limitations and difficulties
from Part VI - Dynamic games
Published online by Cambridge University Press: 05 August 2012
In Chapter 19, we demonstrated how to find perfect equilibrium by backward induction in games with a finite number of nodes, in which a unique player plays at each node. We saw how this solution concept excludes Nash equilibria that rely on non-credible threats. In Chapter 20, we saw how strategic behavior that embodies commitment can be reflected in subgame perfect equilibria found by backward induction.
At the same time, even when backward induction leads us to find a unique subgame perfect equilibrium, there are instances in which this equilibrium is not consistent with players’ actual real-life behavior, nor with our intuition concerning “reasonable” or “foreseeable” behavior of players in the strategic situation at hand. In this chapter, we will present two key examples illustrating the limitations of this solution concept: the “ultimatum game” and the “centipede game.” We will analyze the reasons for the limitations that these games illustrate.
The ultimatum game
This is a very simply structured two-player game. Player 1 gets an amount X of money. She must offer part of it, Y, to player 2. If player 2 accepts the offer, the transaction takes place: player 1 gets the payoff X – Y and player 2 gets the payoff Y. If, however, player 2 refuses the offer, both players get the payoff 0.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.