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arXiv2018

Banking Stability System: Does it Matter if the Rate of Return is Fixed or Stochastic?

The purpose is to compare the perfect Stochastic Return (SR) model like Islamic banks to the Fixed Return (FR) model as in conventional banks by measuring up their impacts at the macroeconomic level. We prove that if the optimal choice of investor share in SR model α* realizes the indifference of the financial institution toward SR and FR models, there exists α less than α* such that the banks strictly prefers the SR model. Also, there exists α, γ and λ verifying the conditions of α-sharing such that each party in economy can be better under the SR model and the economic welfare could be improved in a Pareto-efficient way.

econ.TH↗

arXiv2018

Preference Identification

An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close approximations of the subject's preference, even when the limiting (countably infinite) data are enough to infer the preference perfectly. We provide sufficient conditions on the set of alternatives, preferences, and sequences of pairs so that the observation of finitely many choices allows the experimenter to learn the subject's preference with arbitrary precision. While preferences can be identified under our sufficient conditions, we show that it is harder to identify utility functions. We illustrate our results with several examples, including consumer choice, expected utility, and preferences in the Anscombe-Aumann model.

econ.TH↗

arXiv2018

Dynamic Random Subjective Expected Utility

Dynamic Random Subjective Expected Utility (DR-SEU) allows to model choice data observed from an agent or a population of agents whose beliefs about objective payoff-relevant states and tastes can both evolve stochastically. Our observable, the augmented Stochastic Choice Function (aSCF) allows, in contrast to previous work in decision theory, for a direct test of whether the agent's beliefs reflect the true data-generating process conditional on their private information as well as identification of the possibly incorrect beliefs. We give an axiomatic characterization of when an agent satisfies the model, both in a static as well as in a dynamic setting. We look at the case when the agent has correct beliefs about the evolution of objective states as well as at the case when her beliefs are incorrect but unforeseen contingencies are impossible. We also distinguish two subvariants of the dynamic model which coincide in the static setting: Evolving SEU, where a sophisticated agent's utility evolves according to a Bellman equation and Gradual Learning, where the agent is learning about her taste. We prove easy and natural comparative statics results on the degree of belief incorrectness as well as on the speed of learning about taste. Auxiliary results contained in the online appendix extend previous decision theory work in the menu choice and stochastic choice literature from a technical as well as a conceptual perspective.

econ.TH↗

arXiv2018

A characterization of "Phelpsian" statistical discrimination

We establish that statistical discrimination is possible if and only if it is impossible to uniquely identify the signal structure observed by an employer from a realized empirical distribution of skills. The impossibility of statistical discrimination is shown to be equivalent to the existence of a fair, skill-dependent, remuneration for workers. Finally, we connect the statistical discrimination literature to Bayesian persuasion, establishing that if discrimination is absent, then the optimal signaling problem results in a linear payoff function (as well as a kind of converse).

econ.TH↗

arXiv2020

Robust Pricing with Refunds

Before purchase, a buyer of an experience good learns about the product's fit using various information sources, including some of which the seller may be unaware of. The buyer, however, can conclusively learn the fit only after purchasing and trying out the product. We show that the seller can use a simple mechanism to best take advantage of the buyer's post-purchase learning to maximize his guaranteed-profit. We show that this mechanism combines a generous refund, which performs well when the buyer is relatively informed, with non-refundable random discounts, which work well when the buyer is relatively uninformed.

cs.GT↗

arXiv2018

Network-based Referral Mechanism in a Crowdfunding-based Marketing Pattern

Crowdfunding is gradually becoming a modern marketing pattern. By noting that the success of crowdfunding depends on network externalities, our research aims to utilize them to provide an applicable referral mechanism in a crowdfunding-based marketing pattern. In the context of network externalities, measuring the value of leading customers is chosen as the key to coping with the research problem by considering that leading customers take a critical stance in forming a referral network. Accordingly, two sequential-move game models (i.e., basic model and extended model) were established to measure the value of leading customers, and a skill of matrix transformation was adopted to solve the model by transforming a complicated multi-sequence game into a simple simultaneous-move game. Based on the defined value of leading customers, a network-based referral mechanism was proposed by exploring exactly how many awards are allocated along the customer sequence to encourage the leading customers' actions of successful recommendation and by demonstrating two general rules of awarding the referrals in our model setting. Moreover, the proposed solution approach helps deepen an understanding of the effect of the leading position, which is meaningful for designing more numerous referral approaches.

