In their book, Gigerenzer and Selten (2001) described human being as an organism that adaptively reacts to its environment by selecting ecologically rational heuristics that are contingent on task demands; that is, adaptivity assumption. Empirical evidence of the adaptivity assumption is, however, mixed. In this paper, I review prior experiments related to testing the adaptivity assumption and criticize some of the past findings. From this criticism, the research questions are formed. The research objective of this paper is to test whether or not people choose their decision strategy as a reaction to environmental conditions. In this dissertation, the use of the take-the-best (TTB) heuristic is investigated for different treatments, which are information structure, information cost, and social rationality. Participants go through 180 trials of a pair comparison task. Using the proportion of TTB trials as a dependent variable, three hypotheses regarding the effects of three treatments are tested. The results of the experiments indicate that only the social rationality is a significant factor in promoting the TTB heuristic. Besides the test of the hypothesis, an exploratory analysis of participants’ data is presented.

A consequence of the Hahn-Banach theorem is the classical bipolar theorem which states that the bipolar of a subset of a locally convex vector pace equals its closed convex hull. The space $\L$ of real-valued random variables on a probability space $\OF$ equipped with the topology of convergence in measure fails to be locally convex so that - a priori - the classical bipolar theorem does not apply. In this note we show an analogue of the bipolar theorem for subsets of the positive orthant $\LO$, if we place $\LO$ in duality with itself, the scalar product now taking values in $[0, \infty]$. In this setting the order structure of $\L$ plays an important role and we obtain that the bipolar of a subset of $\LO$ equals its closed, convex and solid hull. In the course of the proof we show a decomposition lemma for convex subsets of $\LO$ into a "bounded" and "hereditarily unbounded" part, which seems interesting in its own right. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

In this paper we study the behavior of boundedly rational agents in a two good economy where trading is costly with respect to time. All individuals have a fixed time budget and may spend time for the production of good one, the production of good two and trading. They update their strategies, which determine their time allocation, according to a simple imitation type learning rule with noise. In a setup with two different type of agents with different production technologies we show by the means of simulations that both direct trade and trade via mediators who specialize in trading can emerge. We can also observe the transition from a pure production economy via direct trade to an economy with mediated trade. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Many domains, such as emergency assistance, agriculture, construction, and planetary exploration, will increasingly require effective coordination of teams of robots and humans to accomplish a collection of spatially distributed heterogeneous tasks. Such coordination problems range from those that require loosely coordinated teams in which agents independently perform their assigned tasks, to those that require tightly coordinated teams where all actions of the team members need to be tightly synchronized. The scenarios of interest to this thesis lie between these two extremes, where some tasks are independent and others are related by constraints such as precedence, simultaneity, or proximity. These constraints may be a result of different factors including the complementary capabilities of different types of agents which require them to cooperate to achieve certain goals. The manner in which the constraints are satisfied influences the overall utility of the team. This thesis explores the problem of task allocation, scheduling, and routing for heterogeneous teams with such cross-schedule dependencies. We first describe and position this coordination problem in the larger space of multi-robot task allocation problems and propose an enhanced taxonomy for this space of problems. Recognizing that solution quality is important in many domains, we then present a mathematical programming approach to computing a bounded-optimal solution to the task allocation, scheduling and routing problem with cross-schedule dependencies. Specifically, we present a branch-and-price algorithm operating on a set-partitioning formulation of the problem, with side constraints. This bounded optimal “anytime” algorithm computes progressively better solutions and bounds, until it eventually terminates with the optimal solution. By examining the behavior of this algorithm, we gain insight into the impact on problem difficulty of various problem features, particularly different types of cross-schedule dependencies. Lastly, the thesis presents a flexible execution strategy for the resulting team plans with cross-schedule dependencies, and results demonstrating the approach on a team of indoor robots

