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

Flows and Decompositions of Games: Harmonic and Potential Games

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to "nearby" games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games

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

The effects of entry on incumbent innovation and productivity

How does firm entry affect innovation incentives in incumbent firms? Microdata suggest that there is heterogeneity across industries. Specifically, incumbent productivity growth and patenting is positively correlated with lagged greenfield foreign firm entry in technologically advanced industries, but not in laggard industries. In this paper we provide evidence that these correlations arise from a causal effect predicted by Schumpeterian growth theory—the threat of technologically advanced entry spurs innovation incentives in sectors close to the technology frontier, where successful innovation allows incumbents to survive the threat, but discourages innovation in laggard sectors, where the threat reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro panel data for the United Kingdom. We control for the endogeneity of entry by exploiting major European and U.K. policy reforms, and allow for endogeneity of additional factors. We complement the analysis for foreign entry with evidence for domestic entry and entry through imports