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At least 19 recordsLinked to original sources
arXiv2021

Constructive Decision Theory

In most contemporary approaches to decision making, a decision problem is described by a sets of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has preferences. Most interesting decision problems, however, do not come with a state space and an outcome space. Indeed, in complex problems it is often far from clear what the state and outcome spaces would be. We present an alternative foundation for decision making, in which the primitive objects of choice are syntactic programs. A representation theorem is proved in the spirit of standard representation theorems, showing that if the DM's preference relation on objects of choice satisfies appropriate axioms, then there exist a set S of states, a set O of outcomes, a way of interpreting the objects of choice as functions from S to O, a probability on S, and a utility function on O, such that the DM prefers choice a to choice b if and only if the expected utility of a is higher than that of b. Thus, the state space and outcome space are subjective, just like the probability and utility; they are not part of the description of the problem. In principle, a modeler can test for SEU behavior without having access to states or outcomes. We illustrate the power of our approach by showing that it can capture decision makers who are subject to framing effects.

cs.GT↗
arXiv2020

Rational Groupthink

We study how long-lived rational agents learn from repeatedly observing a private signal and each others' actions. With normal signals, a group of any size learns more slowly than just four agents who directly observe each others' private signals in each period. Similar results apply to general signal structures. We identify rational groupthink---in which agents ignore their private signals and choose the same action for long periods of time---as the cause of this failure of information aggregation.

cs.GT↗
arXiv2018

Trading Networks with Bilateral Contracts

We consider a model of matching in trading networks in which firms can enter into bilateral contracts. In trading networks, stable outcomes, which are immune to deviations of arbitrary sets of firms, may not exist. We define a new solution concept called trail stability. Trail-stable outcomes are immune to consecutive, pairwise deviations between linked firms. We show that any trading network with bilateral contracts has a trail-stable outcome whenever firms' choice functions satisfy the full substitutability condition. For trail-stable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness, and comparative statics of firm entry and exit. We also introduce weak trail stability which is implied by trail stability under full substitutability. We describe relationships between the solution concepts.

cs.GT↗
arXiv2015

Money as Minimal Complexity

We consider mechanisms that provide traders the opportunity to exchange commodity $i$ for commodity $j$, for certain ordered pairs $ij$. Given any connected graph $G$ of opportunities, we show that there is a unique mechanism $M_{G}$ that satisfies some natural conditions of "fairness" and "convenience". Let $\mathfrak{M}(m)$ denote the class of mechanisms $M_{G}$ obtained by varying $G$ on the commodity set $\left\{1,\ldots,m\right\} $. We define the complexity of a mechanism $M$ in $\mathfrak{M(m)}$ to be a certain pair of integers $τ(M),π(M)$ which represent the time required to exchange $i$ for $j$ and the information needed to determine the exchange ratio (each in the worst case scenario, across all $i\neq j$). This induces a quasiorder $\preceq$ on $\mathfrak{M}(m)$ by the rule \[ M\preceq M^{\prime}\text{if}τ(M)\leqτ(M^{\prime})\text{and}π(M)\leqπ(M^{\prime}). \] We show that, for $m>3$, there are precisely three $\preceq$-minimal mechanisms $M_{G}$ in $\mathfrak{M}(m)$, where $G$ corresponds to the star, cycle and complete graphs. The star mechanism has a distinguished commodity -- the money -- that serves as the sole medium of exchange and mediates trade between decentralized markets for the other commodities. Our main result is that, for any weights $λ,μ>0,$ the star mechanism is the unique minimizer of $λτ(M)+μπ(M)$ on $\mathfrak{M}(m)$ for large enough $m$.

cs.GT↗
arXiv2015

Graphical Exchange Mechanisms

Consider an exchange mechanism which accepts diversified offers of various commodities and redistributes everything it receives. We impose certain conditions of fairness and convenience on such a mechanism and show that it admits unique prices, which equalize the value of offers and returns for each individual. We next define the complexity of a mechanism in terms of certain integers $τ_{ij},π_{ij}$ and $k_{i}$ that represent the time required to exchange $i$ for $j$, the difficulty in determining the exchange ratio, and the dimension of the message space. We show that there are a finite number of minimally complex mechanisms, in each of which all trade is conducted through markets for commodity pairs. Finally we consider minimal mechanisms with smallest worst-case complexities $τ=\maxτ_{ij}$ and $π=\maxπ_{ij}$. For $m>3$ commodities, there are precisely three such mechanisms, one of which has a distinguished commodity -- the money -- that serves as the sole medium of exchange. As $m\rightarrow \infty$ the money mechanism is the only one with bounded $\left( π,τ\right) $.

