  Periodic double auctions (PDA) have applications in many areas such as in
e-commerce, intra-day equity markets, and day-ahead energy markets in
smart-grids. While the trades accomplished using PDAs are worth trillions of
dollars, finding a reliable bidding strategy in such auctions is still a
challenge as it requires the consideration of future auctions. A participating
buyer in a PDA has to design its bidding strategy by planning for current and
future auctions. Many equilibrium-based bidding strategies proposed are complex
to use in real-time. In the current exposition, we propose a scale-based
bidding strategy for buyers participating in PDA. We first present an
equilibrium analysis for single-buyer single-seller multi-unit single-shot
k-Double auctions. Specifically, we analyze the situation when a seller and a
buyer trade two identical units of quantity in a double auction where both the
buyer and the seller deploy a simple, scale-based bidding strategy. The
equilibrium analysis becomes intractable as the number of participants
increases. To be useful in more complex settings such as wholesale markets in
smart-grids, we model equilibrium bidding strategy as a learning problem. We
develop a deep deterministic policy gradient (DDPG) based learning strategy,
DDPGBBS, for a participating agent in PDAs to suggest an action at any auction
instance. DDPGBBS, which empirically follows the obtained theoretical
equilibrium, is easily extendable when the number of buyers/sellers increases.
We take Power Trading Agent Competition's (PowerTAC) wholesale market PDA as a
testbed to evaluate our novel bidding strategy. We benchmark our DDPG based
strategy against several baselines and state-of-the-art bidding strategies of
the PowerTAC wholesale market PDA and demonstrate the efficacy of DDPGBBS
against several benchmarked strategies.
