McTaggart’s paradox and his A-theory and B-theory are basic notions in the contemporary philosophy of time. It is well known that the paradox was introduced by McTaggart’s paper called “The Unreality of Time” published in 1908, so that it has a one-hundred-year history. As for A-theory and B-theory, in contrast, McTaggart himself didn’t consider both of them at all. The notions of A-theory and B-theory came much later, 60 years after the paradox. Moreover, they had not been as popularized as they are today until quite recently, at least after the 1990s. This paper aims to trace the origin of the notions of A-theory and B-theory and show how the debates behind them, especially objections to “spatialising time,” form the notions.

Since its inception, analytic philosophy has failed to attain dominance in Japan. However, the 21st century has seen analytic philosophy gain traction among Japanese philosophers. This paper, which examines the status quo of analytic philosophy in Japan since 2000, consists of two parts. The first part deals primarily with organizations—specifically, relevant associations, journals, conferences, universities, and publishers are illustrated. The second part explores key works in each area—namely, philosophy of science, philosophy of language, philosophy of logic and mathematics, philosophy of mind, and metaphysics. Key works in other areas are also briefly addressed.

Imitation is simple behavior which uses successful actions of others in order to deal with one’s own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or not, game theory is suitable for specifying situations where imitation can be successful. One of the concepts describing successfulness of imitation in repeated two-player symmetric games is unbeatability. For infinitely repeated two-player symmetric games, a necessary and sufficient condition for some imitation strategy to be unbeatable was specified. However, situations where imitation can be unbeatable in multi-player games are still not clear. In order to analyze successfulness of imitation in multi-player situations, here we introduce a class of totally symmetric games called unexploitable games, which is a natural extension of two-player symmetric games without exploitation cycles. We then prove that, for infinitely repeated unexploitable games, there exist unbeatable imitation strategies. Furthermore, we also prove that, for infinitely repeated non-trivial unexploitable games, there exist unbeatable zero-determinant strategies, which unilaterally enforce some relationships on payoffs of players. These claims are demonstrated in the public goods game, which is the simplest unexploitable game. These results show that there are situations where imitation is unbeatable even in multi-player games.

We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the oppo-nent in the repeated prisoners' dilemma game. We provide a necessary condi-tion for memory-two deterministic strategies to form symmetric equilibria. We then provide three examples of memory-two deterministic strategies which form symmetric mutual reinforcement learning equilibria. We also prove that mu-tual reinforcement learning equilibria formed by memory-two strategies are also mutual reinforcement learning equilibria when both players use reinforcement learning of memory-n strategies with n > 2.

Zero-determinant strategies are memory-one strategies in repeated　games which unilaterally enforce linear relations between expected payoffs of　players. Recently, the concept of zero-determinant strategies was extended　to　the class of memory-n strategies with n _ 1, which enables more compli-cated control of payoffs by one player. However, what we can do by　memory-n　zero-determinant strategies is still not clear. Here, we show that memory-n　zero-determinant strategies in repeated games can be used to control condi-tional expectations of payoffs. Equivalently, they can be used to control ex-pected payoffs in biased ensembles, where a history of action pro_les with large　value of bias function is more weighted. Controlling conditional expectations　of payoffs is useful for strengthening zero-determinant strategies, because play-ers can choose conditions in such a way that only unfavorable action pro_les　to one player are contained in the conditions. We provide several examples　of memory-n zero-determinant strategies in the repeated prisoner's dilemma　game. We also explain that a deformed version of zero-determinant strategies　is easily extended to the memory-n case.

Zero-determinant strategies are a class of memory-one strategies in repeated games which unilaterally enforce linear relationships between payoffs. It has long been unclear for what stage games zero-determinant strategies exist. We provide a necessary and sufficient condition for the existence of zero-determinant strategies. This condition can be interpreted as the existence of two different actions which unilaterally adjust the total value of a linear combination of payoffs. A relation between the class of stage games where zero-determinant strategies exist and other class of stage games is also provided.

The quadratic unconstrained binary optimization (QUBO) problem is categorized as an NP-hard combinatorial optimization problem. The variable neighborhood search (VNS) algorithm is one of the leading algorithms used to solve QUBO problems. As neighborhood structure change is the central concept in the VNS algorithm, the design of the neighborhood structure is crucial. This paper presents a modified VNS algorithm called "B-VNS", which can be used to solve QUBO problems. A binomial trial was used to construct the neighborhood structure, and this was used with the aim of reducing computation time. The B-VNS and VNS algorithms were tested on standard QUBO problems from Glover and Beasley, on standard max-cut problems from Helmberg-Rendl, and on those proposed by Burer, Monteiro, and Zhang. Finally, Mann-Whitney tests were conducted using α = 0.05, to statistically compare the performance of the two algorithms. It was shown that the B-VNS and VNS algorithms are able to provide good solutions, but the B-VNS algorithm runs substantially faster. Furthermore, the B-VNS algorithm performed the best in all of the max-cut problems, regardless of problem size, and it performed the best in QUBO problems, with sizes less than 500. The results suggest that the use of binomial distribution, to construct the neighborhood structure, has the potential for further development.