Multiple equilibria in theory and practice

The first part of the thesis studies equilibrium selection. We use a stochastic evolutionary model characterised by small probability shocks or mutations which perturb the system away from its deterministic evolution, allowing it to move between equilibria over a long period of time. Much of the literature has concentrated on the result that, in the limit as the mutation rate approaches zero, the stationary distribution becomes concentrated on the risk-dominant equilibrium because it is easier to flow into. However, it has been shown that in models of local interaction, allowing player movement eases the flow into the efficient equilibrium. We look at the consequences of such player movement when there are capacity constraints which limit the number of agents who can reside at each location. The limit distribution may then become concentrated on a mixed state in which different locations coordinate on different equilibria. The second part looks at the problem of characterising equilibria in multiunit auctions. Surprisingly little is known about optimal mechanism design for multi-unit auctions relative to the single-unit auctions. This is highlighted by the continuing debate on whether the US Treasury should use a discriminatory or uniform pricing rule. These questions have become of wider practical interest as a result of the innovative use of auction theory in the England and Wales Electricity Pool. We compare the two pricing rules in a common-value model with capacity constraints and uncertain demand and show that the discriminatory pricing rule performs better. We also present a model of the Electricity Pool and show that a discriminatory pricing rule would lead to more competitive prices than the current uniform pricing rule. The ranking holds even in the repeated game case, despite the problem of multiple equilibria