A variety of market mechanisms have been proposed and implemented around the world in order to create competitive electricity pools and exchanges. However, it is an open question whether pool-based daily auctions or continuous bilateral trading deliver different prices under conditions of market power. In this paper we present a computationally intensive simulation model of the wholesale electricity market in England and Wales to isolate and systematically test the potential impact of alternative trading arrangements on electricity prices. After eight years of trading under a pool-based system, proposals were initiated in 1998 to change the market in England and Wales to bilateral trading. This paper uses an agent-based simulation to evaluate two important aspects of that proposal. The results show that daily bidding with Pay SMP settlement, as in the original Pool day-ahead market, produces the lowest prices while hourly bidding with Pay Bid settlement, as proposed for the bilateral model, produces the highest prices.