Essays on Bargaining and Social Choice

Sammanfattning: This thesis consists of three theoretical essays on Bargaining and Social Choice. The first essay addresses the problem of retaining the uniqueness of equilibrium when extending the Rubinstein model to accommodate more than two players. We achieve a unique subgame perfect equilibrium in a bargaining model with three players by assuming that the players make demands in a clockwise order and practice good-faith bargaining. Good-faith bargaining implies that they may not subsequently raise their demands. In equilibrium, agreement is reached in the first period. In the limit, as the discount factor approaches unity, the agreement is an equal split of the surplus (i.e. a third each). The second essay addresses the fact that people seems to use conventions (or fairness-norms) rather than strategic reasoning when coordinating their actions to an agreement. We look for candidates for such a convention in an alternating-offers bargaining game with outside option. The concept of a modified evolutionary stable strategy (MESS), which takes complexity as well as payoff considerations, is used to derive evolutionary stable strategies. Strategies are modeled as automata and complexity is measured by the number of states an automaton has. It turns out that quite a few partitions can be supported by a MESS automaton, in fact all that lie between the outside option principle partition and the partition that assigns the entire “pie” to the player with the outside option, given that the outside option exceeds half the pie. For a bargaining game in which the outside option is not greater than half the pie, we establish the existence of a MESS. The third essay characterize strategy-proof social choice functions (SCF:s) for the allocation of multiple public goods. If the public good is composed of several categories, preferences are separable and the SCF only has to be coordinate-wise onto, then the Gibbard-Satterthwaite theorem cannot directly be applied. We find that if the range of SCF is decomposable, it is uniquely decomposed and the SCF is dictatorial in each component of the range. If the range cannot be decomposed, then the SCF is dictatorial. If, however, a component of the range only has two alternatives (we assume at least three) then there are non-dictatorial SCF:s, e.g. voting by committees.