econ.TH↗

arXiv2018

Existence of Equilibrium Prices: A Pedagogical Proof

Under the same assumptions made by Mas-Colell et al. (1995), I develop a short, simple, and complete proof of existence of equilibrium prices based on excess demand functions. The result is obtained by applying the Brouwer fixed point theorem to a trimmed simplex which does not contain prices equal to zero. The mathematical techniques are based on some results obtained in Neuefeind (1980) and Geanakoplos (2003).

econ.TH↗

arXiv2018

Mechanism Design with News Utility

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.

econ.TH↗

arXiv2022

Latent Agents in Networks: Estimation and Targeting

We consider a network of agents. Associated with each agent are her covariate and outcome. Agents influence each other's outcomes according to a certain connection/influence structure. A subset of the agents participate on a platform, and hence, are observable to it. The rest are not observable to the platform and are called the latent agents. The platform does not know the influence structure of the observable or the latent parts of the network. It only observes the data on past covariates and decisions of the observable agents. Observable agents influence each other both directly and indirectly through the influence they exert on the latent agents. We investigate how the platform can estimate the dependence of the observable agents' outcomes on their covariates, taking the latent agents into account. First, we show that this relationship can be succinctly captured by a matrix and provide an algorithm for estimating it under a suitable approximate sparsity condition using historical data of covariates and outcomes for the observable agents. We also obtain convergence rates for the proposed estimator despite the high dimensionality that allows more agents than observations. Second, we show that the approximate sparsity condition holds under the standard conditions used in the literature. Hence, our results apply to a large class of networks. Finally, we apply our results to two practical settings: targeted advertising and promotional pricing. We show that by using the available historical data with our estimator, it is possible to obtain asymptotically optimal advertising/pricing decisions, despite the presence of latent agents.

cs.SI↗

arXiv2023

The strategy of conflict and cooperation

This paper introduces a unified framework called cooperative extensive form games, which (i) generalizes standard non-cooperative games, and (ii) allows for more complex coalition formation dynamics than previous concepts like coalition-proof Nash equilibrium. Central to this framework is a novel solution concept called cooperative equilibrium system (CES). CES differs from Nash equilibrium in two important respects. First, a CES is immune to both unilateral and multilateral `credible' deviations. Second, unlike Nash equilibrium, whose stability relies on the assumption that the strategies of non-deviating players are held fixed, CES allows for the possibility that players may regroup and adjust their strategies in response to a deviation. The main result establishes that every cooperative extensive form game, possibly with imperfect information, possesses a CES. For games with perfect information, the proof is constructive. This framework is broadly applicable in contexts such as oligopolistic markets and dynamic political bargaining.

econ.TH↗

arXiv2018

Catch-Up: A Rule that Makes Service Sports More Competitive

Service sports include two-player contests such as volleyball, badminton, and squash. We analyze four rules, including the Standard Rule (SR), in which a player continues to serve until he or she loses. The Catch-Up Rule (CR) gives the serve to the player who has lost the previous point - as opposed to the player who won the previous point, as under SR. We also consider two Trailing Rules that make the server the player who trails in total score. Surprisingly, compared with SR, only CR gives the players the same probability of winning a game while increasing its expected length, thereby making it more competitive and exciting to watch. Unlike one of the Trailing Rules, CR is strategy-proof. By contrast, the rules of tennis fix who serves and when; its tiebreaker, however, keeps play competitive by being fair - not favoring either the player who serves first or who serves second.

math.HO↗

arXiv2020

The Structure of Equilibria in Trading Networks with Frictions

Several structural results for the set of competitive equilibria in trading networks with frictions are established: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, and a group-incentive-compatibility result hold with imperfectly transferable utility and in the presence of frictions. While our results are developed in a trading network model, they also imply analogous (and new) results for exchange economies with combinatorial demand and for two-sided matching markets with transfers.

