
on Microeconomics 
Issue of 2012‒10‒20
fourteen papers chosen by JingYuan Chiou IMT Lucca Institute for Advanced Studies 
By:  Ori Haimanko (BGU); Atsushi Kajii (KIER, Kyoto University) 
Abstract:  We relax the Kajii and Morris (1997a) notion of equilibrium ro bustness by allowing approximate equilibria in close incomplete infor mation games. The new notion is termed "approximate robustness". The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium corre spondence. As a corollary of the upper hemicontinuity, it is shown that approximately robust equilibria exist in all twoplayer zerosum games and all twoplayer twostrategy games, whereas (exactly) robust equilibria may fail to exist for some games in these categories. 
Keywords:  incomplete information, robustness, Bayesian Nash equi librium, ?equilibrium, upper hemicontinuity, zerosum games. 
JEL:  C72 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:bgu:wpaper:1209&r=mic 
By:  Fabrizio, Germano; Peio, Zuazo Garín 
Abstract:  We extend Aumann's [3] theorem deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for nonrational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, joint pbelief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain pbelief constraints and characterize the topological structure of the resulting set of prational outcomes. We establish continuity in the parameters p and show that, for p su ciently close to one, the prational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's [4] theorem on rational expectations of interim types to the broader prational belief systems, and also discuss the case of noncommon priors. 
Keywords:  bounded rationality, correlated equilibrium, aproximate common knowledge, prational blief system, common prior, information noncooperative game 
Date:  2012–07–16 
URL:  http://d.repec.org/n?u=RePEc:ehu:ikerla:8757&r=mic 
By:  Seidl, Christian 
Abstract:  In 1713 Nicolas Bernoulli sent to de Montmort several mathematical problems, the fifth of which was at odds with the then prevailing belief that the advantage of games of hazard follows from their expected value. In spite of the infinite expected value of this game, no gambler would venture a major stake in this game. In this year, de Montmort published this problem in his Essay d'analyse sur les jeux de hazard. By dint of this book the problem became known to the mathematics profession and elicited solution proposals by Gabriel Cramer, Daniel Bernoulli (after whom it became known as the Petersburg Paradox), and Georges de Buffon. Karl Menger was the first to discover that bounded utility is a necessary and sufficient condition to warrant a finite expected value of the Petersburg Paradox. It was, in particular, Menger's article which provided an important cue for the development of expected utility by von Neumann and Morgenstern. The present paper gives a concise account of the origin of the Petersburg Paradox and its solution proposals. In its third section, it provides a rigorous analysis of the Petersburg Paradox from the uniform methodological vantage point of d'Alembert's ratio text. Moreover, it is shown that appropriate mappings of the winnings or of the probabilities can solve or regain a Petersburg Paradox, where the use of probabilities seems to have been overlooked by the profession.  
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:zbw:cauewp:201210&r=mic 
By:  Midjord, Rune 
Abstract:  A manager/mechanism designer must allocate a set of money prizes ($1, $2, .., $n) between n agents working in a team. The agents know the state i.e. who contributed most, second most, etc. The agents' prefer ences over prizes are state independent. We incorporate the possibility that the manager knows the state with a tiny probability and present a simple mechanism that uniquely implement prizes that respects the true state. 
Keywords:  full implementation, direct mechanism, verifiable information, rank order tournaments 
JEL:  D82 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:ehu:dfaeii:8771&r=mic 
By:  Hanna Halaburda (Strategy Unit, Harvard Business School); Yaron Yehezkel (Faculty of Management, TelAviv University) 
Abstract:  This paper considers platform competition in a twosided market that includes buyers and sellers. One of the platforms benefits from a favorable coordination bias in the market, in that the two sides are more likely to join the advantaged platform. We find that the degree of the coordination bias affects the platform's decision regarding the business model (i.e., whether to subsidize buyers or sellers), the access fees and the size of the platform. A slight increase in the coordination bias may induce the advantaged platform to switch from subsidizing sellers to subsidizing buyers, or induce the disadvantaged platform to switch from subsidizing buyers to subsidizing sellers. Moreover, in the former case the advantaged platform switches from oversupplying to undersupplying sellers, while in the latter case the disadvantaged platform switches from undersupplying to oversupplying sellers. 
