The long-run behavior of the stochastic replicator dynamics

Fudenberg and Harris' stochastic version of the classical replicator dynamics is considered. The behavior of this diffusion process in the presence of an evolutionarily stable strategy is investigated. Moreover, extinction of dominated strategies and stochastic stability of strict Nash equilibria are studied. The general results are illustrated in connection with a discrete war of attrition. A persistence result for the maximum effort strategy is obtained and an explicit expression for the evolutionarily stable strategy is derived.Comment: Published at http://dx.doi.org/10.1214/105051604000000837 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bonus Pools and the Informativeness Principle

Previous work on moral-hazard problems has shown that, under certain conditions, bonus contracts create optimal individual incentives for risk-neutral workers. In our paper we demonstrate that, if a firm employs at least two workers, it may further bene.t from combining worker compensation via a bonus-pool contract and relative performance evaluation. Such combination leads to saved rents under a wide class of luck distributions. In addition, if the employer is wealth-constrained, complementing individual bonus contracts by the possibility of pooling bonuses can increase the set of implementable effort levels. All our results hold even though workers’ outputs are technically and stochastically independent so that, in view of Holmstrom’s informativeness principle, individual bonus contracts would be expected to dominate bonus-pool contracts

Time averages, recurrence and transience in the stochastic replicator dynamics

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.Comment: Published in at http://dx.doi.org/10.1214/08-AAP577 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uniform approximation of eigenvalues in Laguerre and Hermite beta-ensembles by roots of orthogonal polynomials

We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite beta-ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal polynomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence. --Gaussian ensemble,random matrix,rate of convergence,Weyl?s inequality,Wishart matrix

Imitation Processes with Small Mutations

This note characterizes the impact of adding rare stochastic muta- tions to an "imitation dynamic," meaning a process with the properties that any state where all agents use the same strategy is absorbing, and all other states are transient. The work of Freidlin and Wentzell [10] and its extensions implies that the resulting system will spend almost all of its time at the absorbing states of the no-mutation process, and provides a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a sim- pler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K x K Markov matrix on the K homogeneous states, where the probability of a transit from "all play i" to "all play j" is the probability of a transition from the state "all agents but 1 play i, 1 plays j" to the state "all play j. "

X-ray sensor development for magnetospheric research

The ARPA-301 data on the P78-1 satellite provide information on the long-term X-ray environment; specifically, the distributions in total X-ray intensities and energy spectral parameters and the spatial extents of the X-ray sources. The average X-ray intensity near noontime was found to decrease with increasing local time whereas the opposite trend occurs around midnight. At both of these local times, the average flux increases with increasing level of geomagnetic activity. The distributions in flux are also considered for given local time intervals and these span a large dynamic range. The temporal correlation between the X-ray flux in different local time sectors is found to decrease with increasing difference in local time. The average spectral shapes do not depend significantly upon local time or geomagnetic activity

Tournaments with Gaps

A standard tournament contract specifies only tournament prizes. If agents’ performance is measured on a cardinal scale, the principal can complement the tournament contract by a gap which defines the minimum distance by which the best performing agent must beat the second best to receive the winner prize. We analyze a tournament with two risk averse agents. Under unlimited liability, the principal strictly benefits from a gap by partially insuring the agents and thereby reducing labor costs. If the agents are protected by limited liability, the principal sticks to the standard tournament

Constitutional Design: Separation of Financing and Project Decision

We examine the provision of public projects under separate tax and subsidy rules. We find that tax rules separated from project cum subsidy decisions exhibit several advantages when incentive problems of the agenda-setter are taken into account. In particular, tax rules may prevent the proposal of inefficient projects which benefit only a small lobby group. We propose “redistribution efficiency” as a socially desirable property of proposals and find that tax rules always guarantee redistribution efficiency. We show that rules on subsidies combined with discretion regarding taxes always yield socially inferior proposals. Finally, tax rules induce the agenda-setter to look for potential improvements of public projects.constitutional design, provision of public projects, voting, taxes and subsidies

Teacher\u27s Reception of the PISA-Study. Beliefs and Attitudes

Nach der Veröffentlichung der Ergebnisse der PISA-Studie im Dezember 2001 wurden starke öffentliche Reaktionen registriert. Dabei stellt sich auch die Frage, wie Lehrer und Lehrerinnen diese Berichte wahrnehmen, weil davon möglicherweise ihre Bereitschaft und ihr Engagement abhängen, sich mit der Problematik professionell und differenziert auseinander zu setzen. In einer Fragebogenstudie wurden Meinungen und Einstellungen von Lehrern und Lehrerinnen zur PISA-Studie erhoben. Befragt wurden 185 Lehrer und Lehrerinnen in verschiedenen schulischen Funktionen. Die Ergebnisse zeigen, dass die Informiertheit der Befragten stark variiert und Informationsangebote sehr unterschiedlich genutzt werden. Zugleich wird deutlich, dass zwischen Informiertheit und der Bereitschaft, sich an Bemühungen um Qualitätsverbesserungen zu beteiligen, ein enger Zusammenhang besteht. Durchführung einer Schulvergleichsstudie und Publikation der Ergebnisse sollten demnach durch eine sorgfältig durchgeführte Rückmeldung der Ergebnisse ergänzt werden. (ZPID)The publication of the results of the PISA - study in December 2001 (Baumert et al., 2001) has raised much public interest and the need for change within the school system has received public attention. In this context, it is crucial to know how teachers perceive the publication of international school efficiency studies, because their willingness to participate both in the public and in the professional discussion may depend on their views. This study presents a survey of opinions and attitudes related to the PISA-study. A sample of 185 teachers across different positions participated in the survey study. Results show that the degree of information varies considerably, just as the information sources that teachers draw on. The feeling of having broad and useful information and the willingness to participate in quality improvement programs are closely related. In conclusion, careful administration of feedback is to be viewed as an indispensable component of school efficiency studies. (DIPF/Orig.