Essays on auctions and Bayesian games with endogenous expectations

The dissertation consists of three self contained, though interrelated chapters. In the first two chapters, I apply the behavioural model of reference dependence to two different games of incomplete information; auctions and bargaining. The main contribution of the models is that they pin down the reference point by endogenising it as the expected price of a good in equilibrium. Modelling games where the utility of a player depends on her beliefs over endogenous variables, introduces mathematical complexity. Indeed, such games lack an existence result, and in the final chapter, I extend methods available in the literature to provide sufficient conditions for the existence of monotone equilibrium in games with endogenous beliefs.

In the first chapter, I model auctions where bidders have reference dependent preferences and may be loss averse. The reference point is defined either as the ex-ante or interim expected price of the good, depending on whether bidders are naive or sophisticated. Equilibrium with consistent reference points are shown to exist and are fully characterised. The model predicts that in equilibrium, bidders both overbid and underbid in comparison to the standard risk neutral Nash equilibrium.

The second chapter extends the model a two player $k$-double auction, where players are assumed to have preferences that exhibit reference dependence. The expected price of the good is modelled as a player's reference point. In equilibrium the endogenous reference point is said to be consistent if behaviour given the reference point, yields an expected price equal to the reference point itself. Bias is introduced as an exogenous deviation of the reference point from the expected price of the good. We study the effects of reference dependence and bias on the ex-post efficiency of the auction.In the absence of bias, reference dependence does not alter the efficiency of the model, however we find that efficiency is decreasing in the level of bias.

In the final chapter, I consider a class of Bayesian games where an individual's payoff depends on her beliefs over the actions of her opponents. I model this feedback effect as endogenous (rational) beliefs over equilibrium outcomes, which are influenced by the actions of all players. A consistent Bayesian equilibrium is defined, where behaviour given equilibrium beliefs, yields the same beliefs on the equilibrium outcome. Sufficient conditions for equilibrium existence are listed; I use lattice theoretic techniques and exploit monotonicity of equilibrium strategies to show existence. Also provided are comparative static results with respect to the primitive type distributions. The model is then applied to two distinct sub-fields in economics; reference dependent preferences with endogenous reference points and Cournot markets with network effects.