cs.GT↗
arXiv2016

A/B Testing of Auctions

For many application areas A/B testing, which partitions users of a system into an A (control) and B (treatment) group to experiment between several application designs, enables Internet companies to optimize their services to the behavioral patterns of their users. Unfortunately, the A/B testing framework cannot be applied in a straightforward manner to applications like auctions where the users (a.k.a., bidders) submit bids before the partitioning into the A and B groups is made. This paper combines auction theoretic modeling with the A/B testing framework to develop methodology for A/B testing auctions. The accuracy of our method %, assuming the auction is directly comparable to ideal A/B testing where there is no interference between A and B. Our results are based on an extension and improved analysis of the inference method of Chawla et al. (2014).

cs.GT↗
arXiv2018

Decentralized Bayesian learning in dynamic games: A framework for studying informational cascades

We study the problem of Bayesian learning in a dynamical system involving strategic agents with asymmetric information. In a series of seminal papers in the literature, this problem has been investigated under a simplifying model where myopically selfish players appear sequentially and act once in the game, based on private noisy observations of the system state and public observation of past players' actions. It has been shown that there exist information cascades where users discard their private information and mimic the action of their predecessor. In this paper, we provide a framework for studying Bayesian learning dynamics in a more general setting than the one described above. In particular, our model incorporates cases where players are non-myopic and strategically participate for the whole duration of the game, and cases where an endogenous process selects which subset of players will act at each time instance. The proposed framework hinges on a sequential decomposition methodology for finding structured perfect Bayesian equilibria (PBE) of a general class of dynamic games with asymmetric information, where user-specific states evolve as conditionally independent Markov processes and users make independent noisy observations of their states. Using this methodology, we study a specific dynamic learning model where players make decisions about public investment based on their estimates of everyone's types. We characterize a set of informational cascades for this problem where learning stops for the team as a whole. We show that in such cascades, all players' estimates of other players' types freeze even though each individual player asymptotically learns its own true type.

cs.GT↗
arXiv2019

Consistent Approval-Based Multi-Winner Rules

This paper is an axiomatic study of consistent approval-based multi-winner rules, i.e., voting rules that select a fixed-size group of candidates based on approval ballots. We introduce the class of counting rules and provide an axiomatic characterization of this class based on the consistency axiom. Building upon this result, we axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin--Courant rule. Our results demonstrate the variety of multi-winner rules and illustrate three different, orthogonal principles that multi-winner voting rules may represent: individual excellence, diversity, and proportionality.

cs.GT↗
arXiv2017

Pricing in non-convex markets with quadratic deliverability costs

The problem of obtaining market-clearing prices for markets with non-convexities has been widely studied in the literature. This is particularly the case in electricity markets, where worldwide deregulation leads to markets in which non-convexities arise from the decisions of market operators regarding which generators are committed to provide electricity power. Here, we extend seminal results in this area to address the problem of obtaining market-clearing prices for markets in which beyond non-convexities, it is relevant to account for convex quadratic market costs. In a general market, such costs arise from quadratic commodity costs or transactions costs. In an electricity market, such quadratic costs arise when ramping costs need to be considered due to the presence of renewable energy sources, which continue to increase their participation in electricity markets. To illustrate our results, we compute and analyze the clearing prices of a classical market problem with the addition of ramping costs.

math.OC↗
arXiv2017

Good signals gone bad: dynamic signalling with switching efforts

This paper examines signalling when the sender exerts effort and receives benefits over time. Receivers only observe a noisy public signal about the effort, which has no intrinsic value. The modelling of signalling in a dynamic context gives rise to novel equilibrium outcomes. In some equilibria, a sender with a higher cost of effort exerts strictly more effort than his low-cost counterpart. The low-cost type can compensate later for initial low effort, but this is not worthwhile for a high-cost type. The interpretation of a given signal switches endogenously over time, depending on which type the receivers expect to send it. JEL classification: D82, D83, C73. Keywords: Dynamic games, signalling , incomplete information

econ.GN↗
arXiv2021

Identification of hedonic equilibrium and nonseparable simultaneous equations

This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models, where products are differentiated along more than one dimension and agents are characterized by several dimensions of unobserved heterogeneity. With products differentiated along a quality index and agents characterized by scalar unobserved heterogeneity, single crossing conditions on preferences and technology provide identifying restrictions in Ekeland, Heckman and Nesheim (2004) and Heckman, Matzkin and Nesheim (2010). We develop similar shape restrictions in the multi-attribute case. These shape restrictions, which are based on optimal transport theory and generalized convexity, allow us to identify preferences for goods differentiated along multiple dimensions, from the observation of a single market. We thereby derive nonparametric identification results for nonseparable simultaneous equations and multi-attribute hedonic equilibrium models with (possibly) multiple dimensions of unobserved heterogeneity. One of our results is a proof of absolute continuity of the distribution of endogenously traded qualities, which is of independent interest.