econ.TH↗

arXiv2020

Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response

We derive Nash equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as a smooth Nash equilibrium problem. The existence and uniqueness of solutions are proven for all smoothing parameters. Accumulation points of Nash equilibria exist for a decreasing sequence of these smoothing parameters and we show that these candidates fulfill the conditions of s-stationarity and are Nash equilibria to the multi-leader-follower game. Finally, we propose an update on the leader variables for efficient computation and numerically compare nonsmooth Newton and subgradient methods.

math.OC↗

arXiv2018

Downstream Effects of Affirmative Action

We study a two-stage model, in which students are 1) admitted to college on the basis of an entrance exam which is a noisy signal about their qualifications (type), and then 2) those students who were admitted to college can be hired by an employer as a function of their college grades, which are an independently drawn noisy signal of their type. Students are drawn from one of two populations, which might have different type distributions. We assume that the employer at the end of the pipeline is rational, in the sense that it computes a posterior distribution on student type conditional on all information that it has available (college admissions, grades, and group membership), and makes a decision based on posterior expectation. We then study what kinds of fairness goals can be achieved by the college by setting its admissions rule and grading policy. For example, the college might have the goal of guaranteeing equal opportunity across populations: that the probability of passing through the pipeline and being hired by the employer should be independent of group membership, conditioned on type. Alternately, the college might have the goal of incentivizing the employer to have a group blind hiring rule. We show that both goals can be achieved when the college does not report grades. On the other hand, we show that under reasonable conditions, these goals are impossible to achieve even in isolation when the college uses an (even minimally) informative grading policy.

cs.GT↗

arXiv2018

Repeated Coordination with Private Learning

We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et al., 2008), but do not coordinate in every equilibrium. We show that there exist stable equilibria in which players can overcome unfavorable signal realizations and eventually coordinate on the correct action, for any discount factor. For high discount factors, we show that in addition players can also achieve efficient payoffs.

econ.TH↗

arXiv2020

The Indirect Cost of Information

We study the indirect cost of information from sequential information cost minimization. A key sub-additivity condition, together with monotonicity equivalently characterizes the class of indirect cost functions generated from any direct information cost. Adding an extra (uniform) posterior separability condition equivalently characterizes the indirect cost generated from any direct cost favoring incremental evidences. We also provide the necessary and sufficient condition when prior independent direct cost generates posterior separable indirect cost.

econ.TH↗

arXiv2018

The Core of an Economy with an Endogenous Social Division of Labour

This paper considers the core of a competitive market economy with an endogenous social division of labour. The theory is founded on the notion of a "consumer-producer", who consumes as well as produces commodities. First, we show that the Core of such an economy with an endogenous social division of labour can be founded on deviations of coalitions of arbitrary size, extending the seminal insights of Vind and Schmeidler for pure exchange economies. Furthermore, we establish the equivalence between the Core and the set of competitive equilibria for continuum economies with an endogenous social division of labour. Our analysis also concludes that self-organisation in a social division of labour can be incorporated into the Edgeworthian barter process directly. This is formulated as a Core equivalence result stated for a Structured Core concept based on renegotiations among fully specialised economic agents, i.e., coalitions that use only fully developed internal divisions of labour. Our approach bridges the gap between standard economies with social production and coalition production economies. Therefore, a more straightforward and natural interpretation of coalitional improvement and the Core can be developed than for coalition production economies.

econ.TH↗

arXiv2018

A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity

We map the recently proposed notions of algorithmic fairness to economic models of Equality of opportunity (EOP)---an extensively studied ideal of fairness in political philosophy. We formally show that through our conceptual mapping, many existing definition of algorithmic fairness, such as predictive value parity and equality of odds, can be interpreted as special cases of EOP. In this respect, our work serves as a unifying moral framework for understanding existing notions of algorithmic fairness. Most importantly, this framework allows us to explicitly spell out the moral assumptions underlying each notion of fairness, and interpret recent fairness impossibility results in a new light. Last but not least and inspired by luck egalitarian models of EOP, we propose a new family of measures for algorithmic fairness. We illustrate our proposal empirically and show that employing a measure of algorithmic (un)fairness when its underlying moral assumptions are not satisfied, can have devastating consequences for the disadvantaged group's welfare.

cs.LG↗