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

Amissibility and Common Belief

The concept of ‘fully permissible sets ’ is defined by an algorithm that eliminate strategy subset . It is characterized as choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominate the latter on the sets of all opponent strategie or on the union of the choice sets that are deemed possible for the opponent. the concept refines the Dekel-Fudenberg procedure and captures aspects of forward induction.Admissibility; Denkel-Fudenberg; common belief;

Stochastic approximations and differential inclusions II: applications

We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaim, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine

Consistency of vanishing smooth fictitious play

We discuss consistency of Vanishing Smooth Fictitious Play, a strategy in the context of game theory, which can be regarded as a smooth fictitious play procedure, where the smoothing parameter is time-dependent and asymptotically vanishes. This answers a question initially raised by Drew Fudenberg and Satoru Takahashi.Comment: 17 page

Learning in games using the imprecise Dirichlet model

We propose a new learning model for finite strategic-form two-player games based on fictitious play and Walley’s imprecise Dirichlet model [P. Walley, Inferences from multinomial data: learning about a bag of marbles, J. Roy. Statist. Soc. B 58 (1996) 3–57]. This model allows the initial beliefs of the players about their opponent’s strategy choice to be near-vacuous or imprecise instead of being precisely defined. A similar generalization can be made as the one proposed by Fudenberg and Kreps [D. Fudenberg, D.M. Kreps, Learning mixed equilibria, Games Econ. Behav. 5 (1993) 320–367] for fictitious play, where assumptions about immediate behavior are replaced with assumptions about asymptotic behavior. We also obtain similar convergence results for this generalization: if there is convergence, it will be to an equilibrium

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)

Evolutionary games in the multiverse

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players. As long as we have only two strategies, many results from two player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions do no longer hold. For two player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players $\boldsymbol{d}$ with any number of strategies n, there can be at most (d-1)^(n-1) isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied for specific cases, e.g. public goods games or multiplayer stag hunts