隨機狀態變換下的動態說服

Abstract

我們考慮兩個玩家的動態貝式說服模型，該兩名玩家為長期玩家(long-lived players)，並假設狀態變換為馬可夫過程，我們考慮玩家使用馬可夫策略(Markov strategy)，並討論了有限期和無窮期的賽局。我們發現在有限期時，這個賽局有唯一的馬可夫完美均衡(Markov perfect equilibrium)，並且雙方的目標價值函數為分段線性，並且說服者的目標價值函數為凹函數，而被說服者為凸函數。無限期時，我們發現定態馬可夫均衡不總是存在，在特定的折現和馬可夫狀態矩陣下，目標價值函數的變動具有週期性。

A patient with some symptoms comes into a clinical room for cure. The doctor provides test to persuade the patient choosing treatment to cure the disease or wait for further information. However, the diseases has states transition as time goes by and doctor and patient have different interests about treatment. We study this dilemma in dynamic persuasion model with stochastic state transition in Markov strategy. We find that there is a unique Markov perfect equilibrium in finite periods. In infinite periods, the value functions converge if we rule out finite period convergent case in stopping game setting. It does not hold in non-stopping case.