Distributed energy resources (DERs), such as solar panels, are growing rapidly and reshaping power systems. To promote DERs, utility companies usually adopt feed-in-tariff (FIT) to pay DER owners (aka prosumers) fixed rates for supplying energy to the grid. As an alternative to FIT, consumers and prosumers can trade energy in a peer-to-peer (P2P) fashion. In this paper, we focus on a P2P market using double auctions, in which the payoffs of energy consumers/prosumers are determined by their bids and auction mechanisms. Special features of a P2P energy auction, however, including zero marginal cost and publicly-known reserve prices, may invalidate many theories on auction design and hinder market development. We discuss the impacts of such features on four specific clearing mechanisms: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -double, Vickrey, McAfee and maximum volume matching (MVM). Furthermore, we propose an automated bidding framework based on multi-agent, multi-armed bandit learning, in which each agent only needs to utilize their own bidding history to determine how to bid in the next round through certain regret-minimizing algorithms. Numerical results show that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -double and McAfee auction appear to perform better in terms of bidders’ surplus. However, if the auctioneer also requires compensation, MVM can yield the most profit for the auctioneer.