Keywords:  platform competition, twosided markets, coordination bias 
JEL:  L11 L14 
Date:  2012–08 
URL:  http://d.repec.org/n?u=RePEc:net:wpaper:1203&r=mic 
By:  Bar Ifrach (Management Science and Engineering, Stanford University); Costis Maglaras (Columbia Business School, Columbia University); Marco Scarsini (Dipartimento di Economia e Finanza, LUISS) 
Abstract:  A monopolist offers a product to a market of consumers with heterogeneous quality preferences. Although initially uninformed about the product quality, they learn by observing past purchase decisions and reviews of other consumers. Our goal is to analyze the social learning mechanism and its effect on the seller's pricing decision. Consumers follow an intuitive nonBayesian decision rule and, under some conditions, eventually learn the product's quality. We show how the learning trajectory can be approximated in settings with high demand intensity via a meanfield approximation that highlights the dynamics of this learning process, its dependence on the price, and the market heterogeneity with respect to quality preferences. Two pricing policies are studied: a static price, and one with a single price change. Finally, numerical experiments suggest that pricing policies that account for social learning may increase revenues considerably relative to policies that do not. 
Keywords:  learning, information aggregation, bounded rationality, pricing, optimal pricing 
JEL:  D49 D83 
Date:  2012–08 
URL:  http://d.repec.org/n?u=RePEc:net:wpaper:1201&r=mic 
By:  Alp Atakan; Mehmet Ekmekci 
Abstract:  We study a market in which k identical and indivisible objects are allocated using a uniformprice auction where n > k bidders each demand one object. Before the auction, each bidder receives an informative but imperfect signal about the state of the world. The good that is auctioned is a commonvalue object for the bidders, and a bidder’s valuation for the object is determined jointly by the state of the world and an action that he chooses after winning the object but before he observes the state. We show that there are equilibria in which the auction price is completely uninformative about the state of the world and aggregates no information even in an arbitrarily large auction. In the equilibrium that we construct, because prices do not aggregate information, agents have strict incentives to acquire costly information before they participate in the market. Also, market statistics other than price, such as the amount of rationing and bid distributions contain extra information about the state. Our findings sharply contrast with past work which shows that in large auctions where there is no expost action, the auction price aggregates information. 
Keywords:  Auctions, Large markets, Information Aggregation JEL Classification Numbers: C73, D44, D82, D83. 
Date:  2012–10–10 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1553&r=mic 
By:  De Frutos, María Ángeles; Espinosa Alejos, María Paz 
Abstract:  This paper analyzes auctions where bidders face nancial constraints that may force them to resell part of the property of the good (or subcontract part of a project) at a resale market. First we show that the ine¢ cient speculative equilibria of second price auctions (Garratt and Tröger, 2006) generalizes to situations with partial resale where only the high value bidder is nancially constrained. However, when all players face nancial constraints the ine¢ cient speculative equilibria disappear. Therefore, for auctioning big facilities or contracts where all bidders are nancially constrained and there is a resale market, the second price auction remains a simple and appropriate mechanism to achieve an e¢ cient allocation. 
Keywords:  auctions, resale, financial constraints, subcontracting 
JEL:  L1 D44 D82 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:ehu:dfaeii:8758&r=mic 
By:  Motta, Massimo; Vasconcelos, Helder 
Abstract:  In this paper we provide a new way of modelling twosided markets, and we then use this model to study anticompetitive conduct in an asymmetric twosided market which captures the main features of some recent antitrust cases. We show that belowcost pricing on one market side can allow an incumbent firm to exclude a more efficient rival which does not have a customer base yet. This exclusionary behaviour is the more likely to occur the more mature the market and the stronger the established customer base of the incumbent. 
