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on Microeconomics |
| By: | Hugo Hopenhayn; Maryam Saeedi |
| Abstract: | This paper considers the design of an optimal rating system, in a market with adverse selection. We address two critical questions about rating design: First, given a number of categories, what are the criteria for setting the boundaries between them? Second, what are the gains from increasing the number of categories? A rating system helps reallocate sales from lower- to higher-quality producers, thus mitigating the problem of adverse selection. We focus on two main sources of market heterogeneity that determine the extent and effect of this reallocation: the distribution of firm qualities and the responsiveness of sellers' supply to prices. We provide a simple characterization for the optimal rating system as the solution to a standard k-means clustering problem, and discuss its connection to supply elasticity and the skewness of firm qualities. Our results show that a simple two-tier rating can achieve a large share of full information surplus. Additionally, we characterize the conflicting interests of consumers and producers in the design of a rating system. |
| JEL: | D21 D60 D82 L11 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26221&r=all |
| By: | Ian Ball |
| Abstract: | I introduce a model of scoring. A receiver tries to predict a latent characteristic of the sender. The sender has a vector of features, which can be distorted at a cost. An intermediary observes the features of the sender and assigns a linear score, which is passed to the receiver. The optimal scoring rule downweights features on which gaming is heterogeneous. Optimal scoring discourages sender manipulation and allows the receiver to make more accurate predictions than full transparency. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.01888&r=all |
| By: | Yuval Heller (Bar Ilan University, Israel); Christoph Kuzmics (University of Graz, Austria) |
| Abstract: | We define and characterize renegotiation-proof equilibria of coordination games with preplay communication in which players have private preferences over the feasible coordinated outcomes. These are such that players never miscoordinate, players coordinate on their jointly preferred outcome whenever there is one, and players communicate only the ordinal part of their preferences. This set of renegotiation proof equilibrium strategies does not depend on the distribution of private preferences, and is thus robust to changes in players’ beliefs. Moreover, these equilibria are interim Pareto efficient and evolutionarily stable. |
| Keywords: | Coordination games; Renegotiation-proof; Equilibrium entrants; Secret handshake; Incomplete information; Evolutionary robustness |
| JEL: | C72 C73 D82 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:grz:wpaper:2019-10&r=all |
| By: | Hitoshi Matsushima (University of Tokyo); Shunya Noda (University of British Columbia) |
| Abstract: | We investigate the general mechanism design problems in which agents take ex-ante hidden actions (or investments) that influence state distribution. We show that the variety of action choices drastically shrinks the set of mechanisms that induce targeted actions in the sense that there is a one-to-one tradeoff between the dimensionality of action space and that of payment rules with which the targeted action profile is taken in an equilibrium. This result comprehends the observations made by previous works. When agents can take unilateral deviations to change the state distribution in various directions, we have equivalence properties with respect to ex-post payoffs, payments, and revenues. In particular, the pure-VCG mechanism, the simplest form of the canonical VCG mechanism, becomes the only mechanism that induces an efficient action profile. Contrarily, the popular pivot mechanism generically fails to induce efficient actions, even when the action space is one-dimensional. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf464&r=all |
| By: | Dinard van der Laan; Zaifu Yang |
| Abstract: | A seller has several heterogeneous indivisible items like tickets to sell over time before a deadline. These items become worthless after the deadline. Buyers arrive sequentially and randomly and have their own private valuations over items. Each buyer may acquire more than one item. We formulate this as an incentive compatible revenue maximization problem and characterize optimal allocation policies and derive various properties. |
| Keywords: | Revenue Maximization, Random and Sequential Assignment, Heterogeneity |
| JEL: | C61 D21 D82 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:19/13&r=all |
| By: | Seungjin Han |
| Abstract: | This paper studies the class of robust equilibria in a general competing mechanism game for decentralized markets with frictions in which non-deviating sellers punish a deviator with dominant strategy incentive compatible (DIC) direct mechanisms. Given one-dimensional, independent, and private types, the lower bound of a seller's payoff in such equilibria is his minmax value over all DIC direct mechanisms if a seller can deviate to a contract that determines a menu of any complex mechanisms conditional on buyers' messages and he chooses a mechanism he wants from it. In applications, the number of sellers is endogenized given a number of buyers and fixed entry costs. As the number of buyer increases, a unique equilibrium emerges and the equilibrium ratio of buyers to sellers converges to the point where a seller's net profit is zero with the monopoly terms of trade. |
| Keywords: | competing mechanisms, dominant strategy incentive compatibility, frictions, implicit collusion |
| JEL: | C72 D82 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2019-09&r=all |
| By: | Silvia Albrizio (Yonsei University) |
| Abstract: | In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization. |
