Pre-play negotiations, learning and Nash equilibrium
A solution concept maps strategic games into strategy predictions. Nash equilibrium is the most widely used solution concept in game theory. Three main explanations have been used to argue why players should end up playing Nash equilibrium: 1) introspective reasoning, 2) communication 3) learning. Careful study of these has shown that the case for the Nash equilibrium is not entirely unambiguous. In this thesis, we conclude with new insights into why Nash equilibrium may be too restrictive a prediction in the context of pre-play communication and learning. Experiments suggest that communication increases the contribution to public goods. There is also evidence that, when contemplating a lie, people trade off their private benefit from the lie with the harm it inflicts on others. In the first chapter, we develop a theory of bilateral pre-play negotiation that assumes the latter and implies the former. We show that a preference for not lying enables non-Nash outcomes. In symmetric games, pre-play negotiations crucially depend on whether actions are strategic complements or substitutes. With strategic substitutes commitment power tends to decrease in efficiency whereas the opposite may be true with strategic complements. In the second chapter we consider negotiation with an alternating offer protocol. As opposed to previous contributions we show that impatience may be beneficial for a player. In the third chapter we illustrate how the complexity of conjectures about opponents' strategies in the analogy-based expectation equilibrium (ABEE) corresponds to various other equilibrium concepts in the learning literature. We also introduce a payoff- confirming refinement of the ABEE where the sample of own payoffs induced by the true equilibrium strategies must confirm the conjectures about opponents' strategies. We show that there may be non-Bayesian-Nash payoff-confirming ABEE. We provide a sufficient condition for this and show that the condition is also necessary in an interesting class of games.