These two equations can be viewed as a combination of behavior and strategy. $\mathcal N$ is a normal distribution with a mean of \(2a_{gridX}(\alpha_{sv}-\alpha_{M})\) or \(2a_{gridY}(\alpha_{sv}-\alpha_{M})\), and a standard deviation of \(\delta_x\) or \(\delta_y\), which are tuned according to the grid distance of the Markov transitional matrix. \(\alpha_{M}\) is given by the middle point of the transitional probability, which equals to 0.5 in this work. \(a_{gridX}\) and \(a_{gridY}\) are given by the shape of the transitional probability matrices. Ideally, the direction of fight or yield should be defined according to the gradient of risk-field \cite{Kolekar2020}. To simplify, the direction of fight is given by the direction of shortening the distance of the two subjects, and the direction of yield is vice versa. The transitional probability we use are shown in Figure \ref{244402}.