Game Theory_lecture10a_08

Game Theory_lecture10a_08 - EF4484 - Game Theory - Lecture...

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

View Full Document Right Arrow Icon
11/26/08 Dynamic Games of Complete Information Dynamic Games of Complete and Imperfect Information 11/26/08 EF4484 - Game Theory - Lecture 10 2 Repeated game ± People often interact in ongoing relationships. ± For example: ± Most employment relationships last a long time. ± Countries competing over tariff levels know that they will be affected by each others’ policies far into the future. ± Firms in an industry know that they are not playing a static game but one in which they compete everyday over time. 11/26/08 EF4484 - Game Theory - Lecture 10 3 Repeated game ± In all of these dynamic situations, the way in which a party behaves at any given time is influenced by what this party and others did in the past. ± In other words, players “condition” their decisions on the history of their relationship. ± An employee may choose to work hard only if his employer gave him a good bonus in the preceding month. ± One country may set a low import tariff only if its trading partners had maintained low tariffs in the past. ± Repeated Games help explain why ongoing economic phenomena produce behavior very different from those observed in a one-time interaction. 4 Repeated Game vs. One-Shot Game ± If players believe that future behavior will be affected by the nature of current interaction, they may behave in ways that they would not otherwise. ± The prospect of reciprocity, either by way of rewards or punishments, is what separates a repeated game from a one-shot game. ± Rewards or punishments have to be credible in the sense that players will only believe them if they are part of a subgame perfect equilibrium. ± If a player believes that 1. “no good deed today will go unrewarded tomorrow”, then he will have a greater reason to do a good deed 2. “no bad deed today will go unpunished tomorrow”, he may be less inclined to do a bad deed today. 11/26/08 EF4484 - Game Theory - Lecture 10 5 Definition ± Stage game: ± Let G = {A 1 , A 2 ; u 1 , u 2 } denote a static game of complete game in which player 1 chooses an action a 1 from the action space A 1 and player 2 chooses an action a 2 from the action space A 2 , and payoffs are u 1 and u 2 , respectively. ± The game G will be called the stage game of the repeated game. ± Complete game: each player’s payoff function is common knowledge among all players. 11/26/08 EF4484 - Game Theory - Lecture 10 6 Definition: Finitely Repeated Game ± Finitely repeated game: ± Given a stage game G, let G(T) denote the finitely repeated game in which G is played T times, with the outcomes of all preceding plays observed before the next play begins. ± The payoffs for G(T) are simply the sum of the
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 / 5

Game Theory_lecture10a_08 - EF4484 - Game Theory - Lecture...

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