We derive a system that characterizes out-of-equilibrium dynamics of prices in this market which is structurally equivalent to the Nos\'e-Hoover thermostat equation in non-equilibrium thermodynamics. We explore the time series properties of these prices and find that they exhibit fat tails of returns distributions, volatility clustering and power laws.


E.J. Dockner und A. Gaunersdorfer, Dynamic investment strategies with demand-side and cost side risks, Applied Mathematics and Computation 217 (2010), pp.1001-1009.

Investments in cost reductions are critical for the long run success of companies that operate in dynamic and stochastic market environments. This paper stud- ies optimal investment in cost reductions as a real option under the assumption that a single firm faces two di®erent sources of risk, stochastic demand and input prices. We derive optimal investment strategies for a monopoly as well as a firm in a perfectly competitive market and show that in case of high marginal costs, cost reductions take place earlier in competitive than in monopoly markets. While the existence of an option to invest in cost reductions increases firm value it also increases a firm's systematic risk. Risk can be smaller in a monopolistic than in a competitive industry.


E.J. Dockner, H. Elsinger, and A. Gaunersdorfer, The Strategic Role of Dividends and Debt in Markets with Imperfect Competition
Dynamic Games and Applications, 2018

In a seminal paper Brander and Lewis (Am Econ Rev 76:956–970, 1986) show that oligopolistic firms with limited liability follow a more aggressive output strategy as their leverage increases. In a follow-up paper Glazer (J Econ Theory 62:428–443, 1994) points out that when debt is long term and rival firms choose their equilibrium quantities in two consecutive periods, they have an incentive to be more collusive in the first period than static oligopolists would be. In this paper we argue that the incentive to collude is driven by limited liability and the dividend policy of the firm. We find that increasing leverage causes firms in both periods to increase their output and hence to be more aggressive. Additionally, we find that it is always optimal to pay out profits immediately. Moreover, we show that the symmetric game admits multiple equilibria some of which cause firms to choose asymmetric product market strategies.

http://rdcu.be/Ied2 (open access)