Economics

We present an analysis of the Proof-of-Work consensus algorithm, used on the Bitcoin blockchain, using a Mean Field Game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted to mining the blockchain (hashrate). From a simple setting we show how the master equation approach allows us to enrich the model by relaxing most of the simplifying assumptions. The essential structure of the game is preserved across all the enrichments. In deterministic settings, the hashrate ultimately reaches a steady state in which it increases at the rate of technological progress. In stochastic settings, there exists a target for the hashrate for every possible random state. As a consequence, we show that in equilibrium the security of the underlying blockchain is either i) constant, or ii) increases with the demand for the underlying cryptocurrency.

People employ their knowledge to recognize things. This paper is concerned with how to measure people's knowledge for recognition and how it changes. The discussion is based on three assumptions. Firstly, we construct two evolution process equations, of which one is for uncertainty and knowledge, and the other for uncertainty and ignorance. Secondly, by solving the equations, formulas for measuring the levels of knowledge and the levels of ignorance are obtained in two particular cases. Thirdly, a new concept of knowledge entropy is introduced. Its similarity with Boltzmann's entropy and its difference with Shannon's Entropy are examined. Finally, it is pointed out that the obtained formulas of knowledge and knowledge entropy reflect two fundamental principles: (1) The knowledge level of a group is not necessarily a simple sum of the individuals' knowledge levels; and (2) An individual's knowledge entropy never increases if the individual's thirst for knowledge never decreases.

We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to lotteries, initial play in games, and human generation of random sequences. We discover considerable variation in the completeness of existing models, which sheds light on whether to focus on developing better models with the same features or instead to look for new features that will improve predictions. We also illustrate how and why completeness varies with the experiments considered, which highlights the role played in choosing which experiments to run.

We develop a tool akin to the revelation principle for mechanism design with limited commitment. We identify a canonical class of mechanisms rich enough to replicate the payoffs of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. We show how this insight can be used to transform the designer's problem into a constrained optimization one: To the usual truthtelling and participation constraints, one must add the designer's sequential rationality constraint.

News utility is the idea that the utility of an agent depends on changes in her beliefs over consumption and money. We introduce news utility into otherwise classical static Bayesian mechanism design models. We show that a key role is played by the timeline of the mechanism, i.e. whether there are delays between the announcement stage, the participation stage, the play stage and the realization stage of a mechanism. Depending on the timing, agents with news utility can experience two additional news utility effects: a surprise effect derived from comparing to pre-mechanism beliefs, as well as a realization effect derived from comparing post-play beliefs with the actual outcome of the mechanism. We look at two distinct mechanism design settings reflecting the two main strands of the classical literature. In the first model, a monopolist screens an agent according to the magnitude of her loss aversion. In the second model, we consider a general multi-agent Bayesian mechanism design setting where the uncertainty of each player stems from not knowing the intrinsic types of the other agents. We give applications to auctions and public good provision which illustrate how news utility changes classical results. For both models we characterize the optimal design of the timeline. A timeline featuring no delay between participation and play but a delay in realization is never optimal in either model. In the screening model the optimal timeline is one without delays. In auction settings, under fairly natural assumptions the optimal timeline has delays between all three stages of the mechanism.

Economic theory has provided an estimable intuition in understanding the perplexing ideologies in law, in the areas of economic law, tort law, contract law, procedural law and many others. Most legal systems require the parties involved in a legal dispute to exchange information through a process called discovery. The purpose is to reduce the relative optimisms developed by asymmetric information between the parties. Like a head or tail phenomenon in stochastic processes, uncertainty in the adjudication affects the decisions of the parties in a legal negotiation. This paper therefore applies the principles of aleatory analysis to determine how negotiations fail in the legal process, introduce the axiological concept of optimal transaction cost and formulates a numerical methodology based on backwards induction and stochastic options pricing economics in estimating the reasonable and fair bargain in order to induce settlements thereby increasing efficiency and reducing social costs.

A rich class of mechanism design problems can be understood as incomplete-information games between a principal who commits to a policy and an agent who responds, with payoffs determined by an unknown state of the world. Traditionally, these models require strong and often-impractical assumptions about beliefs (a common prior over the state). In this paper, we dispense with the common prior. Instead, we consider a repeated interaction where both the principal and the agent may learn over time from the state history. We reformulate mechanism design as a reinforcement learning problem and develop mechanisms that attain natural benchmarks without any assumptions on the state-generating process. Our results make use of novel behavioral assumptions for the agent -- centered around counterfactual internal regret -- that capture the spirit of rationality without relying on beliefs.

We study a game of strategic information design between a sender, who chooses state-dependent information structures, a mediator who can then garble the signals generated from these structures, and a receiver who takes an action after observing the signal generated by the first two players. We characterize sufficient conditions for information revelation, compare outcomes with and without a mediator and provide comparative statics with regard to the preferences of the sender and the mediator. We also provide novel conceptual and computational insights about the set of feasible posterior beliefs that the sender can induce, and use these results to obtain insights about equilibrium outcomes. The sender never benefits from mediation, while the receiver might. Strikingly, the receiver benefits when the mediator's preferences are not perfectly aligned with hers; rather the mediator should prefer more information revelation than the sender, but less than perfect revelation.

An important question in economics is how people choose between different payments in the future. The classical normative model predicts that a decision maker discounts a later payment relative to an earlier one by an exponential function of the time between them. Descriptive models use non-exponential functions to fit observed behavioral phenomena, such as preference reversal. Here we propose a model of discounting, consistent with standard axioms of choice, in which decision makers maximize the growth rate of their wealth. Four specifications of the model produce four forms of discounting -- no discounting, exponential, hyperbolic, and a hybrid of exponential and hyperbolic -- two of which predict preference reversal. Our model requires no assumption of behavioral bias or payment risk.

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon's differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.