This paper models trading in a dealer market as a two-stage game. In the first page, risk averse dealers compete in a Bertrand fashion for liquidity-motivated public orders. The resulting inventories are private information. In the second stage, dealers share inventory risk by posting anonymous limit orders in a limit order book. The game is modeled as a sealed bid k-double auction. Predictions from the model include: (i) the public market spread is increasing in the risk aversion of dealers, the volatility of the stock, and the average size of trades: (ii) the public market spread is decreasing in the spread-elasticity of public liquidity demand; and (iii) the public market spread is lower than it would be absent interdealer trading.