Bargaining and contribution games with deadlines

This thesis considers play in bargaining games subject to Endogenous Commitment and in contribution games with a sunk cost. In bargaining games, Endogenous Commitment (EC) describes a common feature in negotiation: once an offer is made, neither would the proposer offer nor would the respondent accept anything worse. Similarly, in contribution games, the notion of sunk cost implies an irrevocability similar to EC: it is impossible for either contributor to reduce his or her contribution, so far as the cost is sunk. Another similarity between the bargaining and contribution games in our thesis is that we assume (most of) them to be finite, meaning that there is a deadline effect: when approaching the deadline, the final negotiator/contributor has a stronger incentive to reach an agreement/complete the project. The deadline effect puts the final negotiator/contributor in a relatively weaker position. With these two similarities, the bargaining and contribution games in our thesis share some similar features. In the first chapter, we conduct a literature review. In the second chapter, we study two player alternating finite/infinite bargaining games with Endogenous Commitment. In both cases, the outcomes are affected by the assumption of EC. In the third chapter, we apply Endogenous Commitment in bargaining games with protocols involving uncertainty. The settlement timings then exhibit a U-shaped pattern: players reach an agreement at the first or the last stage of the game. In the fourth chapter, we turn to contribution games with sunk cost and heterogeneous valuations. We show that a minor difference in valuation could affect the total welfare significantly. In our thesis, we adopt several settings in all chapters. As all models include two players, we refer to player 1 as male and to player 2 as female for convenience. When no specific player is referred to, we use i and j to indicate the two players, assuming i to be male and j to be female. When player 1 makes an offer (in bargaining games) or makes a contribution (in contribution games) in stage t (t\in[1,2,...T], T is the length of the game), we denote it as x_{t}; and when player 2 does so, we denote it as y_{t}. Similarly, we denote player i's and player j's choice as m_{t} and n_{t}