Adaptive agent models are supposed to result in the same limit behavior as models with perfectly rational agents. In this article we show that this claim cannot by accepted in general, even in a simple capital market model, where the agents apply sample autocorrelation learning to perform their forecasts. By applying this learning algorithm, the agents use sample means, the sample autocorrelation coefficient, and the sample variances of prices to predict the future prices, and to determine the demand for the risky asset. Therefore, even if the agents are not perfectly rational, we require that the agents' forecasts are consistent with the underlying information. In this article a sufficient condition for convergence is derived analytically, and checked by means of simulations. The price sequence as well as the sequence of parameters - estimated by means of sample autocorrelation learning - converge, if the initial value of the price sequence is sufficiently close to the steady-state equilibrium, and a random variable derived from the dividend process is not too volatile to skip the price trajectory out of the attracting region. Therefore, the market price can even diverge, and the region of convergence could become very small depending on the underlying parameters. Thus, divergence of the price sequences is not a pathological example, since it possibly occurs over a wide range of parameters. Therefore, the often claimed coincidence of adaptive agents models and ration agent models cannot be observed even in a simple capital market model. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Zugl.: Bremen, Univ., Diss., 2007

Abstract In this thesis, we will study very small full trios and full AFLs inside the family of context-free languages. Especially, we are interested in the existence of the smallest nontrivial full trios and full AFLs. This is an old research subject, and it has not been studied much since the 1970s. A conjecture by Autebert et al. states that there does not exist a nontrivial minimal full trio inside the family of context-free languages (2) (see also (1)). First, we will show that there does not exist a nontrivial minimal full trio or a nontrivial minimal full AFL with respect to the bounded context-free languages. This result solves another old conjecture stated by Autebert et al. (1). Then we will try to generalize our result to also concern unbounded context-free languages. We will make some progress, but the problem still remains open.

Distributed real-time database systems demand consistency and timeliness. One approach for this problem is eventual consistency which guarantees local consistency within predictable time. Global consistency can be reached by best effort mechanisms but for some scenarios, e.g. an alarm signal, this may not be suffcient. Bounded delay replication, which provides global consistency in bounded time, ensures that after the local commit of a transaction updates are propagated to and integrated at any remote node within bounded time. The DRTS group at the University of Skövde is working on a project called DeeDS, which is a distributed real-time database prototype. In this prototype, eventual consistency with as soon as possible (ASAP) replication is implemented. The goal of this dissertation is to further develop replication in this prototype in coexistence to the existing eventual consistency which implies the extension of both the theory and the implementation. The main issue with bounded time replication is to make all parts, which are involved in the replication process predictable and simultaneously support eventual consistency with as soon as possible replication.

The main study of this thesis is the holomorphic functional calculi for three classes of unbounded operators: sectorial, strip-type and half-plane. The functional calculus for sectorial operators was introduced by McIntosh as an extension of the Riesz-Dunford model for bounded operators. More recently Haase has developed an abstract framework which incorporates analogous constructions for strip-type and half-plane operators. These operators are of interest since they arise naturally as generators of C₀-(semi)groups. The theory of bounded H^∞-calculus for sectorial operators is well established and it has been found to have many applications in operator theory and parabolic evolution equations. We survey these known results, first on Hilbert space and then on general Banach space. Our main goal is to fill the gaps in the parallel theory for strip-type operators. Whilst some of this can be deduced by taking exponentials and applying known results for sectorial operators, in general this is insu_cient to obtain our desired results and so we pursue an independent approach. Starting on Hilbert space, we broaden known characterisations of the bounded H^∞-calculus for strip-type operators by introducing a notion of absolute calculus which is an analogue to the established notion for the sectorial case. Moving to general Banach space, we build on the work of Vörös, broadening his characterisation for strip-type operators in terms of weak integral estimates by introducing a new, but equivalent, notion of the bounded H^∞-calculus, which we call the m-bounded calculus. We also demonstrate that these characterisations fail for half-plane operators and instead present a weaker form of the bounded H-calculus which is more natural for these operators. This allows us to obtain new and simple proofs of well known generation theorems due to Gomilko and Shi-Feng, with extensions to polynomially bounded semigroups. The connection between the bounded H-calculus of semigroup generators and polynomial boundedness of their associated Cayley Transforms is also explored. Finally we present a series of results on sums of operators, in connection with maximal regularity. We also establish stability results for the bounded H^∞-calculus for strip-type operators by showing it is preserved under suitable bounded perturbations, which at time requires further assumptions on the underlying Banach space. This relies heavily on intermediate characterisations of the bounded H^∞-calculus due to Kalton and Weis.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22980号 / 理博第4657号 / 新制||理||1669(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 長谷川 真人, 准教授 照井 一成, 准教授 河村 彰星 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM