We give a general analysis of a class of pairs of positive self-adjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h-10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator-(d2/A2) + x2 on L2(R, dx) and let B = 1 x 1-s. The eigenvectors and eigenvalues of A are, of course, well known to be the Hermite functions, H,(x), n = 0, l,... and E, = 2n + 1. Klauder then considers the eigenvectors of A + XB (A> 0) by manipulations with the ordinary differential equation (we consider the domain questions, which Klauder ignores, below). He finds that the eigenvalues E,(X) and eigenvectors &(A) do not converge to 8, and H, but rather AO) + (en 4 Ho+, J%(X)-+ gn+1 I n = 0, 2,..., We wish to discuss in detail the general phenomena which Klauder has uncovered. We freely use the techniques of quadratic forms and strong resolvent convergence; see e.g. [3], [5]. Once one decides to analyze Klauder’s phenomenon in the language of quadratic forms, the phenomenon is quite easy to understand and control. In fact, the theory is implicit in Kato’s book [3, VIII.31.

Trust is a judgement of unquestionable utility — as humans we use it every day of our lives. However, trust has suffered from an imperfect understanding, a plethora of definitions, and informal use in the literature and in everyday life. It is common to say “I trust you, ” but what does that mean? This thesis provides a clarification of trust. We present a formalism for trust which provides us with a tool for precise discussion. The formalism is implementable: it can be embedded in an artificial agent, enabling the agent to make trust-based decisions. Its applicability in the domain of Distributed Artificial Intelligence (DAI) is raised. The thesis presents a testbed populated by simple trusting agents which substantiates the utility of the formalism. The formalism provides a step in the direction of a proper understanding and definition of human trust. A contribution of the thesis is its detailed exploration of the possibilities of future work in the area. Summary 1. Overview This thesis presents an overview of trust as a social phenomenon and discusses it formally. It argues that trust is: • A means for understanding and adapting to the complexity of the environment. • A means of providing added robustness to independent agents. • A useful judgement in the light of experience of the behaviour of others. • Applicable to inanimate others. The thesis argues these points from the point of view of artificial agents. Trust in an artificial agent is a means of providing an additional tool for the consideration of other agents and the environment in which it exists. Moreover, a formalisation of trust enables the embedding of the concept into an artificial agent. This has been done, and is documented in the thesis. 2. Exposition There are places in the thesis where it is necessary to give a broad outline before going deeper. In consequence it may seem that the subject is not receiving a thorough treatment, or that too much is being discussed at one time! (This is particularly apparent in the first and second chapters.) To present a thorough understanding of trust, we have proceeded breadth first in the introductory chapters. Chapter 3 expands, depth first, presenting critical views of established researchers.

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We review studies conducted by ourselves and coauthors that document a "self-serving " bias in judgments of fairness and demonstrate that the bias is an important cause of impasse in negotiations. We discuss experimental evidence showing that (a) the bias causes impasse; (b) it is possible to reduce impasses by debiasing bargainers; and (c) the bias results from selective evaluation of information. We also review results from a field study of negotiations between teachers ' unions and school boards in Pennsylvania that both documents the fairness bias in a naturalistic setting and demonstrates its impact on strikes. A major unsolved riddle facing the social sciences is the cause of impasse in negotiations. The consequences of impasse are evident in the amount of private and public resources spent on civil litigation, the costs of labor unrest, the psychic and pecuniary wounds of domestic strife, and in clashes between religious, ethnic and regional groups. Impasses in these settings are not only pernicious, but somewhat paradoxical since negotiations typically unfold over long periods of time, offering ample opportunities for interaction between the parties. Economists, and more specifically, game theorists, typically attribute delays in settlement to incomplete information. Bargainers possess private information about factors such as their alternatives to negotiated agreements and costs to delay, causing the bargainers to be mutually uncertain about the other side's reservation value. Uncertainty produces impasse because bargainers use costly delays to signal to

This paper is an exploratory and tentative study of the specific differentia of medical care as the object of normativeconomics. It is contended here, on the basis of comparison of obvious characteristics of the medical-care industry with the norms of welfare economics,

It is possible to design cooperative work tools based only on "common sense " and good intuitions. But the history of technology is replete with examples of good theories greatly aiding the development of useful technology. Where, then, might we look for theories to help us design computer-supported cooperative work tools? In this paper, we will describe one possible perspective-the interdisciplinary study of coordination-that focuses, in part, on how people work together now and how they might do so differently with new information technologies. In one sense, there is little that is new about the study of coordination. Many different disciplines--including computer science, sociology, political science, management science, systems theory, economics, linguistics, and psychology--have all dealt, in one way or another, with fundamental questions about coordination. Furthermore, several previous writers have suggested that theories about coordination are likely to be important for designing cooperative work tools (e.g., Holt8], (Wino86]). We hope to suggest here, however, that the potential for fruitful interdisciplinary connections concerning coordination is much greater than has as yet been widely

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Automated intelligent agents inhabiting a shared environmentmust coordinate their activities. Cooperation { not merely coordination { may improve the performance of the individual agents or the overall behavior of the system they form. Research in Distributed Arti cial Intelligence (DAI) addresses the problem of designing automated intelligent systems which interact e ectively. DAI is not the only eld to take on the challenge of understanding cooperation and coordination. There are a variety of other multi-entity environments in which the entities coordinate their activity and cooperate. Among them are groups of people, animals, particles, and computers. We argue that in order to address the challenge of building coordinated and collaborated intelligent agents, it is bene cial to combine AI techniques with methods and techniques from a range of multi-entity elds, such as game theory, operations research, physics and philosophy. To support this claim, we describe some of our projects, where we have successfully taken an interdisciplinary approach. We demonstrate the bene ts in applying multi-entity methodologies and show the adaptations, modi cations and extensions necessary for solving the DAI problems.