Kosuke Toda

Kosuke Toda, Naomi Kuze, Toshimitsu Ushio

To maintain blockchain-based services with ensuring its security, it is an important issue how to decide a mining reward so that the number of miners participating in the mining increases. We propose a dynamical model of decision-making for miners using an evolutionary game approach and analyze the stability of equilibrium points of the proposed model. The proposed model is described by the 1st-order differential equation. So, it is simple but its theoretical analysis gives an insight into the characteristics of the decision-making. Through the analysis of the equilibrium points, we show the transcritical bifurcations and hysteresis phenomena of the equilibrium points. We also design a controller that determines the mining reward based on the number of participating miners to stabilize the state that all miners participate in the mining. Numerical simulation shows that there is a trade-off in the choice of the design parameters.

Kosuke Toda, Masakiyo Teranishi, Keisuke Kushiro et al.

With the development of measurement technology, data on the movements of actual games in various sports can be obtained and used for planning and evaluating the tactics and strategy. Defense in team sports is generally difficult to be evaluated because of the lack of statistical data. Conventional evaluation methods based on predictions of scores are considered unreliable because they predict rare events throughout the game. Besides, it is difficult to evaluate various plays leading up to a score. In this study, we propose a method to evaluate team defense from a comprehensive perspective related to team performance by predicting ball recovery and being attacked, which occur more frequently than goals, using player actions and positional data of all players and the ball. Using data from 45 soccer matches, we examined the relationship between the proposed index and team performance in actual matches and throughout a season. Results show that the proposed classifiers predicted the true events (mean F1 score $>$ 0.483) better than the existing classifiers which were based on rare events or goals (mean F1 score $<$ 0.201). Also, the proposed index had a moderate correlation with the long-term outcomes of the season ($r =$ 0.397). These results suggest that the proposed index might be a more reliable indicator rather than winning or losing with the inclusion of accidental factors.

Kosuke Toda, Naomi Kuze, Toshimitsu Ushio

It is an important decision-making problem for a miner in the blockchain networks if he/she participates in the mining so that he/she earns a reward by creating a new block earlier than other miners. We formulate this decision-making problem as a noncooperative game, because the probability of creating a block depends not only on one's own available computational resources, but also those of other miners. Through theoretical and numerical analyses, we show a hysteresis phenomenon of Nash equilibria depending on the reward and a jump phenomenon of miner decisions by a slight change in reward. We also show that the reward for which miners decide not to participate in the mining becomes smaller as the number of miners increases.