Three essays on game theory and bargaining

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

Equilibrium Outcomes of Repeated Two-Person Zero-Sum Games - We consider discounted repeated two-person zero-sum games. We show that even when players have different discount factors (in which case the repeated game is not a zero-sum game), an outcome is subgame perfect if and only if all of its components are Nash equilibria of the stage game. This implies that in all subgame perfect equilibria, each player's payoff is equal to his minmax payoff. In conclusion, the competitive nature of two-player zero-sum games is not altered when the game is repeated.

A Constructive Proof of the Nash Bargaining Solution - We consider the classical axiomatic Nash bargaining framework and propose a constructive proof of its solution. On the first part of this paper we prove Nash’s solution is the result of a maximization problem; on the second part, through the properties of maximand’s indifference curves we derive that it must be equal to xy.

Equilibria and Outcomes in Multiplayer Bargaining - Multiplayer bargaining is a game in which all possible divisions are equilibrium outcomes. This paper presents the classical subgame perfect equilibria strategies and analyses their weak robustness, namely the use of weakly dominated strategies. The paper then develops a refined equilibrium concept, based on trembling hand perfection, in order to overcome such weakness. Concluding that none of the classical equilibrium strategies survives the imposition of the extra robustness and, albeit using more complex strategies, the equilibrium outcomes don't change.