Essays on real-life allocation problems and game theory

This work contributes to three different literatures: Resource allocation, sequential bargaining, and utility representation of preferences.; Chapters 2 and 3 deal with the house allocation problem. A prominent feature of many real-life house allocation problems is the existence of tenants already living in a house and having the right to keep on doing so. The unique solution to this class of problems in the literature, the top trading cycles (TTC) solution from random orderings proposed by Abdulkadiroglu and Sonmez (JET 88, 1999, pp. 233-260) eliminates inefficiency losses of the existing real-life mechanisms. However, the TTC solution from random orderings results in inequitable outcomes and it is not ordinally efficient. These observations motivate our work: we propose a new solution, the probabilistic serial solution with endowments. Our solution achieves ordinal efficiency and equity. However, it is not immune to strategic manipulation. In our framework, existing fairness notions are unreasonably demanding and we introduce a new operational criterion: no justified-envy. We also extend our solution to the full preference domain with indifference permitted.; Chapter 4 deals with the reputation effects in sequential bargaining games with incomplete information. The central component of our model is the notion of commitment type strategies. Our approach is to emphasize the role of players' insistency on compromise divisions. We model this bargaining posture in a simple way: A commitment type player demands a share always from a particular range, and always rejects any offer that is less than the lower bound of this range. We construct an equilibrium for the finite horizon model with insistent type players and alternating offers, where players engage in a reputation formation process: while one player of non-commitment type tries to masquerade as commitment type, the other player of commitment type tries to masquerade as non-commitment type.; Chapter 5 is on the utility representation of incomplete preferences by means of a vector-valued utility function. We obtain representation results under near-completeness and suitable separability assumptions.