Interaction Sheaves on Continuous Domains

We introduce a description of the power structure which is inherent in a strategic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003).Nash equilibrium; strong equilibrium; solvability; effectivity; acyclicity

Rational Fear of Floating: A Simple Model of Exchange Rates and Income Distribution

We consider a simple two-country model, where each country produces a consumption good from a single input. Production takes time, and the model is considered over two consecutive periods. There are three categories of economic agents, namely factor owners, entrepreneurs, and financial intermediaries. The latter offers credits to entrepreneurs and are funded by sale internationally transferable bonds. We assume that the national credit markets are monopolistic but that other markets are competitive. Exchange rate policy is introduced in two different ways, either as a market intervention by a government, sustained by intervention in the commodity market, and, more realistically, as a policy commitment by the monetary authorities, which in equilibrium is taken into consideration by the financial intermediary. The results of the simple model show that an increase in the value of the domestic currency from an equilibrium position will in most cases decrease aggregate welfare of the country, but it will improve welfare of the financial intermediaries. Thus, in the simple framework of our model, a specific sector – and one with a considerable influence on policy choices – stands to gain from this exchange rate policy.fear of floating; income distribution; financial intermediaries

Entropy and typical properties of Nash equilibria in two-player games

We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse the properties of typical Nash equilibria, which are exponentially dominant in number. We find that a randomly chosen equilibrium realizes almost always equal payoffs to either player. This value and the fraction of strategies played at an equilibrium point are calculated as a function of the correlation between the two payoff matrices. The picture is complemented by the calculation of the properties of Nash equilibria in pure strategies.Comment: 6 pages, was "Self averaging of Nash equilibria in two player games", main section rewritten, some new results, for additional information see http://itp.nat.uni-magdeburg.de/~jberg/games.htm

Oversigt over undersøgelser og forsøg vedrørende fluebekæmpelsen 1949. (II.)

Oversigt over undersøgelser og forsøg vedrørende fluebekæmpelsen 1949. (II.

Statistical mechanics of random two-player games

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate quantities such as the number of equilibrium points, the expected payoff, and the fraction of strategies played with non-zero probability as a function of the correlation between the payoff matrices of both players and compare the results with numerical simulations.Comment: 16 pages, 6 figures, for further information see http://itp.nat.uni-magdeburg.de/~jberg/games.htm

A new approach of nonparametric estimation of incidence and lifetime risk based on birth rates and incident events

<p>Abstract</p> <p>Background</p> <p>Incidence and lifetime risk of diabetes are important public health measures. Traditionally, nonparametric estimates are obtained from survey data by means of a Nelson-Aalen estimator which requires data information on both incident events and risk sets from the entire cohort. Such data information is rarely available in real studies.</p> <p>Methods</p> <p>We compare two different approaches for obtaining nonparametric estimates of age-specific incidence and lifetime risk with emphasis on required assumptions. The first and novel approach only considers incident cases occurring within a fixed time window–we have termed this <it>cohort-of-cases </it>data–which is linked explicitly to the birth process in the past. The second approach is the usual Nelson-Aalen estimate which requires knowledge on observed time at risk for the entire cohort and their incident events. Both approaches are used on data on anti-diabetic medications obtained from Odense Pharmacoepidemiological Database, which covers a population of approximately 470,000 over the period 1993–2003. For both methods we investigate if and how incidence rates can be projected.</p> <p>Results</p> <p>Both the new and standard method yield similar sigmoidal shaped estimates of the cumulative distribution function of age-specific incidence. The Nelson-Aalen estimator gives somewhat higher estimates of lifetime risk (15.65% (15.14%; 16.16%) for females, and 17.91% (17.38%; 18.44%) for males) than the estimate based on cohort-of-cases data (13.77% (13.74%; 13.81%) for females, 15.61% (15.58%; 15.65%) for males). Accordingly the projected incidence rates are higher based on the Nelson-Aalen estimate–also too high when compared to observed rates. In contrast, the cohort-of-cases approach gives projections that fit observed rates better.</p> <p>Conclusion</p> <p>The developed methodology for analysis of cohort-of-cases data has potential to become a cost-effective alternative to a traditional survey based study of incidence. To allow more general use of the methodology, more research is needed on how to relax stationarity assumptions.</p