Keywords:  Demand externalities; Predation; Twosided markets 
JEL:  L11 L13 L41 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9164&r=mic 
By:  Hélène Le Cadre (LIMA  CEA, LIST, Laboratory of Information, Models and Learning  CEA : SACLAY); Bedo JeanSébastien (Orange/FranceTélécom  Telecom Orange) 
Abstract:  In this article, we focus on the identification of emerging economic organizations while agents are learning hidden individual sequences modeling renewable energy production and microgrid instantaneous needs in a decentralized hierarchical network. The network is made of 3 categories of agents: producers, providers and end users belonging to microgrids. In this uncertain context, providers are penalized in case where they cannot satisfy the entire demand of the associated microgrid. Identically, producers are penalized in case where they cannot deliver the quantity of energy booked by the providers. Service providers need to make efficient forecasts about the hidden individual sequences to optimize their decisions concerning the quantities of energy to book and the prices of the energy. We prove that there exists prices that provide to the producers a guarantee to avoid penalties. Additionally, under external regret minimization, collaborative learning through a grand coalition where the providers share their information and align their forecasts, enables them to minimize their average loss. As an illustration, we compare the convergence rates of the collaborative learning strategy with rates resulting from selfish learning based on external and internal regret minimization in a 2 producers, 3 providers network. The results confirm the theory: collaboration is better for the providers. 
Keywords:  Distributed Learning; Regret; Algorithmic Game Theory; Coalition 
Date:  2012–07–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal00740893&r=mic 
By:  Ritxar Arlegi (Departamento de EconomíaUPNA) 
Abstract:  In this paper we argue, inspired by some psychological literature, that choices are the outcome of the interplay of different, potentially conflicting motivations. We propose an axiomatic approach with two motivations, which we assume to be singlepeaked over a certain given dimension. We first consider the case in which motivations are given and stable, and then introduce the possibility for motivations to change. We show first that in the nomotivation change case, certain choice behaviours that appear to be inconsistent from the standard rational choice point of view may be explained in our framework as the outcome of conflicting motivations. Afterwards, in the case of motivation change, we present two psychologicallyflavoured assumptions about how motivations are influenced by choices. We show that, with some additional weak assumptions of rationality, motivation change leads to a smaller range of potentially inconsistent choices and not to a larger one as one may think. In particular, conflicts between two motivations can eventually be resolved by choosing different actions and consequently a definite and final preference for an action be revealed. 
Keywords:  Motivation, Pleasure, SelfImage, Conflict, Preference Reversal, Dissonance reduction. 
JEL:  D01 D03 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:nav:ecupna:1208&r=mic 
By:  José Alvaro RodriguesNeto 
Abstract:  A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posterior beliefs for the players is consistent (i.e., there is a common prior). We describe the lattice properties of monotonic models, develop a test to check if a model is monotonic, propose a simple sufficient condition for nonmonotonicity, and provide some examples. We also study models having circular orders, a weakening of monotonicity. 
JEL:  C02 D80 D82 D83 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:acb:cbeeco:2012586&r=mic 
By:  Timothy C. Johnson 
Abstract:  We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, onedimensional, It\^o diffusions, payoff functions that need not be smooth and statedependent discounting. This is done within a framework based on dynamic programming techniques employing variational inequalities and links to the probabilistic approaches employing $r$excessive functions and martingale theory. The aim of this paper is to facilitate the the solution of a wide variety of problems, particularly in finance or economics. 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1210.2617&r=mic 
By:  Walther, A. 
Abstract:  In financial markets with asymmetric information, traders may have an incentive to forgo profitable deals today in order to preserve their informational advantage for future deals. This sort of manipulative behaviour has been studied in markets with one informed trader (Kyle 1985, Chakraborty and Yilmaz 2004). The effect is slower social learning. Using an extension of Glosten and Milgrom’s (1985) trading model, we study this effect in markets with N informed traders. As N grows large, each trader’s price impact subsides, and so does manipulation in equilibrium. However, the impact of manipulation on social learning can be increasing in N. As N increases, each trader individually manipulates less. But nonetheless, the increased number of manipulative actions introduces enough noise to exacerbate the impact of manipulation on learning. 
Keywords:  Price manipulation, asset pricing, asymmetric information, GlostenMilgrom model 
JEL:  D80 D82 G10 G14 
Date:  2012–10–08 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:1242&r=mic 