This paper studies commitment strategies in three-player negotiation settings comprising human players and computer agents. We defined a new game called the Contract Game which is analogous to real-world market settings in which participants need to reach agreement over contracts in order to succeed. The game comprises three players, two service providers and one customer. The service providers compete to make repeated contract offers to the customer consisting of resource exchanges in the game. We formally analyzed the game and defined sub-game perfect equilibrium strategies for the customer and service providers that involve commitments. We conducted extensive empirical studies of these strategies in three different countries, the U.S., Israel and China. We ran several configurations in which two human participants played a single agent using the equilibrium strategies in various role configurations in the game (both customer and service providers). Our results showed that the computer agent using equilibrium strategies for the customer role was able to outperform people playing the same role in all three countries. In contrast, the computer agent playing the role of the service provider was not able to outperform people. Analysis reveals this difference in performance is due to the contracts proposed in equilibrium being significantly beneficial to the customer players, as well as irrational behavior taken by human customer players in the game.