The article presents a game-theoretic model of a multistage game with imperfect information War of Attrition, first investigated by John Maynard Smith, 1974. In this model, players (animals) fight for a resource (territory, sphere of influence, etc.), but are not aware of the adversary’s real capacity and can evaluate it after each stage of the fight. The fight consists of repeated iterations of one type of interaction. We suggest a model of the adaptive behavior of players based on dynamic programming and an evaluation method based on Bayesian updating. Thereby, we study the properties of non-homogeneous random walks in the space of parameters that represent the current number of the player’s wins and losses. The optimal rule for stopping the fight is determined for each player. The results of numerical experiments are reported.