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arXiv2022

Attraction versus Persuasion: Information Provision in Search Markets

We consider a model of oligopolistic competition in a market with search frictions, in which competing firms with products of unknown quality advertise how much information a consumer's visit will glean. In the unique symmetric equilibrium of this game, the countervailing incentives of attraction and persuasion yield a payoff function for each firm that is linear in the firm's realized effective value. If the expected quality of the products is sufficiently high (or competition is sufficiently fierce), this corresponds to full information--firms provide the first-best level of information. If not, this corresponds to information dispersion--firms randomize over signals.

math.PR↗

arXiv2019

Optimization-Based Algorithm for Evolutionarily Stable Strategies against Pure Mutations

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a mutation strategy that is initially rare. Finding such a strategy has been shown to be difficult from a theoretical complexity perspective. We present an algorithm for the case where mutations are restricted to pure strategies, and present experiments on several game classes including random and a recently-proposed cancer model. Our algorithm is based on a mixed-integer non-convex feasibility program formulation, which constitutes the first general optimization formulation for this problem. It turns out that the vast majority of the games included in the experiments contain ESS with small support, and our algorithm is outperformed by a support-enumeration based approach. However we suspect our algorithm may be useful in the future as games are studied that have ESS with potentially larger and unknown support size.

cs.GT↗

arXiv2018

Reputation is required for cooperation to emerge in dynamic networks

Melamed, Harrell, and Simpson have recently reported on an experiment which appears to show that cooperation can arise in a dynamic network without reputational knowledge, i.e., purely via dynamics [1]. We believe that their experimental design is actually not testing this, in so far as players do know the last action of their current partners before making a choice on their own next action and subsequently deciding which link to cut. Had the authors given no information at all, the result would be a decline in cooperation as shown in [2].

physics.soc-ph↗

arXiv2018

Forex trading and Twitter: Spam, bots, and reputation manipulation

Currency trading (Forex) is the largest world market in terms of volume. We analyze trading and tweeting about the EUR-USD currency pair over a period of three years. First, a large number of tweets were manually labeled, and a Twitter stance classification model is constructed. The model then classifies all the tweets by the trading stance signal: buy, hold, or sell (EUR vs. USD). The Twitter stance is compared to the actual currency rates by applying the event study methodology, well-known in financial economics. It turns out that there are large differences in Twitter stance distribution and potential trading returns between the four groups of Twitter users: trading robots, spammers, trading companies, and individual traders. Additionally, we observe attempts of reputation manipulation by post festum removal of tweets with poor predictions, and deleting/reposting of identical tweets to increase the visibility without tainting one's Twitter timeline.

cs.SI↗

arXiv2018

Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game

Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in two-player zero-sum games, but no guarantees in non-zero-sum games or in games with more than two players. We describe an agent that is able to defeat a variety of realistic opponents using an exact Nash equilibrium strategy in a 3-player imperfect-information game. This shows that, despite a lack of theoretical guarantees, agents based on Nash equilibrium strategies can be successful in multiplayer games after all.

cs.GT↗

arXiv2018

A Dynamic Analysis of Nash Equilibria in Search Models with Fiat Money

We study the rise in the acceptability fiat money in a Kiyotaki-Wright economy by developing a method that can determine dynamic Nash equilibria for a class of search models with genuine heterogenous agents. We also address open issues regarding the stability properties of pure strategies equilibria and the presence of multiple equilibria. Experiments illustrate the liquidity conditions that favor the transition from partial to full acceptance of fiat money, and the effects of inflationary shocks on production, liquidity, and trade.

econ.EM↗

arXiv2018

Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamics

In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces to a homogenized smooth BRD, where persistent payoff heterogeneity averages to homogeneous transitory payoff shocks. In this paper, we consider deterministic evolutionary dynamics in heterogeneous population and develop the stronger concept of local stability by imposing robustness to persistent payoff heterogeneity. It is known that nonaggregability holds generically if the switching rate in a given evolutionary dynamic correlates with the payoff gain from a switch. To parameterize the payoff sensitivity of an evolutionary dynamic, we propose to use tempered best response dynamics with bounded support of switching costs.

