Economics

We study private-good allocation mechanisms where an arbitrary constraint delimits the set of feasible joint allocations. This generality provides a unified perspective over several prominent examples that can be parameterized as constraints in this model, including house allocation, roommate assignment, and social choice. We first characterize the set of two-agent strategy-proof and Pareto efficient mechanisms, showing that every mechanism is a "local dictatorship." For more than two agents, we leverage this result to provide a new characterization of group strategy-proofness. In particular, an N-agent mechanism is group strategy-proof if and only if all its two-agent marginal mechanisms (defined by holding fixed all but two agents' preferences) are individually strategy-proof and Pareto efficient. To illustrate their usefulness, we apply these results to the roommates problem to discover the novel finding that all group strategy-proof and Pareto efficient mechanisms are generalized serial dictatorships, a new class of mechanisms. Our results also yield a simple new proof of the Gibbard-Satterthwaite Theorem.

Delays in the availability of vaccines are costly as the pandemic continues. However, in the presence of adjustment costs firms have an incentive to increase production capacity only gradually. The existing contracts specify only a fixed quantity to be supplied over a certain period and thus provide no incentive for an accelerated buildup in capacity. A high price does not change this. The optimal contract would specify a decreasing price schedule over time which can replicate the social optimum.

Liquid democracy allows members of an electorate to either directly vote over alternatives, or delegate their voting rights to someone they trust. Most of the liquid democracy literature and implementations allow each voter to nominate only one delegate per election. However, if that delegate abstains, the voting rights assigned to her are left unused. To minimise the number of unused delegations, it has been suggested that each voter should declare a personal ranking over voters she trusts. In this paper, we show that even if personal rankings over voters are declared, the standard delegation method of liquid democracy remains problematic. More specifically, we show that when personal rankings over voters are declared, it could be undesirable to receive delegated voting rights, which is contrary to what liquid democracy fundamentally relies on. To solve this issue, we propose a new method to delegate voting rights in an election, called breadth-first delegation. Additionally, the proposed method prioritises assigning voting rights to individuals closely connected to the voters who delegate.

In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In {\em bidding games}, however, the players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token: both players simultaneously submit bids and the higher bidder moves the token. The bidding mechanisms differ in their payment schemes. Bidding games were largely studied with variants of {\em first-price} bidding in which only the higher bidder pays his bid. We focus on {\em all-pay} bidding, where both players pay their bids. Finite-duration all-pay bidding games were studied and shown to be technically more challenging than their first-price counterparts. We study for the first time, infinite-duration all-pay bidding games. Our most interesting results are for {\em mean-payoff} objectives: we portray a complete picture for games played on strongly-connected graphs. We study both pure (deterministic) and mixed (probabilistic) strategies and completely characterize the optimal sure and almost-sure (with probability 1 ) payoffs that the players can respectively guarantee. We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical properties of their first-price counterparts; namely, an equivalence with {\em random-turn games} in which in each turn, the player who moves is selected according to a (biased) coin toss. The equivalences for all-pay bidding are more intricate and unexpected than for first-price bidding.

This paper generalizes the concept of Bayes correlated equilibrium (Bergemann and Morris, 2016) to multi-stage games. We demonstrate the power of our characterization results by applying them to a number of illustrative examples and applications.

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private values. Assuming that the seller adopts the optimal auction due to Myerson (1981) in response, we characterize both the buyer-optimal information structure, which maximizes the buyers' surplus, and the sellerworst information structure, which minimizes the seller's revenue. We translate both information design problems into finite-dimensional, constrained optimization problems in which one can explicitly solve for the optimal information structures. In contrast to the case with one buyer (Roesler and Szentes, 2017 and Du, 2018), we show that with two or more buyers, the symmetric buyer-optimal information structure is different from the symmetric seller-worst information structure. The good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both symmetric information structures converge to no disclosure. We also show that in an ex ante symmetric setting, an asymmetric information structure is never seller-worst but can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.

We develop a result on expected posteriors for Bayesians with heterogenous priors, dubbed information validates the prior (IVP). Under familiar ordering requirements, Anne expects a (Blackwell) more informative experiment to bring Bob's posterior mean closer to Anne's prior mean. We apply the result in two contexts of games of asymmetric information: voluntary testing or certification, and costly signaling or falsification. IVP can be used to determine how an agent's behavior responds to additional exogenous or endogenous information. We discuss economic implications.

We study informed-principal problems in a simple bilateral trade environment with interdependent values. This interdependency causes the problem of multiple equilibria in the mechanism-selection game, while bilateral asymmetric information creates some difficulties in refinement analyses. Applying general methodologies of mechanism design, we show that only the principal's worst equilibrium allocation survives the intuitive criterion. We also characterize the ex-ante social surpluses in intuitive allocations. These intuitive allocations are inefficient in general owing to the effects of signaling and screening.

We study a model of innovation with a large number of firms that create new technologies by combining several discrete ideas. These ideas can be acquired by private investment or via social learning. Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates learning from others. Their decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a learning network. Higher interaction rates impose both positive and negative externalities on other firms, as there is more learning but also more competition. We show that the equilibrium learning network is at a critical threshold between sparse and dense networks. At equilibrium, the positive externality from interaction dominates: the innovation rate and even average firm profits would be dramatically higher if the network were denser. So there are large returns to increasing interaction rates above the critical threshold. Nevertheless, several natural types of interventions fail to move the equilibrium away from criticality. One policy solution is to introduce informational intermediaries, such as public innovators who do not have incentives to be secretive. These intermediaries can facilitate a high-innovation equilibrium by transmitting ideas from one private firm to another.

We study several models of growth driven by innovation and imitation by a continuum of firms, focusing on the interaction between the two. We first investigate a model on a technology ladder where innovation and imitation combine to generate a balanced growth path (BGP) with compact support, and with productivity distributions for firms that are truncated power-laws. We start with a simple model where firms can adopt technologies of other firms with higher productivities according to exogenous probabilities. We then study the case where the adoption probabilities depend on the probability distribution of productivities at each time. We finally consider models with a finite number of firms, which by construction have firm productivity distributions with bounded support. Stochastic imitation and innovation can make the distance of the productivity frontier to the lowest productivity level fluctuate, and this distance can occasionally become large. Alternatively, if we fix the length of the support of the productivity distribution because firms too far from the frontier cannot survive, the number of firms can fluctuate randomly.