In the first chapter, “Repeated signalling and reputation”, a signaller repeatedly signals his type to an uninformed player. The paper adapts the divinity refinements of the static signalling game to the repeated signalling game, selecting a dynamic version of the Riley equilibrium, defined iteratively, in which types separate minimally in each period. The model provides an alternative framework for studying reputation, generating under appropriate limits a modified Stackelberg property: each type above the lowest takes the action that maximizes Stackelberg payoffs, subject to separating from the lowest type. In contrast to the usual approach to reputation there are no behavioural types. It can be solved under arbitrary discount factors of both players: if the signaller discounts, the result above holds with the signaller's Stackelberg payoffs replaced by simply defined “discounted Stackelberg” payoffs. If the respondent has preferences not only over the actions but also over the type of the signaller, a differential equation characterizes the limit, combining reputational and pure type-signalling motives. Applications include work incentives, reputations for product quality, and limit pricing.

The second chapter, “A two-way repeated signalling model of reciprocation”, studies a model with two signallers who signal their good will to each other by acting generously. The incentive to signal good will is that preferences of each type are dependent not only on one's own good-will but also on the perceived good-will of the other. The model is found to be solvable as a finite game and as an infinite game under a Markov assumption and the solution is characterized.

The third chapter, “Mobility and redistribution under general taxes”, studies taxation and redistribution in a multi-regional setting with free mobility. The situation is described by a two-stage game with policy setting by regional governments and then migration and work choice by the population. When taxes are allowed to be non-linear and can discriminate between residents and immigrants, competition for taxable workers implies severe restrictions on redistribution in a stable equilibrium. The restrictions are independent of how policies in each region are generated, as long as policies are locally Pareto efficient. The formulation allows the study of tax policy under both moral hazard and mobility. There is a clean division between these two issues, both of which reduce the ability of regions to redistribute wealth.