Incentives for Collective Innovation

Identical agents exert hidden effort to produce randomly-sized improvements in a technology they share. Their payoff flow grows as the technology develops, but so does the opportunity cost of effort, due to a resource trade-off between using and improving the technology. The game admits a unique strongly symmetric equilibrium, and it is Markov; that is, no form of punishment is sustainable. Moreover, in this equilibrium, small innovations may hurt all agents as they severely reduce effort. Allowing each agent to discard the innovations she produces (after observing their size) increases equilibrium effort and welfare. If agents can instead conceal innovations for a period of time, there exists an equilibrium in which improvements are refined in secret until they are sufficiently large, and progress stops after a single disclosure. Although concealment is inefficient due to forgone benefits and the risk of redundancy, under natural conditions, this equilibrium induces higher welfare than all equilibria with forced disclosure

Screening for breakthroughs

We identify a new dynamic agency problem: that of incentivising the prompt disclosure of productive information. To study it, we introduce a general model in which a technological breakthrough occurs at an uncertain time and is privately observed by an agent, and a principal must incentivise disclosure via her control of a payoff-relevant physical allocation. We uncover a deadline structure of optimal mechanisms: they have a simple deadline form in an important special case, and a graduated deadline structure in general. We apply our results to the design of unemployment insurance schemes

Screening for breakthroughs: Omitted proofs

This document contains all proofs omitted from our working paper 'Screening for breakthroughs'; specifically, the November 2021 version of the paper (arXiv:2011.10090v6).Comment: arXiv admin note: text overlap with arXiv:2011.1009

Agenda-manipulation in ranking

A committee ranks a set of alternatives by sequentially voting on pairs, in an order chosen by the committee's chair. Although the chair has no knowledge of voters' preferences, we show that she can do as well as if she had perfect information. We characterise strategies with this 'regret-freeness' property in two ways: (1) they are efficient, and (2) they avoid two intuitive errors. One regret-free strategy is a sorting algorithm called insertion sort. We show that it is characterised by a lexicographic property, and is outcome-equivalent to a recursive variant of the much-studied amendment procedure

Stochastic games and monotone comparative statics

In Chapter 1, I study decision problems under uncertainty involving the choice of a rule mapping states into actions. I show that for any rule, there exists an increasing rule inducing larger expected payoffs for all payoff functions that are supermodular in action and state. I present five applications. The main ones are 1. A planner implementing a subsidy based on household data, subject to a budget constraint, may improve any schedule failing to transfer more to households with data indicating larger returns, even without knowing their specific utility functions. 2. A monopolist price-discriminating in a market where wealthier buyers are less pricesensitive should charge them more, even if there is a positive demand externality. Shifting high prices onto wealthier buyers while preserving the price distribution is profitable. 3. If an insurer selling a single product to several buyers has access to a signal of the shocks affecting them, she should offer an insurance that pays more when signals indicating larger shocks are observed, even if the shocks and the buyers’ degrees of risk-aversion are heterogeneous. In Chapters 2 and 3, I analyse a new class of dynamic public-good games arising among innovators of a common technology who share improvements with one other. Innovators could be firms part of an R&amp;D; alliance or an informal disclosure agreement. The game is novel as firms induce randomly-sized increments in the stock (innovations), and their payoffs are a general function of private effort (R&amp;D;) and the current stock (the technology level). In Chapter 2, I characterise the social-welfare benchmark, and compute the unique symmetric Markov equilibrium of the game. I show that, in the welfare benchmark, agents decrease their effort and are better-off as the stock grows. In contrast, innovations may be detrimental in the symmetric equilibrium. Namely, if the opportunity cost of effort does not depend on the current stock, then any innovation is beneficial. However, if the cost of effort is sufficiently increasing in the stock, and there are sufficiently many agents, moderate innovations are detrimental early on. In Chapter 3, I characterise the payoff-maximising equilibrium of the two-player game with binary effort, when strategies may depend on time and the past trajectory of the stock. I show that the equilibrium is asymmetric and non-Markov. In particular, only one agent exerts effort after the stock exceeds a certain cutoff and, before this occurs, agents face an equal chance of being the ones to do so. Moreover, I extend the game by allowing agents to conceal the innovations they obtain for an arbitrary period of time, foregoing their benefits. I derive necessary and sufficient conditions for the symmetric equilibrium of the baseline model with full disclosure to carry over to the game with concealment. I conjecture that, whether or not this is the case, there exists an equilibrium in which innovations are disclosed if and only if they exceed a common cutoff. Moreover, this equilibrium is more efficient than the old one. In Chapter 4, my coauthor and me show that the set of all preferences over a totallyranked set of alternatives is a complete lattice when ordered according to single-crossing dominance, and characterise joins and meets of arbitrary sets of preferences. We also give necessary and sufficient conditions on the underlying pre-order of the alternatives for the existence of joins and meets, as well as for their uniqueness. We present five applications. In particular 1. We derive monotone comparative statics results showing that (a) when the set of preferences of a group agents increases, so does the set of alternatives preferred by all agents, and (b) when a set known to contain the true preferences of an agent increases, so does the smallest set guaranteed to contain her preferred alternative(s). 2. We characterise a general class of ‘maxmin’ preferences as precisely minimum upper bounds with respect to ‘more ambiguity-averse than’. 3. We characterise when aggregation of individual preferences (respecting a suitable Pareto criterion) is possible if, for some given pairs of alternatives, society may rank one above the other only with the consent of all individuals.</p

