Essays in economic theory

Abstract

In the first chapter, entitled ‘Communication with partially verifiable endogenous information’ I study the following problem. An expert can covertly acquire information about the state of the world before communicating with a decision maker in order to influence her action. The expert’s information acquisition is unrestricted and costless but her ability to prove to the decision maker what she privately learnt is limited. I study how the verifiability of the expert’s acquired information affects equilibrium information acquisition and transmission. Even when acquired information is only partially verifiable, I prove an unravelling result: all equilibria in which the expert influences the decision maker involve full revelation of the expert’s private information. I compare different verifiability environments and prove a comparative statics result, characterizing the sense in which more verifiability is never worse for the expert. I then study optimal verifiability environments, giving necessary and sufficient conditions for optimality for each of the two agents. Expert-optimal environments are credibly rich in the sense that, even when facing a sceptical decision maker, the expert has access to a rich language to communicate her information. I show that this is akin to her having a large amount of commitment power. The optimum for the decision maker restricts the expert’s ability to credibly communicate intermediate results, inducing the expert to acquire and disclose full information in equilibrium. The second chapter, entitled ‘Strategic research funding’, is joint work with Ludvig Sinander. We study a dynamic game in which information arrives gradually as long as a principal funds research, and an agent takes an action in each period. In equilibrium, the principal’s patience is the key determinant of her information provision: the lower her discount rate, the more eagerly she funds. When she is sufficiently patient, her information provision and value function are well-approximated by the ‘Bayesian persuasion’ model. If the conflict of interest is purely belief-based and information is valuable, then she provides full information if she is patient. We also obtain a sharp characterisation of the principal’s value function. Our proofs rely on a novel dynamic programming principle rooted in the theory of viscosity solutions of differential equations. The third and final chapter, entitled ‘Strictly strategy-proof auctions’, is also joint work with Ludvig Sinander and studies the following problem. A strictly strategyproof mechanism is one that asks agents to use strictly dominant strategies. In the canonical one-dimensional mechanism design setting with private values, we show that strict strategy-proofness is equivalent to strict monotonicity plus the envelope formula, echoing a well-known characterisation of (weak) strategy-proofness. A consequence is that strategy-proofness can be made strict by an arbitrarily small modification, so that strictness is ‘essentially for free’.