Essays onn-person bargaining games
Yang, Jeong Ae
Doctor of Philosophy
We first analyze a pure bargaining problem where n players can split a pie on a unanimous agreement. All players have the same utility function of the form $\delta s$ where $s$ is the share of a player and $\delta$ the discount factor. We present four simple bargaining processes where a player's acceptance leads to a reduced game. Three propose-response processes yield a unique perfect equilibrium. One demand-response process yields a unique perfect equilibrium when $\delta$ is below a certain critical level and multiple perfect equilibria otherwise. We then generalize the environment so that players may have different preferences over share-delay pairs which satisfy certain axioms. We specify the contracts among the players as the reduction evolves in a simple bargaining process. The bargaining game yields a unique perfect equilibrium outcome. As the time lapse between bargaining rounds goes to zero, the unique perfect equilibrium outcome approaches the Nash bargaining solution. Finally, we analyze a general bargaining problem where a characteristic function prescribes potential worths among n players. We assume the same general environment. When the core of a game is not empty, a Nash-Core solution of the game is uniquely characterized by certain properties.