Stochastic games and monotone comparative statics

In Chapter 1, I study decision problems under uncertainty involving the choice of a rule mapping states into actions. I show that for any rule, there exists an increasing rule inducing larger expected payoffs for all payoff functions that are supermodular in action and state. I present five applications. The main ones are 1. A planner implementing a subsidy based on household data, subject to a budget constraint, may improve any schedule failing to transfer more to households with data indicating larger returns, even without knowing their specific utility functions. 2. A monopolist price-discriminating in a market where wealthier buyers are less pricesensitive should charge them more, even if there is a positive demand externality. Shifting high prices onto wealthier buyers while preserving the price distribution is profitable. 3. If an insurer selling a single product to several buyers has access to a signal of the shocks affecting them, she should offer an insurance that pays more when signals indicating larger shocks are observed, even if the shocks and the buyersâ degrees of risk-aversion are heterogeneous. In Chapters 2 and 3, I analyse a new class of dynamic public-good games arising among innovators of a common technology who share improvements with one other. Innovators could be firms part of an R&D alliance or an informal disclosure agreement. The game is novel as firms induce randomly-sized increments in the stock (innovations), and their payoffs are a general function of private effort (R&D) and the current stock (the technology level). In Chapter 2, I characterise the social-welfare benchmark, and compute the unique symmetric Markov equilibrium of the game. I show that, in the welfare benchmark, agents decrease their effort and are better-off as the stock grows. In contrast, innovations may be detrimental in the symmetric equilibrium. Namely, if the opportunity cost of effort does not depend on the current stock, then any innovation is beneficial. However, if the cost of effort is sufficiently increasing in the stock, and there are sufficiently many agents, moderate innovations are detrimental early on. In Chapter 3, I characterise the payoff-maximising equilibrium of the two-player game with binary effort, when strategies may depend on time and the past trajectory of the stock. I show that the equilibrium is asymmetric and non-Markov. In particular, only one agent exerts effort after the stock exceeds a certain cutoff and, before this occurs, agents face an equal chance of being the ones to do so. Moreover, I extend the game by allowing agents to conceal the innovations they obtain for an arbitrary period of time, foregoing their benefits. I derive necessary and sufficient conditions for the symmetric equilibrium of the baseline model with full disclosure to carry over to the game with concealment. I conjecture that, whether or not this is the case, there exists an equilibrium in which innovations are disclosed if and only if they exceed a common cutoff. Moreover, this equilibrium is more efficient than the old one. In Chapter 4, my coauthor and me show that the set of all preferences over a totallyranked set of alternatives is a complete lattice when ordered according to single-crossing dominance, and characterise joins and meets of arbitrary sets of preferences. We also give necessary and sufficient conditions on the underlying pre-order of the alternatives for the existence of joins and meets, as well as for their uniqueness. We present five applications. In particular 1. We derive monotone comparative statics results showing that (a) when the set of preferences of a group agents increases, so does the set of alternatives preferred by all agents, and (b) when a set known to contain the true preferences of an agent increases, so does the smallest set guaranteed to contain her preferred alternative(s). 2. We characterise a general class of âmaxminâ preferences as precisely minimum upper bounds with respect to âmore ambiguity-averse thanâ. 3. We characterise when aggregation of individual preferences (respecting a suitable Pareto criterion) is possible if, for some given pairs of alternatives, society may rank one above the other only with the consent of all individuals.</p

The comparative statics of persuasion

In the canonical persuasion model, comparative statics has been an open question. We answer it, delineating which shifts of the sender's interim payoff lead her optimally to choose a more informative signal. Our first theorem identifies an ordinal notion of 'increased convexity' that we show characterises those shifts of the sender's interim payoff that lead her optimally to choose no less informative signals. To strengthen this conclusion to 'more informative' requires further assumptions: our second theorem identifies the necessary and sufficient condition on the sender's interim payoff, which strictly generalises the 'S'-shape commonly imposed in the literature. (Note: preliminary and incomplete.