Approximating Mixed Nash Equilibria using Smooth Fictitious Play in Simultaneous Auctions (Short Paper)
نویسندگان
چکیده
We investigate equilibrium strategies for bidding agents that participate in multiple, simultaneous second-price auctions with perfect substitutes. For this setting, previous research has shown that it is a best response for a bidder to participate in as many such auctions as there are available, provided that other bidders only participate in a single auction. In contrast, in this paper we consider equilibrium behaviour where all bidders participate in multiple auctions. For this new setting we consider mixed-strategy Nash equilibria where bidders can bid high in one auction and low in all others. By discretising the bid space, we are able to use smooth fictitious play to compute approximate solutions. Specifically, we find that the results do indeed converge to -Nash mixed equilibria and, therefore, we are able to locate equilibrium strategies in such complex games where no known solutions previously existed.
منابع مشابه
Approximating mixed Nash equilibria using smooth fictitious play in simultaneous auctions
We investigate equilibrium strategies for bidding agents that participate in multiple, simultaneous second-price auctions with perfect substitutes. For this setting, previous research has shown that it is a best response for a bidder to participate in as many such auctions as there are available, provided that other bidders only participate in a single auction. In contrast, in this paper we con...
متن کاملComputing 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 con-tinuous types (G-FACTs). We prove that, if the frequency distribution of actions (fictitiousplay beliefs) converges, then there exists a pure-strategy equilibrium strategy that is con-sistent with i...
متن کاملGeneralised Fictitious Play for a Continuum of Anonymous Players
Recently, efficient approximation algorithms for finding Nash equilibria have been developed for the interesting class of anonymous games, where a player’s utility does not depend on the identity of its opponents. In this paper, we tackle the problem of computing equilibria in such games with continuous player types, extending the framework to encompass settings with imperfect information. In p...
متن کاملUsing Simultaneous Best Response to Find Symmetric Bayes-Nash Equilibria in Auctions
Finding Nash and Bayes-Nash equilibria in games is a hard problem both analytically and computationally. We restrict out attention to symmetric Bayes-Nash equilibria in auctions and propose a computational method that takes advantage of the symmetry of equilibria and structure of auction games. The method is iterated best-response where all players move simultaneously. We present experimental r...
متن کاملLiquid Price of Anarchy
Incorporating budget constraints into the analysis of auctions has become increasingly important, as they model practical settings more accurately. The social welfare function, which is the standard measure of efficiency in auctions, is inadequate for settings with budgets, since there may be a large disconnect between the value a bidder derives from obtaining an item and what can be liquidated...
متن کامل