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We perform an exploratory data analysis on a data-set for the top 16 professional darts players from the 2019 season. We use this data-set to fit player skill models which can then be used in dynamic zero-sum games (ZSGs) that model real-world matches between players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial (DM) model that overcomes limitations in the data. Specifically we introduce two DM-based skill models where the first model borrows strength from other darts players and the second model borrows strength from other regions of the dartboard. We find these DM-based models outperform simpler benchmark models with respect to Brier and Spherical scores, both of which are proper scoring rules. We also show in ZSGs settings that the difference between DM-based skill models and the simpler benchmark models is practically significant. Finally, we use our DM-based model to analyze specific situations that arose in real-world darts matches during the 2019 season. [ABSTRACT FROM AUTHOR]

This paper investigates the main features of the Genoese insurance market between 1564 and 1572, thanks to the analysis of an unpublished tax register that preserves all insurance policies drafted in Genoa in that period. Marine insurance, intended as an archetypical risk-shifting technique, is probably the oldest financial instrument intended solely to protect against the economic consequences of commercial losses. Conventional premium insurance was developed as a tool to transfer risk during the commercial revolution of the late middle ages. This development was first led by Italian cities, among whom Genoa played a key role. However, Genoese operators involved in the insurance sectors, which belonged almost exclusively to the patrician families ruling the republic, acted as a mutual "risk-community" in a semi-closed market: a sort of "syndicate". They shared among them the risks of maritime routes calling at the port of Genoa. Insurance was a zero-sum game, with low losses and gains that did not allow a true single-sector specialisation. [ABSTRACT FROM AUTHOR]

In this paper, we study the stochastic zero-sum differential game in finite horizon in a general case. We first prove that the BSDE associated with a specific generator (the Hamiltonian function for the game) has a unique solution. Then we characterize the value function as that solution to prove the existence of a saddle point for the game. Finally, in the Markovian framework, we show that the value function is the unique viscosity solution for the related partial differential equation. [ABSTRACT FROM AUTHOR]

The concept of forming harmonious coalitions is introduced to both classical and quantum symmetric cooperative games. In both the cases, players are motivated to form coalitions. Also, the main feature of the cooperative game is conserved. [ABSTRACT FROM AUTHOR]