Repeated Sequential Prisoner's Dilemma: The Stackleberg Variant

Asia-Pacific Journal of Operational Research, Forthcoming

23 Pages Posted: 7 Mar 2014 Last revised: 29 Aug 2014

See all articles by Xinglong Qu

Xinglong Qu

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Zhigang Cao

Beijing Jiaotong University - School of Economics and Management

Yifen Mu

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Xiaoguang Yang

Chinese Academy of Sciences (CAS)

Date Written: February 24, 2014

Abstract

We study the Stackleberg variant of the repeated Sequential Prisoner’s Dilemma (SPD for short). The game goes in two stages, and the two players, the leader and the follower, are asymmetric in both stages. In the first stage of the game, the leader chooses a strategy (for the repeated SPD of the second stage), which is immediately known to the follower. In the second stage, they play repeated SPD: in each round the follower moves after observing the leader’s action.

Assuming complete rationality, we find some extraordinary properties of this model. (i) The (sub-game perfect) equilibrium payoff profile is unique, which lies on the corner of the region predicted by classical folk theorems: it is best for the leader and at the same time worst for the follower. (ii) The leader has simple optimal strategies that are one-step memory and stationary. These features are in great contrast with classical results, where either uniqueness cannot be guaranteed and equilibrium strategies are often quite complicated, or bounded rationality is required. Although full cooperation, i.e. the outcome is always (cooperate, cooperate), is not attainable in our model, at least a half of the optimal social welfare can be guaranteed. We also do a non-equilibrium analysis which makes the usual equilibrium analysis more convincing.

Keywords: Prisoner's Dilemma, sequential repeated game, folk theorem, Markov decision process

JEL Classification: C72

Suggested Citation

Qu, Xinglong and Cao, Zhigang and Mu, Yifen and Yang, Xiaoguang, Repeated Sequential Prisoner's Dilemma: The Stackleberg Variant (February 24, 2014). Asia-Pacific Journal of Operational Research, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2405413 or http://dx.doi.org/10.2139/ssrn.2405413

Xinglong Qu

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55, Haidian District
Beijing, 100080, P.R., Beijing 100080
China

Zhigang Cao (Contact Author)

Beijing Jiaotong University - School of Economics and Management ( email )

China

Yifen Mu

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55, Haidian District
Beijing, 100080, P.R., Beijing 100080
China

Xiaoguang Yang

Chinese Academy of Sciences (CAS) ( email )

52 Sanlihe Rd.
Datun Road, Anwai
Beijing, Xicheng District 100864
China

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