Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types

Rabinovich, Zinovi, Naroditskiy, Victor, Gerding, Enrico H. and Jennings, Nicholas R. (2013) Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types. Artificial Intelligence, 195, 106-139. (doi:10.1016/j.artint.2012.09.007).


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We extend the well-known fictitious play (FP) algorithm to compute pure-strategy Bayesian-Nash equilibria in private-value games of incomplete information with finite actions and continuous types (G-FACTs). We prove that, if the frequency distribution of actions (fictitious play beliefs) converges, then there exists a pure-strategy equilibrium strategy that is consistent with it. We furthermore develop an algorithm to convert the converged distribution of actions into an equilibrium strategy for a wide class of games where utility functions are linear in type. This algorithm can also be used to compute pure ?-Nash equilibria when distributions are not fully converged. We then apply our algorithm to find equilibria in an important and previously unsolved game: simultaneous sealed-bid, second-price auctions where various types of items (e.g., substitutes or complements) are sold. Finally, we provide an analytical characterization of equilibria in games with linear utilities. Specifically, we show how equilibria can be found by solving a system of polynomial equations. For a special case of simultaneous auctions, we also solve the equations confirming the results obtained numerically.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.artint.2012.09.007
ISSNs: 0004-3702 (print)
1872-7921 (electronic)
Keywords: algorithmic game theory, bayes-nash equilibrium, epsilon-nash equilibrium, fictitious play, simultaneous auctions
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions : Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Agents, Interactions & Complexity
ePrint ID: 343596
Accepted Date and Publication Date:
February 2013Published
18 September 2012Made publicly available
Date Deposited: 06 Oct 2012 19:05
Last Modified: 31 Mar 2016 14:35
Funded by: EPSRC (EP/I011587/1)
Led by: Nick Jennings
1 January 2011 to 31 December 2015
Further Information:Google Scholar

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