Bitcoin: An Impossibility Theorem for Proof-of-Work based Protocols

Bitcoin’s main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple fake identities. This novel axiomatic formalization allows us to characterize which other protocols are feasible: Every protocol with these properties must have the same reward scheme as Bitcoin. This implies an impossibility result for risk-averse miners: no protocol satisfies the aforementioned constraints simultaneously without giving miners a strict incentive to merge. Furthermore, any protocol either gives up on some degree of decentralization or its reward scheme is equivalent to Bitcoin’s

Bitcoin: An Impossibility Theorem for Proof-of-Work based Protocols

A key part of decentralized consensus protocols is a procedure for random selection, which is the source of the majority of miners cost and wasteful energy consumption in Bitcoin. We provide a simple economic model for random selection mechanism and show that any PoW protocol with natural desirable properties is outcome equivalent to the random selection mechanism used in Bitcoin

The importance of memory for price discovery in decentralized markets

International audienceWe study the dynamics of price discovery in decentralized two-sided markets. We show that there exist memoryless dynamics that converge to the core of the underlying assignment game in which agents' actions depend only on their current payoff. However, we show that for any such dynamic the convergence time can grow exponentially in relation to the population size. We present a natural dynamic in which a player's reservation value provides a summary of his past information and show that this dynamic converges to the core in polynomial time in homogeneous markets

Can open decentralized ledgers be economically secure?

Traditional payment processors are the subject of antitrust concerns and regulations. Open decentralized ledgers (e.g., Bitcoin) provide an alternative. They do not rely on a central authority, avoiding antitrust and monopoly concerns. However, the open nature of these systems gives rise to many challenges, including fundamental questions about their security. To address this question, we consider a framework that combines economic theory and dis- tributed systems theory and define economic security for general permissionless decentralized ledgers. Analysis of Bitcoin’s Nakamoto protocol shows that block rewards are ineffective in pro- viding economic security due to limitations of incentives in environments with many anonymous participants. We present an alternative protocol showing that an open decentralized ledger can be economically secure

A network approach to public goods

Abstract We study settings where each agent can exert costly effort that creates nonrival, heterogeneous benefits for some of the others. For example, municipalities can forgo consumption to reduce pollution. How do the prospects for efficient cooperation depend on asymmetries in the effects of players' actions? We approach this question by analyzing a network that describes the marginal benefits agents can confer on one another. The first set of results explains how the largest eigenvalue of this network measures the marginal gains available from cooperating; as an application, we describe the players whose participation is essential to achieving any Pareto improvement on an inefficient status quo. Next, we examine mechanisms all of whose equilibria are Pareto efficient and individually rational; an outcome is called robust if it is an equilibrium outcome in every such mechanism. Robust outcomes exist and correspond to the Lindahl public goods solutions. The main result is a characterization of effort levels at these outcomes in terms of players' centralities in the benefits network. It entails that an outcome is robust if and only if agents contribute in proportion to how much they value the efforts of those who help them

Essays in Market Design

This dissertation consists of three essays in market design. The first essay studies a dynamic allocation problem. The second presents a new model for many-to-one matching markets where colleges are matched to a large number of students. The third analyzes the effect of the minimum wage on training in internships. In many assignment problems items arrive stochastically over time, and must therefore be assigned dynamically. The first essay studies the social planers ability to dynamically match agents with heterogenous preferences to their preferred items. Impatient agents may misreport their preferences to receive an earlier assignment, causing welfare loss. The first essay presents a tractable model of the problem and mechanisms that minimize the welfare loss. The second essay, which is joint work with Eduardo Azevedo, considers the classical many-to-one matching problem when many students are assigned to a few large colleges. We show that stable matchings have a simple characterization. Any stable matching is equivalent to market clearing cutoffs — admission thresholds for each college. The essay presents a model where a continuum of students is to be matched to a finite number of schools. Using the cutoff representation we show that under broad conditions there is a unique stable matching, and that it varies continuously with respect to the underlying economy. The third essay, which is joint work with Michael Schwarz, looks at on the job training in firms. The firm recovers the cost of training by gradually training the worker over time, paying a wage below the workers marginal product and providing the remaining compensation in the form of training. When the worker’s productivity is close to the minimum wage the firm finds it profitable to front-load training, making the worker more productive and the training faster. A decrease in the minimal wage reduces the firm's incentive to front-load training, and can make training less efficient

Bitcoin: An Impossibility Theorem for Proof-of-Work based Protocols

Bitcoin’s main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple fake identities. This novel axiomatic formalization allows us to characterize which other protocols are feasible: Every protocol with these properties must have the same reward scheme as Bitcoin. This implies an impossibility result for risk-averse miners: no protocol satisfies the aforementioned constraints simultaneously without giving miners a strict incentive to merge. Furthermore, any protocol either gives up on some degree of decentralization or its reward scheme is equivalent to Bitcoin’s

Unbalanced random matching markets

We analyze large random matching markets with unequal numbers of men and women. We find that with high probability, a vanishing fraction of agents have multiple stable partners, i.e., the ‘core ’ is small. Further, we find that being on the short side of the market confers a large advantage. For each agent, assign a rank of 1 to the agent’s most preferred partner, a rank of 2 to the next most preferred partner and so forth. If there are n men and n + 1 women then, we show that with high probability, in any stable matching, the men’s average rank of their wives is no more than 3 log n, whereas the women’s average rank of their husbands is at least n/(3 log n). If there are n men and (1 + λ)n women for λ> 0 then, with high probability, in any stable matching the men’s average rank of wives is O(1), whereas the women’s average rank of husbands is Ω(n). Simulations show that our results hold even for small markets. These findings for unbalanced markets contrast sharply with known results for balanced markets: in particular, our results show that the large core in the balanced case is a knife edge phenomenon that breaks with the slightest imbalance.

On the Definition of Objective Probabilities by Empirical Similarity ∗

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used. 1 Definitions of Probability How should we assign probabilities to events? What is the meaning of a statement of the form, “Event A will occur with probability p"? Or, to be more cautious, under which conditions can we assign probabilities to events, andunderwhichconditionsdopossible meanings of the term apply