Economics

We characterize Pareto optimality via sequential utilitarian welfare maximization: a utility vector u is Pareto optimal if and only if there exists a finite sequence of nonnegative (and eventually positive) welfare weights such that u maximizes utilitarian welfare with each successive welfare weights among the previous set of maximizers. The characterization can be further related to maximization of a piecewise-linear concave social welfare function and sequential bargaining among agents a la generalized Nash bargaining. We provide conditions enabling simpler utilitarian characterizations and a version of the second welfare

We characterize three interrelated concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model for a game with incomplete information. Based on it, we give two groups of characterizations. The first group characterizes permissibility and proper rationalizability. The second group characterizes permissibility in an alternative way and iterated admissibility. In each group, the conditions for the latter are stronger than those for the former, which corresponds to the fact that proper rationalizability and iterated admissibility are two (compatible) refinements of permissibility within the complete information framework. The intrinsic difference between the two groups are the role of rationality: the first group does not need it, while the second group does.

In this paper, a relation between shadow price and the Lagrangian multiplier for nonsmooth problem is explored. It is shown that the Lagrangian Multiplier is the upper bound of shadow price for convex optimization and a class of Lipschtzian optimizations. This work can be used in shadow pricing for nonsmooth situation. The several nonsmooth functions involved in this class of Lipschtzian optimizations is listed. Finally, an application to electricity pricing is discussed.

Consider an application sold on an on-line platform, with the app paying a commission fee and, henceforth, offered for sale on the platform. The ability to sell the application depends on its customer ranking. Therefore, developers may have an incentive to promote their applications ranking in a dishonest manner. One way to do this is by faking positive customer reviews. However, the platform is able to detect dishonest behavior (cheating) with some probability and then proceeds to decide whether to ban the application. We provide an analysis and find the equilibrium behaviors of both the applications developers (cheat or not) and the platform (setting of the commission fee). We provide initial insights into how the platforms detection accuracy affects the incentives of the app developers.

To what extent can agents with misspecified subjective models predict false correlations? We study an "analyst" who utilizes models that take the form of a recursive system of linear regression equations. The analyst fits each equation to minimize the sum of squared errors against an arbitrarily large sample. We characterize the maximal pairwise correlation that the analyst can predict given a generic objective covariance matrix, subject to the constraint that the estimated model does not distort the mean and variance of individual variables. We show that as the number of variables in the model grows, the false pairwise correlation can become arbitrarily close to one, regardless of the true correlation.

We propose and axiomatize the categorical thinking model (CTM) in which the framing of the decision problem affects how agents categorize alternatives, that in turn affects their evaluation of it. Prominent models of salience, status quo bias, loss-aversion, inequality aversion, and present bias all fit under the umbrella of CTM. This suggests categorization is an underlying mechanism of key departures from the neoclassical model of choice. We specialize CTM to provide a behavioral foundation for the salient thinking model of Bordalo et al. (2013) that highlights its strong predictions and distinctions from other models.

We study the strategic simplicity of stable matching mechanisms where one side has fixed preferences, termed priorities. Specifically, we ask which priorities are such that the strategyproofness of deferred acceptance (DA) can be recognized by agents unable to perform contingency reasoning, that is, \emph{when is DA obviously strategyproof} (Li, 2017)? We answer this question by completely characterizing those priorities which make DA obviously strategyproof (OSP). This solves an open problem of Ashlagi and Gonczarowski, 2018. We find that when DA is OSP, priorities are either acyclic (Ergin, 2002), a restrictive condition which allows priorities to only differ on only two agents at a time, or contain an extremely limited cyclic pattern where all priority lists are identical except for exactly two. We conclude that, for stable matching mechanisms, the tension between understandability (in the sense of OSP) and expressiveness of priorities is very high.

The main aim of this paper is to give some clarifications to the recent paper published in Computational and Applied Mathematics by Naz and Chaudhry.

We develop a framework in which individuals' preferences coevolve with their abilities to deceive others about their preferences and intentions. Specifically, individuals are characterised by (i) a level of cognitive sophistication and (ii) a subjective utility function. Increased cognition is costly, but higher-level individuals have the advantage of being able to deceive lower-level opponents about their preferences and intentions in some of the matches. In the remaining matches, the individuals observe each other's preferences. Our main result shows that, essentially, only efficient outcomes can be stable. Moreover, under additional mild assumptions, we show that an efficient outcome is stable if and only if the gain from unilateral deviation is smaller than the effective cost of deception in the environment.

Many markets rely on traders truthfully communicating who has cheated in the past and ostracizing those traders from future trade. This paper investigates when truthful communication is incentive compatible. We find that if each side has a myopic incentive to deviate, then communication incentives are satisfied only when the volume of trade is low. By contrast, if only one side has a myopic incentive to deviate, then communication incentives do not constrain the volume of supportable trade. Accordingly, there are strong gains from structuring trade so that one side either moves first or has its cooperation guaranteed by external enforcement.