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We study the generalised rock-paper-scissors game with five species whose organisms face local epidemic outbreaks. As an evolutionary behavioural survival strategy, organisms of one out of the species move in the direction with more enemies…

The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…

We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…

This paper applies a recently developed power allocation game in Li and Morse (2017) to study the countries' survival problem in networked international environments. In the game, countries strategically allocate their power to support the…

We study the problem of deciding the winner of reachability switching games for zero-, one-, and two-player variants. Switching games provide a deterministic analogue of stochastic games. We show that the zero-player case is NL-hard, the…

Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…

Aim: Present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of…

We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole…

We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the…

In this paper we consider how to evaluate survival distribution predictions with measures of discrimination. This is a non-trivial problem as discrimination measures are the most commonly used in survival analysis and yet there is no clear…

Binomial data with unknown sizes often appear in biological and medical sciences. The previous methods either use the Poisson approximation or the quasi-likelihood approach. A full likelihood approach is proposed by treating unknown sizes…

In this paper, we study the distribution of the number of internal equilibria of a multi-player two-strategy random evolutionary game. Using techniques from the random polynomial theory, we obtain a closed formula for the probability that…

We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…

We consider the game of Zombies and Survivors as introduced by Fitzpatrick, Howell, Messinger and Pike (2016) This is a variation of the game Cops and Robber where the zombies (in the cops' role) are of limited intelligence and will always…

Poker is one of the most popular card games, whose rational investigation represents also one of the major challenges in several scientific areas, spanning from information theory and artificial intelligence to game theory and statistical…

We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…

This study investigates the influence of lattice structure in evolutionary games. The snowdrift games is considered in networks with high clustering coefficients, that use four different strategy-updating. Analytical conjectures using pair…

We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…

Application of discrete-time survival methods for continuous-time survival prediction is considered. For this purpose, a scheme for discretization of continuous-time data is proposed by considering the quantiles of the estimated event-time…