econ.EM↗
arXiv2023

The Limits of Citation Counts

I study the measurement of scientists' influence using bibliographic data. The main result is an axiomatic characterization of the family of citation-counting indices, a broad class of influence measures which includes the renowned h-index. The result highlights several limitations of these indices: they are not suitable to compare scientists across different fields, and they cannot account for indirect influence. I explore how these limitations can be overcome by using richer bibliographic information.

cs.DL↗
arXiv2019

A Random Attention Model

This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any particular attention formation, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the decision-maker's attention. We then develop revealed preference theory within RAM and obtain precise testable implications for observable choice probabilities. Based on these theoretical findings, we propose econometric methods for identification, estimation, and inference of the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results, and showcase their performance using simulations.

econ.EM↗
arXiv2018

Eliminating the effect of rating bias on reputation systems

The ongoing rapid development of the e-commercial and interest-base websites make it more pressing to evaluate objects' accurate quality before recommendation by employing an effective reputation system. The objects' quality are often calculated based on their historical information, such as selected records or rating scores, to help visitors to make decisions before watching, reading or buying. Usually high quality products obtain a higher average ratings than low quality products regardless of rating biases or errors. However many empirical cases demonstrate that consumers may be misled by rating scores added by unreliable users or deliberate tampering. In this case, users' reputation, i.e., the ability to rating trustily and precisely, make a big difference during the evaluating process. Thus, one of the main challenges in designing reputation systems is eliminating the effects of users' rating bias on the evaluation results. To give an objective evaluation of each user's reputation and uncover an object's intrinsic quality, we propose an iterative balance (IB) method to correct users' rating biases. Experiments on two online video-provided Web sites, namely MovieLens and Netflix datasets, show that the IB method is a highly self-consistent and robust algorithm and it can accurately quantify movies' actual quality and users' stability of rating. Compared with existing methods, the IB method has higher ability to find the "dark horses", i.e., not so popular yet good movies, in the Academy Awards.

physics.soc-ph↗
arXiv2018

Greedy Algorithms for Maximizing Nash Social Welfare

We study the problem of fairly allocating a set of indivisible goods among agents with additive valuations. The extent of fairness of an allocation is measured by its Nash social welfare, which is the geometric mean of the valuations of the agents for their bundles. While the problem of maximizing Nash social welfare is known to be APX-hard in general, we study the effectiveness of simple, greedy algorithms in solving this problem in two interesting special cases. First, we show that a simple, greedy algorithm provides a 1.061-approximation guarantee when agents have identical valuations, even though the problem of maximizing Nash social welfare remains NP-hard for this setting. Second, we show that when agents have binary valuations over the goods, an exact solution (i.e., a Nash optimal allocation) can be found in polynomial time via a greedy algorithm. Our results in the binary setting extend to provide novel, exact algorithms for optimizing Nash social welfare under concave valuations. Notably, for the above mentioned scenarios, our techniques provide a simple alternative to several of the existing, more sophisticated techniques for this problem such as constructing equilibria of Fisher markets or using real stable polynomials.

cs.GT↗
arXiv2018

Promoting cooperation by reputation-driven group formation

In previous studies of spatial public goods game, each player is able to establish a group. However, in real life, some players cannot successfully organize groups for various reasons. In this paper, we propose a mechanism of reputation-driven group formation, in which groups can only be organized by players whose reputation reaches or exceeds a threshold. We define a player's reputation as the frequency of cooperation in the last $T$ time steps. We find that the highest cooperation level can be obtained when groups are only established by pure cooperators who always cooperate in the last $T$ time steps. Effects of the memory length $T$ on cooperation are also studied.

physics.soc-ph↗
arXiv2026

Measuring Information Burden: From Coalition-Based Reasoning to the Price System

The price system is often said to economize on information. This paper asks how much information it saves. I develop a formal framework for measuring the informational burden that agents would have to bear if they had to reason individually over feasible coalitional alternatives. Taking the convergence theorem of Debreu and Scarf (1963) as the benchmark, I ask how much coalition-feasibility information must be held, and how it must be distributed, for individual acceptance decisions to recover the core. Agents' information is represented as finite sets of meaning-bearing sentences in a formal language, and reasoning is modeled as proof in Gentzen's sequent calculus. The main result characterizes the minimal informational structure under which unanimous acceptability coincides with the core for all transferable-utility games on a fixed player set: every coalition must be known to at least one of its members. Removing information about even a single coalition from all of its members suffices to break the equivalence for some game. Applying this result to the $k$-fold replica economy, I identify and count the load-bearing coalitions whose feasibility information must be distributed across the population. The associated average per-agent informational burden grows as $Θ(4^k/k^{3/2})$ -- exponentially in the size of the economy. This is, precisely and formally, what the price system saves.

econ.TH↗