On the Approximation Performance of Fictitious Play in Finite Games

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essentially matching upper bound of 1/2 - O(1/n)

SPLENIC HOMOTRANSPLANTATION.

During the past 12 months, five clinical whole-organ splenic homotransplantations have been carried out with the objective of providing active immunologic tissue for the recipient patients. In one case with hypogammaglobulinemia, it was hoped that the transplanted tissue would alleviate a state of immunologic deficiency. In the other four, all of whom had terminal malignancies, the purpose was to superimpose a state of altered immunologic reactivity upon the host in the hope of thereby suppressing the inexorable growth of the neoplasms. As will be described, these procedures can now be judged in each instance to have been without benefit. Nevertheless, full documentation of the cases seems justified not only because of the many implications of transplantation of immunologically competent tissue, but also because of the potentially important observations made during the care of these patients. In addition, a full account will be presented of the supporting canine studies of splenic homotransplantation, inasmuch as many of the principles of clinical therapy and investigation derived from prior observations in the dog. The fact that it is possible to obtain viable splenic homografts in the dog for as long as two-thirds of a year without the production of runt disease or other harmful effects may have application in future research on bone marrow, other lymphoid, or hepatic homografts

Game Theory Models for Multi-Robot Patrolling of Infraestructures

Abstract This work is focused on the problem of performing multi‐robot patrolling for infrastructure security applications in order to protect a known environment at critical facilities. Thus, given a set of robots and a set of points of interest, the patrolling task consists of constantly visiting these points at irregular time intervals for security purposes. Current existing solutions for these types of applications are predictable and inflexible. Moreover, most of the previous centralized and deterministic solutions and only few efforts have been made to integrate dynamic methods. Therefore, the development of new dynamic and decentralized collaborative approaches in order to solve the aforementioned problem by implementing learning models from Game Theory. The model selected in this work that includes belief‐based and reinforcement models as special cases is called Experience‐Weighted Attraction. The problem has been defined using concepts of Graph Theory to represent the environment in order to work with such Game Theory techniques. Finally, the proposed methods have been evaluated experimentally by using a patrolling simulator. The results obtained have been compared with previous availabl

Lymphocyte Culture: Induction of Colonies by Conditioned Medium from Human Lymphoid Cell Lines

It has been shown that macrophage and granulocyte colonies can be induced m semisolid agar (1-3) in the presence of substances termed colony-stimulating factors (CSF), which are released predominantly by monocytes (4). However, attempts to induce formation of lymphoid colonies with CSF have so far proved unsuccessful. In the mouse, B lymphoid colonies are formed in the presence of 2-mercaptoethanol (5), and T lymphoid colonies can be induced with the plant lectins phytohemagglutinin (PHA) and concanavalin A (6). T lymphoid colonies can also be established from human peripheral blood lymphocytes in the presence of PHA (7-9), whereas with pokeweed mitogen mixed T and B lymphoid colonies are formed (9). Established human lymphoid cell lines multiply spontaneously in the absence of plant lectins or mercaptoethanol, and it seemed possible that such cells might release growth-stimulating substances into the culture medium. We have therefore investigated the ability of conditioned medium (CM) obtained from lymphoid cell lines to induce normal human peripheral blood lymphocytes (PBL) to form lymphoid colonies in agar