Essays on the selection and design of information structures
This thesis consists of three chapters, each of which is a self-contained analysis of a distinct theoretical setting. The chapters are linked by the overarching theme of choices about information structures. In each, I consider an agent or agents facing a choice about information provision, modelled as the selection of an information structure that determines the probability of a receiver observing particular messages, given particular states of the world being realised. Chapter 1: Confirmation Bias and Markets for Information If consumers of information suffer from confirmation bias, they may prefer a biased information source to a perfectly accurate one. This is a potential explanation for the existence of biased reporting in news media. I show how confirmation bias can be expressed in terms of utility derived directly from the relationship between a consumer’s prior and posterior beliefs, and that this can induce preferences over signals. I derive the optimal signal for consumers, both when their preferences are entirely dictated by confirmation bias, and when an instrumental value of information is also present, showing that in each case consumers may prefer biased signals. When audience-maximising firms compete to offer information sources to consumers with these preferences, I show that the strategic environment is equivalent to a one-dimensional location game, and that results analogous to those in the existing literature on location games extend to this setting: in duopoly, the firms locate at the median of consumer preferences, but ‘spread out’ as the number of firms rises. Chapter 2: How Informed should Voters be? Ex ante identical agents participate in a simple majority vote on whether to adopt a new policy, of uncertain value to each agent. A utilitarian social planner chooses the information structure through which agents learn about their own IID, private valuations of the policy. With mandatory voting, perfect information is optimal if and only if a particular symmetry condition holds on the distribution of valuations. Otherwise, restricting information such that relatively-ambivalent voters sometimes make mistakes can increase total expected utility, by reducing the incidence of ‘tyranny of the majority’ outcomes. When indifferent voters are allowed to abstain, perfect information becomes non-optimal for symmetrical distributions as well, provided that the number of voters is sufficiently large. Chapter 3: Information Sharing in Continuous Two-Player Games Two ex ante identical agents with uncertain payoff types play a two-stage game. In the first stage, before learning their own payoff type, they select an information structure for their opponent; they may choose to reveal their payoff type to their opponent, conceal it, or partially reveal. Each player then draws one of two possible payoff types, observes their own type, and receives a message about the opponent’s type generated by the structure their opponent chose in the first stage. In the second stage players choose actions from an interval. Payoffs depend only on the second stage actions (in which they are continuous) and a player’s own type. This framework encompasses versions of models in the literature on information sharing in oligopoly, extending them to allow for ‘persuasive’ information sharing rather than simply choosing revelation or concealment (or adding unbiased noise). I show how this clarifies existing results, by laying out the incentives to provide a more or less informative signal as marginal effects. This sheds some light on the known difference between Cournot and (differentiated) Bertrand competition when considering sharing of cost information (revelation in Cournot, concealment in Bertrand), which I show results from the fact that in Bertrand competition, there is a direct, cost-dependent impact of the opponent’s action on a player’s payoff that is not mediated through the player’s own action. I also provide sufficient conditions for the existence of equilibrium in games of this type, and analyse some alternative second stage games, showing that there exist games and forms of payoff uncertainty for which multiple equilibria of the overall game exist, including equilibria with partial revelation, and despite equilibrium uniqueness being guaranteed for every second stage subgame.