This dissertation builds a model of information exchange, where the information is skills. A two-sided matching market for skills is employed that includes two distinct sides, skilled and unskilled agents, and the matches that connect these agents. The unskilled agents wish to purchase skills from the skilled agents, who each possess one valuable and unique skill. Skilled agents may match with many unskilled agents, while each unskilled agent may match with only one skilled agent. Direct interaction is necessary between the agents to teach and learn the skill. Thus, there must be mutual consent for a match to occur and the skill to be exchanged. In this market for skills, a discrete, simultaneous move game is employed where all agents announce their strategies at once, every skilled agent announcing a price and every unskilled agent announcing the skill she wishes to purchase. First, both Nash equilibria and a correlated equilibrium are determined for an example of this skills market game. Next, comparative statics are employed on this discrete, simultaneous move game through computer simulations. Finally, a continuous, simultaneous move game is studied where all agents announce their strategies at once, every skilled agent announcing a price and every unskilled agent announcing a skill and price pair. For this game, an algorithm is developed that if used by all agents to determine their strategies leads to a strong Nash equilibrium for the game. / Economics