Approximating Mixed Nash Equilibria Using Smooth Fictitious Play in Simultaneous
Auctions
(short paper)
Authors: Enrico Gerding, Zinovi Rabinovich, Andrew Byde, Edith Elkind, Nicholas R. Jennings.
Abstract:
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 use smooth fictitious play to compute
approximate solutions. Specifically, we find that the results do indeed
converge to able to locate equilibrium strategies in such complex games where
no known solutions previously existed.