cs.GT↗

arXiv2023

Net gains in evolutionary dynamics: A unifying and intuitive approach to dynamic stability

Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been many attempts to prove this link, especially in evolutionary game theory, yielding both negative and positive results. This paper presents a universal and intuitive approach to this link. We prove that static stability assures dynamic stability if agents' choices of switching strategies are rationalizable by introducing costs and constraints in those switching decisions. This idea guides us to define \textit{net }gains from switches as the payoff improvement after deducting the costs. Under rationalizable dynamics, an agent maximizes the expected net gain subject to the constraints. We prove that the aggregate maximized expected net gain works as a Lyapunov function. It also explains reasons behind the known negative results. While our analysis here is confined to myopic evolutionary dynamics in population games, our approach is applicable to more complex situations.

math.OC↗

arXiv2018

Competitive pricing despite search costs if lower price signals quality

I show that firms price almost competitively and consumers can infer product quality from prices in markets where firms differ in quality and production cost, and learning prices is costly. Bankruptcy risk or regulation links higher quality to lower cost. If high-quality firms have lower cost, then they can signal quality by cutting prices. Then the low-quality firms must cut prices to retain customers. This price-cutting race to the bottom ends in a separating equilibrium in which the low-quality firms charge their competitive price and the high-quality firms charge slightly less.

econ.GN↗

arXiv2018

A rational decentralized generalized Nash equilibrium seeking for energy markets

We propose a method to design a decentralized energy market which guarantees individual rationality (IR) in expectation, in the presence of system-level grid constraints. We formulate the market as a welfare maximization problem subject to IR constraints, and we make use of Lagrangian duality to model the problem as a n-person non-cooperative game with a unique generalized Nash equilibrium (GNE). We provide a distributed algorithm which converges to the GNE. The convergence and properties of the algorithm are investigated by means of numerical simulations.

cs.CE↗

arXiv2019

The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations

The nonuniqueness of rational expectations is explained: in the stochastic, discrete-time, linear, constant-coefficients case, the associated free parameters are coefficients that determine the public's most immediate reactions to shocks. The requirement of model-consistency may leave these parameters completely free, yet when their values are appropriately specified, a unique solution is determined. In a broad class of models, the requirement of least-square forecast errors determines the parameter values, and therefore defines a unique solution. This approach is independent of dynamical stability, and generally does not suppress model dynamics. Application to a standard New Keynesian example shows that the traditional solution suppresses precisely those dynamics that arise from rational expectations. The uncovering of those dynamics reveals their incompatibility with the new I-S equation and the expectational Phillips curve.

econ.GN↗

arXiv2019

Markets Beyond Nash Welfare for Leontief Utilities

We study the allocation of divisible goods to competing agents via a market mechanism, focusing on agents with Leontief utilities. The majority of the economics and mechanism design literature has focused on \emph{linear} prices, meaning that the cost of a good is proportional to the quantity purchased. Equilibria for linear prices are known to be exactly the maximum Nash welfare allocations. \emph{Price curves} allow the cost of a good to be any (increasing) function of the quantity purchased. We show that price curve equilibria are not limited to maximum Nash welfare allocations with two main results. First, we show that an allocation can be supported by strictly increasing price curves if and only if it is \emph{group-domination-free}. A similarly characterization holds for weakly increasing price curves. We use this to show that given any allocation, we can compute strictly (or weakly) increasing price curves that support it (or show that none exist) in polynomial time. These results involve a connection to the \emph{agent-order matrix} of an allocation, which may have other applications. Second, we use duality to show that in the bandwidth allocation setting, any allocation maximizing a CES welfare function can be supported by price curves.

cs.GT↗

arXiv2024

Linear Programming Based Near-Optimal Pricing for Laminar Bayesian Online Selection