| Keywords: | Decision making, Duality, Games, Incomplete preferences, Utility representation, Vector outcomes. |
| JEL: | C02 C72 D01 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2019rwp-146&r=all |
| By: | Azad Gholami, Reza (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics); Ubøe, Jan (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | Supply channels typically face uncertain and time-varying demand. Nonetheless, time-dependent channel optimization while addressing uncertain demand has received limited attention due to the high level of complexity of the ensuing nested equilibrium problems. The level of complexity rises when demand is dependent on current and previous prices. We consider a decentralized supply channel whose two members, a manufacturer and a retailer, must address the demand for a perishable commodity within a multi-period time horizon. Using a general (additive-multiplicative) stochastic model for the price-dependent demand, the purpose of this paper is to provide the channel members with analytic tools to devise optimal pricing and supply strategies at different times. In the first part of the paper, we propose a constructive theorem providing an explicit solution algorithm to obtain equilibrium states for bilevel optimization in decentralized supply channels. We also prove that the resulting equilibria are subgame perfect. In the second part, we allow the retailer to postpone her supply and pricing decisions until demand uncertainty is resolved at each period. Using subgame perfectness of the equilibria, we propose solution algorithms that use the extra information obtained by postponement. Finally, in a number of comparison theorems, we show that postponement strategies are always beneficial for a centralized channel (whose revenue structure is identical to that of a retailer). Whereas for a decentralized channel, due to vertical competitions, there may be scenarios wherein postponement strategies, i.e. access to extra information, turn out to be detrimental to the manufacturer and even to the whole channel. |
| Keywords: | Stochastic optimization; bilevel programming; game theory; pricing theory; stochastic demand; time-dependent demand; price-dependent demand |
| JEL: | C61 C73 D81 |
| Date: | 2019–09–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2019_009&r=all |
| By: | Azad Gholami, Reza (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics); Ubøe, Jan (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We analyze the problem of time-dependent channel coordination in the face of uncertain demand. The channel, composed of a manufacturer and a retailer, is to address a time-varying and uncertain price-dependent demand. The decision variables of the manufacturer are wholesale and (possibly zero) buy-back prices, and those of the retailer are order quantity and retail price. Moreover, at each period, the retailer is allowed to postpone her retail price until demand uncertainty is resolved. In order to place emphasis on the price-decadent nature of demand, we embed a class of memory effects in demand structure, such that current demand at each period demand is affected by pricing history as well as current price. The ensuing equilibria problems, thus, become highly nested in time. We then propose our memory-based solution algorithm which coordinates the channel with optimal buy-back contracts at each period. We show that, contrary to the conventional belief, too generous buy-back prices may not only be suboptimal to the manufacturer, but also decrease the expected profit for the retailer and thus for the whole channel. |
| Keywords: | Stochastic optimization; bilevel programming; game theory; channel coordination; buy-back contracts; price postponement; pricing theory; contract theory |
| JEL: | C61 C73 D81 |
| Date: | 2019–09–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2019_010&r=all |
| By: | Azad Gholami, Reza (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics); Ubøe, Jan (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | Almost every vendor faces uncertain and time-varying demand. Inventory level and price optimization while catering to stochastic demand are conventionally formulated as variants of newsvendor problem. Despite its ubiquity in potential applications, the time-dependent (multi-period) newsvendor problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing optimization problems. The complexity level rises even more when there are more than one decision maker in a supply channel, trying to reach an equilibrium. The purpose of this paper is to construct an explicit and e cient solution procedure for multi-period price-setting newsvendor problems in a Stackelberg framework. In particular, we show that our recursive solution algorithm can be applied to standard contracts such as buy back contracts, revenue sharing contracts, and their generalizations. |
| Keywords: | Stochastic demand; time-dependent demand; price-dependent demand; memory functions; market engineering; demand manipulation; prescriptive analytics; pricing theory |
| JEL: | C61 C73 D81 |
| Date: | 2019–09–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2019_008&r=all |
| By: | James Albrecht; Xiaoming Cai; Pieter A. Gautier; Susan Vroman |
| Abstract: | We consider a labor market with search frictions in which workers make multiple applications and firms can post and commit to general mechanisms that may be conditioned both on the number of applications received and on the number of offers received by its candidate. When the contract space includes application fees, there exists a continuum of equilibria of which only one is socially efficient. In the inefficient equilibria, firms have market power that arises from the fact that the value of a worker’s application portfolio depends on what other firms offer, which allows individual firms to free ride and offer workers less than their marginal contribution. Finally, by allowing for general mechanisms, we are able to examine the sources of inefficiency in the multiple applications literature. |
