This thesis consists of four selfcontained works that are organised by chapter. They are arranged roughly in the chronological order that I worked on them. I provide a short abstract for each below. Chapter 1: The dating game In this chapter, I examine a gametheoretic model of heterosexual courtship. Malefemale pairs are randomly matched and decide whether to make romantic advances towards each other. They receive payoffs that depend on the utility from a romantic match, and the costs of rejection and unwanted advances/harassment. The game has three interesting Nash equilibria: the M↔I equilibrium where males always play the initiator role and females never do, the F↔I equilibrium where females always play the initiator role and males never do, and a completely mixed equilibrium where both males and females play initiator probabilistically. The former two equilibria are evolutionary stable; the latter is not. I argue that the M↔I equilibrium is most likely to describe reality. On the other hand, I show that the F↔I equilibrium is optimal from the social welfare point of view if females are are on average more selective than males. I review evidence that indicates that this is indeed the case. Using data from a speed dating experiment, I estimate that a counterfactual F↔I equilibrium sees a 51% reduction in the incidence of unwanted advances/harassment compared to a counterfactual M↔I equilibrium. The natural policy recommendation from this work is a movement from a cultural norm where males predominantly initiate romantic advances, to one where females do. In particular, this would minimise the social cost of unwanted advances/sexual harassment. Most the theoretical work in this chapter was completed as part of my MSc dissertation at the University of Edinburgh. The new content added during my PhD is the empirical analysis and the extensions section. Chapter 2: General equilibrium theory with incomplete information: the wisdom of crowds and efficient markets In this chapter, I study general equilibrium theory with incomplete information. When agents are not fully informed, they can end up purchasing a bundle of goods that is far from optimal. General equilibrium theory falls short of providing a satisfactory explanation of the ability of real markets to deliver good outcomes under these circumstances. I introduce the wisdom of crowds as a corrective for suboptimal individual behaviour. The wisdom of crowds refers to the empirically observed ability of crowds to show collective intelligence even when their constituent individuals do not. I show that when crowds are wise, aggregate demand, aggregate production and prices all approach their expost Pareto efficient levels. In a neighbourhood of equilibrium, prices follow a martingale process, providing a general equilibrium derivation of the efficient market hypothesis. A spot market that opens after the resolution of uncertainty delivers an outcome that is expost Pareto efficient. This is achieved without any contingent commodities or securities, and agents who act 'naively' and needn't have any ability to predict future prices. Chapter 3: Homophily in the job market and nogo results for affirmative action Affirmative action policies are often justified on the basis that they are temporary  once the desired level of representation has been achieved, affirmative action can cease and the situation will be selfsustaining. This paper presents nogo results that counter this idea. The model is simple and realistic. It consists of jobs and flows of people between them. It is proven that a representative steady state is unstable under very general conditions. Empirically, inbreeding homophily is ubiquitous and it is sufficient to make the representative steady state unstable. If a central planner wished to implement this perfectly representative steady state, it would require constant affirmative action intervention. Chapter 4: General (dis)equilibrium theory I construct a general, game theoretic model of markets. Agents in the model choose how much of each good to supply/demand, and at what prices. Trading can occur at nonmarketclearing prices. There is an explicit rationing mechanism that kicks in if markets fail to clear. The game is very complicated, but a massive simplification occurs in the limit of a large number of players. This allows a proof of existence of a pure strategy equilibrium. I also prove an analogue of the first fundamental theorem of welfare economics. The game is Keynesian in that 1) markets needn't clear at equilibrium so there can be unemployment and 2) there is the possibility of multiple equilibria with different levels of aggregate supply/demand, and distinct Pareto rankings. The model is microfounded and Keynesian. Fiat money can be accommodated as a store of value and a medium of exchange. The model is well placed for investigating dynamics.
