The ability of an electricity-generating firm with market power to influence the market price depends strongly on the volume the firm has pre-sold in the forward, or hedge, markets. However, the choice of hedge level may be a strategic decision in itself. In this analysis we show that the profit-maximizing choice of the hedge level depends on the extent to which the hedge price varies with the firms hedging decision, which relates to the transparency of the forward market. A lack of transparency results in the hedge price being independent of the firms hedge level. In this case, the optimal choice of hedging is an all-or-nothing decision and there was no equilibrium level of hedging in pure strategies. This outcome may explain an observed lack of hedge market liquidities in wholesale electricity markets with substantial market power. We perform the analysis for the monopoly and oligopoly cases and extend it by realistic cost functions and various degrees of competitiveness in the market. These results contribute to the extensive body of research on the price formation and strategic behavior in electricity forward and spot markets, as well as providing implications for transparency initiatives in market design.