The Bayesian online selection problem aims to design a pricing scheme for a sequence of arriving buyers that maximizes the expected social welfare (or revenue) subject to different structural constraints. Inspired by applications with a hierarchy of service, this paper focuses on the cases where a laminar matroid characterizes the set of served buyers. We give the first Polynomial-Time Approximation Scheme (PTAS) for the problem when the laminar matroid has constant depth. Our approach is based on rounding the solution of a hierarchy of linear programming relaxations that approximate the optimum online solution with any degree of accuracy, plus a concentration argument showing that rounding incurs a small loss. We also study another variation, which we call the production-constrained problem. The allowable set of served buyers is characterized by a collection of production and shipping constraints that form a particular example of a laminar matroid. Using a similar LP-based approach, we design a PTAS for this problem, although in this special case the depth of the underlying laminar matroid is not necessarily a constant. The analysis exploits the negative dependency of the optimum selection rule in the lower levels of the laminar family. Finally, to demonstrate the generality of our technique, we employ the linear programming-based approach employed in the paper to re-derive some of the classic prophet inequalities known in the literature -- as a side result.

cs.GT↗

arXiv2018

A Mathematical Model for Optimal Decisions in a Representative Democracy

Direct democracy is a special case of an ensemble of classifiers, where every person (classifier) votes on every issue. This fails when the average voter competence (classifier accuracy) falls below 50%, which can happen in noisy settings where voters have only limited information, or when there are multiple topics and the average voter competence may not be high enough for some topics. Representative democracy, where voters choose representatives to vote, can be an elixir in both these situations. Representative democracy is a specific way to improve the ensemble of classifiers. We introduce a mathematical model for studying representative democracy, in particular understanding the parameters of a representative democracy that gives maximum decision making capability. Our main result states that under general and natural conditions, 1. Representative democracy can make the correct decisions simultaneously for multiple noisy issues. 2. When the cost of voting is fixed, the optimal representative democracy requires that representatives are elected from constant sized groups: the number of representatives should be linear in the number of voters. 3. When the cost and benefit of voting are both polynomial, the optimal group size is close to linear in the number of voters. This work sets the mathematical foundation for studying the quality-quantity tradeoff in a representative democracy-type ensemble (fewer highly qualified representatives versus more less qualified representatives).

cs.GT↗

arXiv2018

Customer Sharing in Economic Networks with Costs

In an economic market, sellers, infomediaries and customers constitute an economic network. Each seller has her own customer group and the seller's private customers are unobservable to other sellers. Therefore, a seller can only sell commodities among her own customers unless other sellers or infomediaries share her sale information to their customer groups. However, a seller is not incentivized to share others' sale information by default, which leads to inefficient resource allocation and limited revenue for the sale. To tackle this problem, we develop a novel mechanism called customer sharing mechanism (CSM) which incentivizes all sellers to share each other's sale information to their private customer groups. Furthermore, CSM also incentivizes all customers to truthfully participate in the sale. In the end, CSM not only allocates the commodities efficiently but also optimizes the seller's revenue.

cs.GT↗

arXiv2018

Self-regulation promotes cooperation in social networks

Cooperative behavior in real social dilemmas is often perceived as a phenomenon emerging from norms and punishment. To overcome this paradigm, we highlight the interplay between the influence of social networks on individuals, and the activation of spontaneous self-regulating mechanisms, which may lead them to behave cooperatively, while interacting with others and taking conflicting decisions over time. By extending Evolutionary game theory over networks, we prove that cooperation partially or fully emerges whether self-regulating mechanisms are sufficiently stronger than social pressure. Interestingly, even few cooperative individuals act as catalyzing agents for the cooperation of others, thus activating a recruiting mechanism, eventually driving the whole population to cooperate.

physics.soc-ph↗

arXiv2018

Investigating Wheat Price with a Multi-Agent Model

In this paper, we build a computational model for the analysis of international wheat spot price formation, its dynamics and the dynamics of internationally exchanged quantities. The model has been calibrated using FAOSTAT data to evaluate its in-sample predictive power. The model is able to generate wheat prices in twelve international markets and wheat used quantities in twenty-four world regions. The time span considered goes from 1992 to 2013. In our study, a particular attention was paid to the impact of Russian Federation's 2010 grain export ban on wheat price and internationally traded quantities. Among other results, we find that wheat average weighted world price in 2013 would have been 3.55\% lower than the observed one if the Russian Federation would not have imposed the export ban in 2010.

econ.TH↗

arXiv2020

Exceeding Expectations: Stochastic Dominance as a General Decision Theory

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized.

econ.TH↗