A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

Osztozkodási játékok (Games of fair division)

In this survey we presented several proportional and envy-free cake-cutting algorithms. We also mentioned some interesting open problems.

Analysis of operational risk of banks – catastrophe modelling

Nowadays financial institutions due to regulation and internal motivations care more intensively on their risks. Besides previously dominating market and credit risk new trend is to handle operational risk systematically. Operational risk is the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. First we show the basic features of operational risk and its modelling and regulatory approaches, and after we will analyse operational risk in an own developed simulation model framework. Our approach is based on the analysis of latent risk process instead of manifest risk process, which widely popular in risk literature. In our model the latent risk process is a stochastic risk process, so called Ornstein- Uhlenbeck process, which is a mean reversion process. In the model framework we define catastrophe as breach of a critical barrier by the process. We analyse the distributions of catastrophe frequency, severity and first time to hit, not only for single process, but for dual process as well. Based on our first results we could not falsify the Poisson feature of frequency, and long tail feature of severity. Distribution of “first time to hit” requires more sophisticated analysis. At the end of paper we examine advantages of simulation based forecasting, and finally we concluding with the possible, further research directions to be done in the future.

Az árfolyamsávok empirikus modelljei és a devizaárfolyam sávon belüli előrejelezhetetlensége = Empirical models of exchange rate target zones

A sávosan rögzített devizaárfolyamok elméleti és gyakorlati vizsgálatai a nemzetközi közgazdaságtan egyik legnépszerűbb témaköre volt a kilencvenes évek elején. A gyakorlati módszerek közül az alkalmazások és hivatkozások száma tekintetében az úgynevezett eltolódással igazítás módszere emelkedett ki. A módszert alkalmazó szerzők szerint amíg a lebegő árfolyamú devizák előrejelzése céltalan feladatnak tűnik, addig sávos árfolyam esetén az árfolyam sávon belüli helyzetének előrejelzése sikeresen végezhető. E tanulmány bemutatja, hogy az Európai Monetáris Rendszer és az északeurópai államok sávos árfolyamrendszereinél e módszer alkalmazásával adódott eredmények például a lebegő árfolyamú amerikai dollárra és az egységgyökfolyamatok többségére is érvényesek. A tanulmány feltárja e látszólagos ellentmondás okait, és bemutat egy olyan, a sávos árfolyamrendszerek főbb megfigyelt jellemzőire épülő modellt, amelynek keretei között a sávon belüli árfolyam előrejelzése nem feltétlenül lehetséges, mert a leértékelés előtti időszakban a sávon belüli árfolyam alakulása kaotikus lehet. / === / Following the development of the first exchange rate target zone model at the end of the eighties dozens of papers analyzed theoretical and empirical topics of currency bands. This paper reviews different empirical methods to analyze the credibility of the band and lays special emphasis on the most widely used method, the so-called drift-adjustment method. Papers applying that method claim that while forecasting a freely floating currency is hopeless, predicting an exchange rate within the future band is successful. This paper shows that the results achieved by applications to EMS and Nordic currencies are not specific to data of target zone currencies. For example, application to US dollar and even to most unit root processes leads qualitatively to the same. This paper explores the solutions of this puzzle and shows a model of target zones in which the exchange rate within the band is not necessarily predictable since the process might follow chaotic dynamics before devaluation.

The multiple hierarchical legislatures in representative democracy

Multiple hierarchical models of representative democracies in which, for instance, voters elect county representatives, county representatives elect district representatives, district representatives elect state representatives and state representatives a president, reduces the number of electors a representative is answerable for, and therefore, considering each level separately, these models could come closer to direct democracy. In this paper we show that worst case policy bias increases with the number of hierarchical levels. This also means that the opportunities of a gerrymanderer increase in the number of hierarchical levels.

Invariance under type morphisms: the bayesian Nash equilibrium

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

Exclusive contracts with vertically differentiated products

In this paper we develop a simple model to analyze the effects of exclusive contracts in vertically integrated markets where both the upstream and the downstream market are characterized as oligopolies and manufacturers produce vertically differentiated products. We find that firms prefer to deal exclusively with retailers. If the extent of consumers' heterogeneity is small, manufacturers offer exclusive contracts unilaterally. On the other hand, if consumers' valuations differ significantly both manufacturers engage in exclusive contracting.

Price discrimination in asymmetric Cournot oligopoly

In this article we examine the eects of third degree price discrimination in asymmetric Cournot oligopolies. We show that the average price is not affected by the extent of price discrimination. We nd that the asymmetry between firms is reflected only by the output produced for the lowest-valuation consumers and firms produce equal quantities to the other consumer groups.

Generalized type spaces

Ordinary type spaces (Heifetz and Samet, 1998) are essential ingredients of incomplete information games. With ordinary type spaces one can grab the notions of beliefs, belief hierarchies and common prior etc. However, ordinary type spaces cannot handle the notions of finite belief hierarchy and unawareness among others. In this paper we consider a generalization of ordinary type spaces, and introduce the so called generalized type spaces which can grab all notions ordinary type spaces can and more, finite belief hierarchies and unawareness among others. We also demonstrate that the universal generalized type space exists.

Az inverzlimesz egy játékelméleti alkalmazása

A nem teljes információs játékok szokásos játékelméleti modellbe foglalásának problémája a véleményrangsorok modellezése. A cél a Harsányi János által bevezetett típustér megkonstruálása. A célunk, hogy megmutassuk miként kapcsolódik a véleményrangsorok kérdése az inverzlimesz fogalmához, illetve egy a mérték inverzlimeszek létezésére kimondott, az ismert tételeknél általánosabb eredmény segítségével egy olyan típustér létezését látjuk be, amely egyetemes, teljes, és a paramétertér, amire épül, tisztán mérhető (nem topologikus).

Price discrimination in asymmetric Cournot oligopoly

In this article we examine the eects of third degree price discrimination in asymmetric Cournot oligopolies. We show that the average price is not affected by the extent of price discrimination. We nd that the asymmetry between firms is reflected only by the output produced for the lowest-valuation consumers and firms produce equal quantities to the other consumer groups.

Common priors for generalized type spaces

The notion of common prior is well-understood and widely-used in the incomplete information games literature. For ordinary type spaces the common prior is defined. Pinter and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for nite belief hierarchies, unawareness among others. In this paper we dene the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light.

Stochastic bankruptcy games

We study bankruptcy games where the estate and the claims have stochastic values. We use the Weak Sequential Core as the solution concept for such games. We test the stability of a number of well known division rules in this stochastic setting and find that most of them are unstable, except for the Constrained Equal Awards rule, which is the only one belonging to the Weak Sequential Core.

Transferable Utility Games with Uncertainty

We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TUgames are convex.