| Keywords: | multiple applications, directed search, competing mechanisms, efficiency, market power |
| JEL: | C78 D44 D83 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7805&r=all |
| By: | Kerem Ugurlu |
| Abstract: | We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space of continuous paths $\O$. We take that the uncertainty set resides in compact sets that are time dependent. In this framework, we solve the robust optimization problem with logarithmic, power and exponential utility functions, explicitly. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.05335&r=all |
| By: | Tommaso Lando; Lucio Bertoli-Barsotti |
| Abstract: | We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a decision maker's preferences in terms of risk aversion and may be used in those situations in which a strong order does not have enough discriminative power, whilst a weaker one is poorly representative of some classes of decision makers. In particular, we focus on the class of power distortion functions, yielding power-distorted stochastic dominance, which seems to be particularly appealing owing to its computational simplicity and some interesting statistical interpretations. Finally, we characterize distorted stochastic dominance in terms of distortion functions yielding isotonic classes of distorted expectations. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.04767&r=all |
| By: | J\"orn Sass; Dorothee Westphal |
| Abstract: | In this paper we investigate a utility maximization problem with drift uncertainty in a continuous-time Black--Scholes type financial market. We impose a constraint on the admissible strategies that prevents a pure bond investment and we include uncertainty by means of ellipsoidal uncertainty sets for the drift. Our main results consist in finding an explicit representation of the optimal strategy and the worst-case parameter and proving a minimax theorem that connects our robust utility maximization problem with the corresponding dual problem. Moreover, we show that, as the degree of model uncertainty increases, the optimal strategy converges to a generalized uniform diversification strategy. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.01830&r=all |
| By: | Nasimeh Heydaribeni; Achilleas Anastasopoulos |
| Abstract: | We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game with asymmetric information. Each player observes privately a noisy version of a (hidden) state of the world $V$, resulting in dependent private observations. We study perfect Bayesian equilibria (PBE) for this game with equilibrium strategies that are linear in players' private estimates of $V$. The main difficulty arises from the fact that players need to construct estimates on other players' estimate on $V$, which in turn would imply that an infinite hierarchy of estimates on estimates needs to be constructed, rendering the problem unsolvable. We show that this is not the case: each player's estimate on other players' estimates on $V$ can be summarized into her own estimate on $V$ and some appropriately defined public information. Based on this finding we characterize the PBE through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, Kalman filter covariance matrices, as well as some other required quantities, are observation-dependent and thus cannot be evaluated off-line through a forward recursion. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.04834&r=all |
| By: | Tetsuya Shinkai (School of Economics, Kwansei Gakuin University); Ryoma Kitamura (Faculty of Economics, Otemon Gakuin University) |
| Abstract: | We consider the product line strategies of duopolistic firms, each of which can supply two vertically-differentiated products under nonnegative output constraints and expectations of their rival's product line reaction. Considering a game of firms with heterogeneous (homogeneous) unit costs for high- (low-) quality products, we derive the equilibria for the game and conduct comparative statics of the equilibria outcomes on the relative superiority of the high-quality product and relative cost efficiency. In two of the equilibria, we find that where the cost-inefficient firm supplies a high-quality good, social welfare can worsen as its unit cost decreases. We also characterize the result using the production substitution of differentiated goods within a firm and the high-quality good between firms. Further, by comparing social welfare in the first-best equilibria with those in the Cournot duopoly equilibria, we find that the social welfare of the market worsens in the multiproduct Cournot duopoly equilibria as the relative superiority of the high-quality good increases. |
| Keywords: | Multiproduct firm; Duopoly; Production substitution; Vertical product differentiation |
| JEL: | D21 D43 L13 L15 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:kgu:wpaper:197&r=all |
| By: | Satoru Fujishige; Zaifu Yang |
| Abstract: | We study a general barter market in which every agent is initially endowed with several inherently indivisible items and wishes to exchange with other agents. There is no medium of exchange like money. Agents have general preferences over bundles of items and may acquire several items. It is well-known that the core of such an economy is typically empty. We propose a new but more general notion of core called a Markovian core. A Markovian core allocation is individually rational, but Pareto-efficient and stable against any possible coalition deviation by comparison with their current assignments instead of their initial endowments. We show that the market has always a nonempty strict Markovian core through a decentralized Pareto-improvement process. |
| Keywords: | Decentralized market, barter market, indivisibility, efficiency, stability, Markovian core. |
| JEL: | C62 D72 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:19/11&r=all |