Section 5: Repeated Games

Key Learning Points

• Introduce the concepts and representations of repeated games: what happens when a simple normal-form game such as Prisoner’s Dilemma is repeatedly infinitely?
• Explain the Folk Theorem.
• Introduce the concepts of bounded rationality and finite-state automata (Moore machine), and machine game.

Activities

1. Read Sections 6.1 of Chapter 6 of the textbook.
2. Watch the following videos on YouTube:
   1. Repeated Games
   2. Infinitely Repeated Games: Utility
   3. Equilibria of Infinitely Repeated Games
3. Select and complete one of the following problems:
   1. The battle of the sexes game, seen in Figure 3.8 of the text, is a classic coordination game in which the players must somehow coordinate to agree upon one of the Nash equilibria. These problems are solved by populations who adopt a social law after some trial and error adaptation phase. For example, in Canada people drive on the right side of the road, while in England they drive on the left. Both solutions are equally valid. Implement a NetLogo program where each patch repeatedly engages in a battle of the sexes game with one of its neighbours, chosen at random. Then try to come up with some adaptation strategy which the agents could use so that the population will quickly converge to an equilibrium. Simple adaptation strategies for solving this problem exist (see: Shoham, Y. and M. Tennenholtz, 1997. On the emergence of social conventions, modeling, analysis, and simulations. Artificial Intelligence, 94: 139–166.). For some complex neighbourhood definitions, see Delgado, J., 2002. Emergence of Social Conventions in Complex Networks. Artificial Intelligence, 141: 171–185.
4. Discuss the following question in the discussion forum: What are the limitations of the normal and extensive forms for modelling large or realistic game-theoretic settings?