Virtual bids were introduced in U.S. wholesale electricity markets to exploit arbitrage opportunities arising from expected price differences between day-ahead and real-time energy markets. These financial instruments have interactions with other elements of the electricity market design. For instance, virtual bids may be intended to move day-ahead electricity prices in a direction that enhances the value of Financial Transmission Rights (FTRs) settling at those energy prices. We consider a model of the day-ahead electricity market at one node in the network, under the assumption that virtual bidding does not affect the real-time dispatch of generators. Theoretical results on interior Nash equilibria are presented, assuming virtual bidders can perfectly predict real-time prices and hold no FTRs. We then adopt a kind of hypergame framework to model the day-ahead market, assuming imperfect prediction of real-time prices by different virtual bidders, and present simulation results with and without FTRs. Finally, we discuss two detection mechanisms that may be used by regulators to distinguish between competitive and manipulative market outcomes, as well as trade-offs between specificity and sensitivity.