The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector

We resume our discussion of the new orbifold-string theories of permutation-type, focusing in the present series on the algebraic formulation of the general bosonic prototype and especially the target space-times of the theories. In this first paper of the series, we construct one twisted BRST system for each cycle $j$ in each twisted sector $\sigma$ of the general case, verifying in particular the previously-conjectured algebra $[Q_{i}(\sigma),Q_{j}(\sigma)]_{+} =0$ of the BRST charges. The BRST systems then imply a set of extended physical-state conditions for the matter of each cycle at cycle central charge $\hat{c}_{j}(\sigma)=26f_{j}(\sigma)$ where $f_{j}(\sigma)$ is the length of cycle $j$.Comment: 31 page

Infinite Dimensional Free Algebra and the Forms of the Master Field

We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and the dual basis is closely related to the planar connected parts. This leads to a number of free-algebraic forms of the master field including an algebraic derivation of the Gopakumar-Gross form. For action theories, these forms of the master field immediately give a number of new free-algebraic packagings of the planar Schwinger-Dyson equations.Comment: 39 pages. Expanded historical remark

On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors

Including world-sheet orientation-reversing automorphisms in the orbifold program, we recently reported the twisted operator algebra and twisted KZ equations in each open-string sector of the general WZW orientation orbifold. In this paper we work out the corresponding classical description of these sectors, including the {\it WZW orientation-orbifold action} -- which is naturally defined on the solid half cylinder -- and its associated WZW orientation-orbifold branes. As a generalization, we also obtain the {\it sigma-model orientation-orbifold action}, which describes a much larger class of open-string orientation-orbifold sectors. As special cases, this class includes twisted open-string {\it free boson} examples, the open-string WZW sectors above and the open-string sectors of the {\it general coset orientation orbifold}. Finally, we derive the {\it orientation- orbifold Einstein equations}, in terms of twisted Einstein tensors -- which hold when the twisted open-string sigma-model sectors are 1-loop conformal.Comment: 77 pages, typos correcte

A Basic Class of Twisted Open WZW Strings

Recently, Giusto and Halpern reported the open-string description of a certain basic class of untwisted open WZW strings, including their associated non-commutative geometry and open-string KZ equations. In this paper, we combine this development with results from the theory of current-algebraic orbifolds to find the open-string description of a corresponding basic class of {\it twisted} open WZW strings, which begin and end on different WZW branes. The basic class of twisted open WZW strings is in 1-to-1 correspondence with the twisted sectors of all closed-string WZW orbifolds, and moreover, the basic class can be decomposed into a large collection of open-string WZW orbifolds. At the classical level, these open-string orbifolds exhibit new {\it twisted non-commutative geometries}, and we also find the relevant {\it twisted open-string KZ equations} which describe these orbifolds at the quantum level. In a related development, we also formulate the closed-string description (in terms of twisted boundary states) of the {\it general} twisted open WZW string.Comment: 65 page

Interactive Unawareness Revisited

We analyze a model of interactive unawareness introduced by Heifetz, Meier and Schipper (HMS). We consider two axiomatizations for their model, which capture different notions of validity. These axiomatizations allow us to compare the HMS approach to both the standard (S5) epistemic logic and two other approaches to unawareness: that of Fagin and Halpern and that of Modica and Rustichini. We show that the differences between the HMS approach and the others are mainly due to the notion of validity used and the fact that the HMS is based on a 3-valued propositional logic.Comment: 26 page

A decision-theoretic approach to reliable message delivery

We argue that the tools of decision theory need to be taken more seriously in the specification and analysis of systems. We illustrate this by considering a simple problem involving reliable communication, showing how considerations of utility and probability can be used to decide when it is worth sending heartbeat messages and, if they are sent, how often they should be sent.Comment: This is the full version of a paper that appears in the Proceedings of the 12th International Symposium on Distributed Computing, 1998, pp. 89-1

Extensive Games with Possibly Unaware Players

Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they may not be aware of moves that they and other agents can make. We show how such games can be represented; the key idea is to describe the game from the point of view of every agent at every node of the game tree. We provide a generalization of Nash equilibrium and show that every game with awareness has a generalized Nash equilibrium. Finally, we extend these results to games with awareness of unawareness, where a player i may be aware that a player j can make moves that i is not aware of, and to subjective games, where payers may have no common knowledge regarding the actual game and their beliefs are incompatible with a common prior.Comment: 45 pages, 3 figures, a preliminary version was presented at AAMAS0

Great Expectations. Part I: On the Customizability of Generalized Expected Utility

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker's beliefs are represented by plausibility measures, and the decision maker's tastes are represented by general (i.e.,not necessarily real-valued) utility functions. We show that every agent, ``rational'' or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage's postulates corresponds to constraints on GEU.Comment: Preliminary version appears in Proc. 18th International Joint Conference on AI (IJCAI), 2003, pp. 291-29

Great Expectations. Part II: Generalized Expected Utility as a Universal Decision Rule

Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent essentially all other decision rules.Comment: Preliminary version appears in Proc. 18th International Joint Conference on AI (IJCAI), 2003, pp. 297-30