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This thesis comprises three chapters centered on two common themes. The first theme is the application of non-cooperative game theory to economic questions; the second is the study of the kind of arrangements that can arise in the labour market as a response to asymmetric information. The first chapter surveys recent developments in non-cooperative game theory, and then attempts an extension of the recent results characterising perfect equilibrium payoffs in repeated games without discounting to more general games. We choose the dynamic game framework for the generalisation, and shows that there are two jointly, but not indi vidually sufficient condi tions for the generalisation to go through. We then turn to an application of these ideas to the theory of longterm contracts. The main motivation for this is that the view that wages and employment are determined by risk-sharing implicit contracts is now a well established alternative to fixed-price and marketclearing theories. In general, long-term arrangements may mitigate inefficiencies in the short-term contract that arise from various sorts of asymmetric information which are likely to be prevalent in worker-firm relationships. In this chapter two things are attempted; first, we try to integrate the game-theoretic approach to contractinq of Radner with the work of Townshend, Rogerson, Roberts and Manning among others, and second, we characterise the optimal contract, and obtain some new results. The labour market is also the topic of the third chapter. Here, we attempt to extend a well-known model of "frictional" labour market equilibrium to the case where onr or both sides of the market differ in inherent characteristics (e.g. skills) which may be observable or unobservable. We show first that the equilibrium may be inefficient even in the absence of externalities which work through the matching technology. Also, the model with unobservable characteristics provides a framework for a theoretical anal;Tsis of the practice of firms of screening workers by unemployment duration. We show that in our model, there are screening equilibria, and also investigate in some detail the impact of exogenous variables on the equilibrium.