Laura M. Harbig: Game-Theoretic Bargaining Solutions in Cooperative Negotiations

This thesis explores cooperative bargaining theory and its application to the negotiation between a consulting firm and their potential client about the terms of a potential project, addressing the research gap of modeling such negotiations game-theoretically.

The first part introduces the concept of utility functions, which represent the preferences of the bargainers over possible outcomes. Thereon, different bargaining solutions and their properties are discussed. Afterward, a negotiation between a consultancy and its potential client about the price and scope of a project is modeled. For this, profit and utility functions of both parties are defined. Their images generate the feasible set defining a bargaining game. To that game, the bargaining solutions are applied. It is found out that, in the specified context, an optimal price for a consulting project lies between AC250000 and AC320000, encompassing between 141 and 150 consultant days. A second key finding is that the less risk-averse the client behaves, the lower are not only the optimal project price and number of consultant days, but also the optimal price per consultant day. This result holds true for all examined bargaining solutions, although some bargaining solutions are more sensitive to changes in the client’s risk aversion than others. The choice of a realistic risk parameter is found to be as important as the choice of a bargaining solution. Ultimately, it is concluded that while no bargaining solution is optimal for the consultancy or the client, the most favorable to the consultancy are the Kalai- Smorodinsky and equal area solution, and the most favorable to the client are the utilitarian and Perles-Maschler solution.