Extremal Pure Strategies and Monotonicity in Repeated Games
- 136 Downloads
The recent development of computational methods in repeated games has made it possible to study the properties of subgame-perfect equilibria in more detail. This paper shows that the lowest equilibrium payoffs may increase in pure strategies when the players become more patient and this may cause the set of equilibrium paths to be non-monotonic. A numerical example is constructed such that a path is no longer equilibrium when the players’ discount factors increase. This property can be more easily seen when the players have different time preferences, since in these games the punishment strategies may rely on the differences between the players’ discount factors. A sufficient condition for the monotonicity of equilibrium paths is that the lowest equilibrium payoffs do not increase, i.e., the punishments should not become milder.
KeywordsRepeated games Minimum payoff Monotonicity Equilibrium path Unequal discount factors Subgame perfection
The author thanks the reviewers for the valuable suggestions for improving the paper, and acknowledges funding from Emil Aaltosen Säätiö through Post doc -pooli.
- Berg, K. (2015). Elementary subpaths in discounted stochastic games. Dynamic Games and Applications. doi: 10.1007/s13235-015-0151-5.
- Berg, K., & Kitti, M. (2015). Equilibrium paths in discounted supergames. Working paper. http://sal.aalto.fi/publications/pdf-files/mber09b.
- Berg, K., & Kärki, M. (2014a). An algorithm for finding the minimal pure-strategy subgame-perfect equilibrium payoffs in repeated games. Working paper.Google Scholar
- Berg, K., & Kärki, M. (2014b). How patient the players need to be to get all the relevant payoffs in the symmetric \(2\times 2\) supergames? Working paper.Google Scholar
- Berg, K., & Schoenmakers, G. (2014). Construction of randomized subgame-perfect equilibria in repeated games. Working paper.Google Scholar
- Burkov, A., & Chaib-draa, B. (2010). An approximate subgame-perfect equilibrium computation technique for repeated games. In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence (pp. 729–736).Google Scholar
- Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge, MA: The MIT Press.Google Scholar
- Salcedo, B., & Sultanum, B. (2012). Computation of subgame-perfect equilibria of repeated games with perfect monitoring and public randomization. Working paper.Google Scholar