This paper analyzes the incentives to trade and the validity of the law of one price in three strategic market games with multiple trading posts. In bilateral oligopolies, where traders have corner endowments in one commodity, all agents participate in all the markets. The law of one price holds in bilateral oligopolies and in the buy-or-sell market game, where equilibrium strategies are locally unique. When traders can simultaneously buy and sell on every market, the law of one price fails and the set of equilibrium prices generically has the same dimension as the number of active markets.