Economics

We consider sender-receiver games, where the sender and the receiver are two distinct nodes in a communication network. Communication between the sender and the receiver is thus indirect. We ask when it is possible to robustly implement the equilibrium outcomes of the direct communication game as equilibrium outcomes of indirect communication games on the network. Robust implementation requires that: (i) the implementation is independent of the preferences of the intermediaries and (ii) the implementation is guaranteed at all histories consistent with unilateral deviations by the intermediaries. Robust implementation of direct communication is possible if and only if either the sender and receiver are directly connected or there exist two disjoint paths between the sender and the receiver.

We study the robust double auction mechanisms, that is, the double auction mechanisms that satisfy dominant strategy incentive compatibility, ex-post individual rationality, ex-post budget balance and feasibility. We first establish that the price in any deterministic robust mechanism does not depend on the valuations of the trading players. We next establish that, with the non-bossiness assumption, the price in any deterministic robust mechanism does not depend on players' valuations at all, whether trading or non-trading, i.e., the price is posted in advance. Our main result is a characterization result that, with the non-bossiness assumption along with other assumptions on the properties of the mechanism, the posted price mechanism with an exogenous rationing rule is the only deterministic robust double auction mechanism. We also show that, even without the non-bossiness assumption, it is quite difficult to find a reasonable robust double auction mechanism other than the posted price mechanism with rationing.

This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed strategies and in pure strategies) and satisfy the important properties of admissibility, aggregate robustness, and ex post robust perfection. These properties strengthen relevant equilibrium results in an extensive literature on strategic interactions among a large number of agents. Illustrative applications to congestion games and potential games are presented. In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique symmetric robust perfect equilibrium.

We study the implications of selling through a voice-based virtual assistant (VA). The seller has a set of products available and the VA decides which product to offer and at what price, seeking to maximize its revenue, consumer- or total-surplus. The consumer is impatient and rational, seeking to maximize her expected utility given the information available to her. The VA selects products based on the consumer's request and other information available to it and then presents them sequentially. Once a product is presented and priced, the consumer evaluates it and decides whether to make a purchase. The consumer's valuation of each product comprises a pre-evaluation value, which is common knowledge, and a post-evaluation component which is private to the consumer. We solve for the equilibria and develop efficient algorithms for implementing the solution. We examine the effects of information asymmetry on the outcomes and study how incentive misalignment depends on the distribution of private valuations. We find that monotone rankings are optimal in the cases of a highly patient or impatient consumer and provide a good approximation for other levels of patience. The relationship between products' expected valuations and prices depends on the consumer's patience level and is monotone increasing (decreasing) when the consumer is highly impatient (patient). Also, the seller's share of total surplus decreases in the amount of private information. We compare the VA to a traditional web-based interface, where multiple products are presented simultaneously on each page. We find that within a page, the higher-value products are priced lower than the lower-value products when the private valuations are exponentially distributed. Finally, the web-based interface generally achieves higher profits for the seller than a VA due to the greater commitment power inherent in its presentation.

The present authors have put forward a quantum game theory based model of market prices movements. By using Fisher information, we present a construction of an equation of Schrödinger type for probability distributions for relationship between demand and supply. Various analogies between quantum physics and market phenomena can be found.

I introduce a model of scoring. An intermediary aggregates multiple features of a sender into a score. A receiver sees this score and takes a decision. The receiver wants his decision to match the sender's latent characteristic. But the sender wants the most favorable decision, and she can distort each of her features at a private cost. I characterize the receiver-optimal scoring rule. This rule underweights some features to deter sender distortion, and overweights other features to keep the score unbiased. The receiver prefers this score to seeing the sender's full features because the coarser information mitigates his commitment problem.

In many settings, multiple uninformed agents bargain simultaneously with a single informed agent in each of multiple periods. For example, workers and firms negotiate each year over salaries, and the firm has private information about the value of workers' output. I study the effects of transparency in these settings; uninformed agents may observe others' past bargaining outcomes, e.g. wages. I show that in equilibrium, each uninformed agent will choose in each period whether to try to separate the informed agent's types (screen) or receive the same outcome regardless of type (pool). In other words, the agents engage in a form of experimentation via their bargaining strategies. There are two main theoretical insights. First, there is a complementary screening effect: the more agents screen in equilibrium, the lower the information rents that each will have to pay. Second, the payoff of the informed agent will have a certain supermodularity property, which implies that equilibria with screening are "fragile" to deviations by uninformed agents. I apply the results to study pay-secrecy regulations and anti-discrimination policy. I show that, surprisingly, penalties for pay discrimination have no impact on bargaining outcomes. I discuss how this result depends on the legal framework for discrimination cases, and suggest changes to enhance the efficacy of anti-discrimination regulations. In particular, anti-discrimination law should preclude the so-called "salary negotiation defense".

We identify a new and pervasive dynamic agency problem: that of incentivising the prompt disclosure of productive information. To study it, we introduce a 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 the agent's utility. We uncover a striking 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.

Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a rich database, with sufficiently diverse rankings, is often beyond reach. Inexperience demands either "on the fly" learning-by-doing or prudence: the arrival of a novel case does not force (i) a revision of current rankings, (ii) dogmatism towards new rankings, or (iii) intransitivity. For this higher-order framework of inductive inference, we derive a suitably unique numerical representation of these rankings via a matrix on eventualities x cases and describe a robust test of prudence. Applications include: the success/failure of startups; the veracity of fake news; and novel conditions for the existence of a yield curve that is robustly arbitrage-free.

We construct a model where people trade assets contingent on an observable signal that reflects public opinion. The agents in our model are replaced occasionally and each person updates beliefs in response to observed outcomes. We show that the distribution of the observed signal is described by a quasi non-ergodic process and that people continue to disagree with each other forever. Our model generates large wealth inequalities that arise from the multiplicative nature of wealth dynamics which makes successful bold bets highly profitable. The flip side of this statement is that unsuccessful bold bets are ruinous and lead the person who makes such bets into poverty. People who agree with the market belief have a low expected subjective gain from trading. People who disagree may either become spectacularly rich, or spectacularly poor.