Abstract:To solve the problem that the current ambush game model has weak adaptability and low efficiency to actual demands, a new kind of ambush game model on a lattice is proposed. Considering the constraints of the ambush resources, the feasible strategy sets of the players are constructed. According to the differences of the defense degrees and the values of the columns, each column is given different weight and the corresponding payment function is constructed, and so the model of weighted ambush game on a lattice is established. The game theory problem is transformed into a constrained optimization problem. Solving the constrained optimization problem, the optimal value is obtained and converted into the value of the model, and so the optimal mixed strategy is also given. A military example validates that the model can comprehensively give a quantitative description of ambush game and so has a certain value of theory and application.