Games and Information: An Introduction to Game Theory by Eric Rasmusen

By Eric Rasmusen

Written in a crisp and approachable type, Games and Information makes use of basic modeling concepts and simple reasons to supply scholars with an realizing of online game conception and data economics.

  • Written for introductory classes looking a bit rigor.
  • The 4th version brings the cloth totally updated and contains new end-of-chapter difficulties and lecture room tasks, in addition to a math appendix.
  • Accompanied through a accomplished site that includes recommendations to difficulties and instructing notes.

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Sample text

Table 5 summarizes the payoffs for the strategies P ress 26 the panel and W ait by the dispenser at the other end. Table 5: Boxed Pigs Small Pig Press Wait 5, 1 → 4, 4 ↓ ↑ 9 , −1 → 0, 0 Press Big Pig Wait Payoffs to: (Big Pig, Small Pig) Boxed Pigs has no dominant strategy equilibrium, because what the big pig chooses depends on what he thinks the small pig will choose. If he believed that the small pig would press the panel, the big pig would wait by the dispenser, but if he believed that the small pig would wait, the big pig would press the panel.

If the couple do not talk, but repeat the game night after night, one may suppose that eventually they settle on one of the Nash equilibria. Each of the Nash equilibria in the Battle of the Sexes is pareto-efficient; no other strategy profile increases the payoff of one player without decreasing that of the other. In many games the Nash equilibrium is not pareto-efficient: (Confess, Confess), for example, is the unique Nash equilibrium of the Prisoner’s Dilemma, although its payoffs of (−8, −8) are pareto- inferior to the (−1, −1) generated by (Deny, Deny).

2 Since the information set includes whatever the player knows about the previous actions of other players, the strategy tells him how to react to their actions. In the Dry Cleaners Game, the strategy set for NewCleaner is just { Enter, Stay Out } , since NewCleaner moves first and is not reacting to any new information. The strategy set for OldCleaner, though, is       High Price if NewCleaner Entered, Low Price if NewCleaner Stayed Out    Low Price if NewCleaner Entered, High Price if NewCleaner Stayed Out    High Price No Matter What       Low Price No Matter What The concept of the strategy is useful because the action a player wishes to pick often depends on the past actions of Nature and the other players.

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