Pablo Daniel Azar

Crowdsourced Bayesian Auctions

We investigate the problem of optimal mechanism design, where an auctioneer wants to sell a set of goods to buyers, in order to maximize revenue. In a Bayesian setting the buyers’ valuations for the goods are drawn from a prior distribution \(\mathcal{D}\), which is often assumed to be known by the seller. In this work, we focus on cases where the seller has no knowledge at all, and “the buyers know each other better than the seller knows them”. In our model, \(\mathcal{D}\) is not necessarily common knowledge. Instead, each player individually knows a posterior distribution associated with \(\mathcal{D}\). Since the seller relies on the buyers’ knowledge to help him set a price, we call these types of auctions crowdsourced Bayesian auctions.

Super-efficient rational proofs

Information asymmetry is a central problem in both computer science and economics. In many fundamental problems, an uninformed principal wants to obtain some knowledge from an untrusted expert. This models several real-world situations, such as a managers relation with her employees, or the delegation of computational tasks in mechanical turk. Because the expert is untrusted, the principal needs some guarantee that the provided knowledge is correct. In computer science, this guarantee is usually provided via a proof, which the principal can verify. Thus, a dishonest expert will get caught and penalized (with very high probability). In many economic settings, the guarantee that the knowledge is correct is usually provided via incentives. That is, a game is played between expert and principal such that the expert maximizes her utility by being honest. A rational proof is an interactive proof where the prover, Merlin, is neither honest nor malicious, but rational. That is, Merlin acts in order to maximize his own utility. Rational proofs have been previously studied when the verifier, Arthur, is a probabilistic polynomial-time machine \cite{AzarMicali}. In this paper, we study super efficient rational proofs, that is, rational proofs where Arthur runs in logarithmic time. Our new rational proofs are very practical. Not only are they much faster than their classical analogues, but they also provide very tangible incentives for the expert to be honest. Arthur only needs a polynomial-size budget, yet he can penalize Merlin by a large quantity if he deviates from the truth. We give the following characterizations of which problems admit super-efficient rational proofs. (1)Uniform TC0 coincides with the set of languages L that admit a rational proof using O(log n) time, O(log n) communication, a constant number of rounds and a polynomial size budget. P║NPcoincides with the set of languages having a rational proof using O(log n) time, poly(n) communication, one round and a polynomial-size budget. Furthermore, we show that when Arthur is restricted to have a polynomial-size budget, the set of languages which admit rational proofs with polynomial time verification, polynomial communication and one round is P║MA

The Wisdom of Twitter Crowds: Predicting Stock Market Reactions to FOMC Meetings via Twitter Feeds

With the rise of social media, investors have a new tool for measuring sentiment in real time. However, the nature of these data sources raises serious questions about its quality. Because anyone on social media can participate in a conversation about markets—whether the individual is informed or not—these data may have very little information about future asset prices. In this article, the authors show that this is not the case. They analyze a recurring event that has a high impact on asset prices—Federal Open Market Committee (FOMC) meetings—and exploit a new dataset of tweets referencing the Federal Reserve. The authors show that the content of tweets can be used to predict future returns, even after controlling for common asset pricing factors. To gauge the economic magnitude of these predictions, the authors construct a simple hypothetical trading strategy based on this data. They find that a tweet-based asset allocation strategy outperforms several benchmarks—including a strategy that buys and holds a market index, as well as a comparable dynamic asset allocation strategy that does not use Twitter information.

Practical Applications of Momentum, Mean-Reversion, and Social Media: Evidence from StockTwits and Twitter

Practical Applications Summary In Momentum, Mean-Reversion, and Social Media: Evidence from StockTwits and Twitter, from the Summer 2018 issue of The Journal of Portfolio Management, Shreyash Agrawal, Pablo D. Azar, Andrew W. Lo, and Taranjit Singh (all at MIT) demonstrate that social media activity can significantly affect liquidity on an intraday basis and that negative sentiment has a much larger effect than positive sentiment on liquidity. The authors propose an intraday trading strategy based on sentiment as reflected by social media and show that the strategy outperforms a basic intraday mean-reversion strategy (before transaction costs).

Momentum, Mean-Reversion and Social Media: Evidence from StockTwits and Twitter

In this article, the authors analyze the relation between stock market liquidity and real-time measures of sentiment obtained from the social-media platforms StockTwits and Twitter. The authors find that extreme sentiment corresponds to higher demand for and lower supply of liquidity, with negative sentiment having a much larger effect on demand and supply than positive sentiment. Their intraday event study shows that booms and panics end when bullish and bearish sentiment reach extreme levels, respectively. After extreme sentiment, prices become more mean-reverting and spreads narrow. To quantify the magnitudes of these effects, the authors conduct a historical simulation of a market-neutral mean-reversion strategy that uses social-media information to determine its portfolio allocations. These results suggest that the demand for and supply of liquidity are influenced by investor sentiment and that market makers who can keep their transaction costs to a minimum are able to profit by using extreme bullish and bearish emotions in social media as a real-time barometer for the end of momentum and a return to mean reversion.

Endogenous Production Networks

We develop a tractable model of endogenous production networks. Each one of a number of products can be produced by combining labor and an endogenous subset of the other products as inputs. Different combinations of inputs generate (prespecified) levels of productivity. Markets are “contestable” in the sense that production technologies are available to a large number of potential producers. We establish the existence and uniqueness of an equilibrium with an endogenous production network and provide comparative static results on how prices and endogenous technology choices (and thus the production network) respond to changes in parameters. These results show that improvements in technology (or reductions in distortions) spread throughout the economy via input-output linkages and reduce all prices, and under reasonable restrictions on the menu of production technologies, also lead to a denser production network. Using a dynamic version of the model, we show that the endogenous evolution of the production network could be a powerful force towards sustained economic growth. At the root of this result is the fact that the arrival of a few new products expands the set of technological possibilities of all existing industries by a large amount — that is, if there are n products, the arrival of one more new product increases the combinations of inputs that each existing product can use from 2 n-1 to 2 n , thus enabling significantly more pronounced cost reductions from the choice of optimal technology combinations. These cost reductions then spread to other industries that benefit from lower input prices and are further incentivized to adopt additional inputs.

The Query Complexity of Scoring Rules

Proper scoring rules are crucial tools to elicit truthful information from experts. A scoring rule maps X, an expert-provided distribution over the set of all possible states of the world, and ω, a realized state of the world, to a real number representing the expert’s reward for his provided information. To compute this reward, a scoring rule queries the distribution X at various states. The number of these queries is thus a natural measure of the complexity of the scoring rule. We prove that any bounded and strictly proper scoring rule that is deterministic must make a number of queries to its input distribution that is a quarter of the number of states of the world. When the state space is very large, this makes the computation of such scoring rules impractical. We also show a new stochastic scoring rule that is bounded, strictly proper, and which makes only two queries to its input distribution. Thus, using randomness allows us to have significant savings when computing scoring rules.