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

Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types
Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types
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.
algorithmic game theory, bayes-nash equilibrium, epsilon-nash equilibrium, fictitious play, simultaneous auctions
106-139
Rabinovich, Zinovi
573422bf-523d-466b-a047-7a92917102e7
Naroditskiy, Victor
8881263c-ee85-49f2-b658-99c31b490e1d
Gerding, Enrico H.
d9e92ee5-1a8c-4467-a689-8363e7743362
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Rabinovich, Zinovi
573422bf-523d-466b-a047-7a92917102e7
Naroditskiy, Victor
8881263c-ee85-49f2-b658-99c31b490e1d
Gerding, Enrico H.
d9e92ee5-1a8c-4467-a689-8363e7743362
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

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).

Record type: Article

Abstract

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.

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More information

e-pub ahead of print date: 18 September 2012
Published date: February 2013
Keywords: algorithmic game theory, bayes-nash equilibrium, epsilon-nash equilibrium, fictitious play, simultaneous auctions
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 343596
URI: https://eprints.soton.ac.uk/id/eprint/343596
PURE UUID: 6c1add5f-48b8-47a6-8346-0558d2d47acb

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Date deposited: 06 Oct 2012 19:05
Last modified: 18 Jul 2017 05:21

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