HO7F10 - GAME THEORY IN THE SOCIAL SCIENCES Political...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 G AME T HEORY IN THE S OCIAL S CIENCES Political Science 135/Economics 110 Hand out on Repeated Games Why study repeated games? Many forms of social interaction involve repeated interaction. Housemates interact repeatedly until the lease is up. High technology firms interact repeatedly in an oligopolistic market. Members of Congress interact repeatedly at least until the next election. States interact repeatedly when they decide how much to spend on arms and for defense. Repeated games are the simplest place to study the effects of repeated interaction. In a repeated game, the players meet every period and play the same “game” over and over again. More precisely, the players repeatedly play the same constituent game, one-shot game, or stage game . In a repeated game, the outcome of previous interactions never changes the situation the players will confront in the next period, i.e. the stage game never changes. In effect, then, repeated games strip out or abstract away from all of the possible other effects that repeated interaction might have in order to focus solely on the effects that repeated interaction can have on the behavior of the actors. What are the effects of repetition? As soon as we allow for repetition, then we are introducing time and in particular the future into the analysis. This means that actors can begin to make threats or promises. Once a future exists, a player can threaten to punish another player in the future if that player does not do what the first player wants in the current period. So, asking what the effects of repetition are is equivalent to asking how the ability to make threats or promises affects the possible outcomes of an interaction. In more technical terms, how do the equilibria of the stage game compare to the Nash equilibria or subgame perfect equilibria of the repeated game. We saw that if the players simply play a Nash equilibrium of the stage game over and over, then this will also be a Nash equilibrium of the repeated game. (Can you see why it is also a subgame perfect equilibrium of the repeated game?) So, asking how repetition affects the possible outcomes really reduces to asking how many more outcomes might we expect to see in a repeated game? The Nash Folk Theorem for Infinitely Repeated Games: From the perspective of wanting to make precise and focused predictions about the outcomes of a strategic interactions, the news from our analysis of repeated games is not very good. The result is: Any individually rational outcome of the stage game can be supported as a Nash equilibrium outcome of the repeated game if the players are sufficiently patient, i.e., if the players
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

HO7F10 - GAME THEORY IN THE SOCIAL SCIENCES Political...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online