Working Papers Series

Papers below are in pdf.

X. H. Wang

WP 09-04
Customization: Ideal Varieties, Product Uniqueness and Price Competition
Oksana Loginova & X.H. Wang

We study customization in the Hotelling model with two rms. In addition to providing ideal varieties, the perceived uniqueness of a customized product contributes independently to consumer utility. We show that only when consumer preferences for uniqueness are high customization occurs in equilibrium.

JEL Codes: D43, L13, C72
Keywords: customization, product dierentiation, product uniqueness, price competition

WP 09-03
Customization with Vertically Dierentiated Products
Oksana Loginova & X.H. Wang

We study an asymmetric duopoly market in which the rms' products are initially dierentiated in both variety and quality. Each consumer has a most preferred variety and a quality valuation. Customization provides ideal varieties for consumers but has no eect on product qualities. The rms rst choose whether to customize their products, then engage in price competition. For the customization stage we consider two dierent games: the simultaneous-move game and the endogenous-timing game. In the latter, whether customization choices are made simultaneously or sequentially is endogenously determined. We show that both quality and the timing of customization choices play important roles in determining the equilibrium outcome. Customization occurs only if the quality dierence is suciently large. Endogenous timing sometimes enables the rms to achieve an outcome that is Pareto superior to that if they were to make their customization choices simultaneously. Although the higher quality rm is more likely to customize, endogenous timing sometimes enables the lower quality rm to obtain an advantage that it would not have in the simultaneous-move game.

JEL Codes: D43, L13, C72
Keywords: customization, horizontal dierentiation, vertical dierentiation, endogenous timing.

WP 08-15
Customization in an Endogenous-Timing Game with Vertical Differentiation
Oksana Loginova & X.H. Wang

We study customization in a duopoly game in which the firms' products have different qualities. Whether customization choices are made simultaneously or sequentially is endogenously determined. Specifically, the customization stage of the game involves two periods. Each firm either selects its product type in period 1 or postpones this decision to period 2. We show that both quality and endogenous timing play important roles in determining the equilibrium outcome. Customization occurs only if the quality difference is sufficiently large. Endogenous timing sometimes enables the firms to achieve an outcome that is Pareto superior to that if they were to make their customization choices simultaneously. Although the higher quality firm is more likely to customize, endogenous timing sometimes enables the lower quality firm to obtain an advantage that it would not have under simultaneous customization choices.

JEL Codes: D43, L13, C72
Keywords: customization, horizontal differentiation, vertical differentiation, endogenous timing

WP 08-14
Mass Customization with Vertically Differentiated Products
Oksana Loginova & X.H. Wang

We analyze a duopoly game in which products are initially differentiated in variety and quality. Each consumer has a most preferred variety and a quality valuation. Customization provides ideal varieties but has no effect on product qualities. The firms first choose whether to customize their products, then engage in price competition. We show that in equilibrium either both firms customize, only the higher quality firm customizes, or no firm customizes. Even if customization is costless, the firms might not customize. This happens when the quality difference between the firms is small. We explore how the total welfare changes with the fixed cost of customization. Interestingly, the relationship is not always monotonic. Contrasting with the situation when customization is not feasible, both consumer surplus and total welfare are higher when one or both firms customize.

JEL Codes: D43, L13, C72
Keywords: customization, horizontal differentiation, vertical differentiation

WP 07-03
Why Are Firms Sometimes Unwilling to Reduce Costs?
X. Henry Wang and Jingang Zhao

This paper establishes three new results for multiproduct oligopolies: 1) it presents the first explicit expression of Nash equilibria for asymmetric multiproduct oligopolies; 2) it shows that reducing a multiproduct firm’s cost in Bertrand oligopolies will reduce its profits if the cost-reducing unit is sufficiently small; and 3) it demonstrates that a multiproduct firm has no incentive to eliminate a product whose sales are zero. Because a single-product firm whose sales are zero is indifferent between exiting and staying, and its cost reductions always increase its profits, our results are unique to the multiproduct firm, and they suggest that extending oligopoly studies from a single product to multi-products could be as significant as the extension of calculus from a single variable to multi-variables.

JEL Codes: C63, D43, L13
Keywords: Effect of cost reduction, multiproduct oligopoly, price competition, quantity competition

WP 06-08
Peer-to-Peer Networks: A Mechanism Design Approach
Oksana Loginova, Haibin Lu and X.H. Wang

In this paper we use mechanism design approach to find the optimal file-sharing mechanism in a peer-to-peer network. This mechanism improves upon existing incentive schemes. In particular, we show that peer-approved scheme is never optimal and service-quality scheme is optimal only under certain circumstances. Moreover, we find that the optimal mechanism can be implemented by a mixture of peer-approved and service-quality schemes.

JEL Codes: D82, C72
Keywords: peer-to-peer networks, mechanism design
Updated in June, 2007

WP 05-14
On Welfare under Cournot and Bertrand Competition in Differentiated Oligopolies
Judy Hsu and X. Henry Wang

Häckner (2000) shows that in a differentiated oligopoly with more than two firms , prices may be higher under Bertrand competition than under Cournot competition, implying that the classical result of Singh and Vives (1984) that Bertrand prices are always lower than Cournot prices is sensitive to the duopoly assumption. Häckner (2000), however, leaves unanswered the important question of whether welfare may be lower under price competition. This note shows that in Häckner’s model both consumer surplus and total surplus are higher under price competition than under quantity competition regardless of whether goods are substitutes or complements.

JEL Codes: D43, L13
Keywords: Bertrand; Cournot; Differentiated oligopoly; Welfare
Published in Review of Industrial Organization, 27(2), (September 2005), pp. 185-191.

WP 04-16
On the Licensing of Innovations under Strategic Delegation
Judy Hsu and X. Henry Wang

This paper uses a three-stage licensing-delegation-quantity game to study the licensing of a cost-reducing innovation by a patent-holding firm to its competitor. It is shown that licensing is less likely to occur under strategic delegation compared to no delegation.

JEL Codes: D45; L10; L20
Keywords: Licensing; Strategic Delegation
Published in Economics Bulletin, 12(6), (September 2004), pp. 1-10.

WP 04-13
Increasing Outer Risk
Carmen F. Menezes and X. Henry Wang

Recent empirical research has established that the distributions of a wide range of economic variables are kurtotic in that they have higher peak(s) in the neighborhood of the mean and greater elongation in the tails than the normal distribution. This paper provides a formal characterization of the empirically significant notions of kurtotic distributions by formulating the concept of outer risk. An increase in outer risk corresponds to a dispersion transfer from the center of a distribution to its tails. In terms of the relocation of probability mass, such a dispersion transfer accentuates the peak(s) of the distribution and elongates its tails. It is shown that ordering distributions by outer risk is equivalent to the ordering of distributions resulting from unanimous choice by all individuals whose utility function has a negative fourth derivative.

JEL Codes: D81
Keywords: Outer Risk, Outer Risk Aversion
Published in Journal of Mathematical Economics, 41(7), (November 2005), pp.875-886

WP 02-04
The Precautionary Premium and the Risk-Downside Risk Tradeoff
Carmen F. Menezes and X. Henry Wang

This paper shows that the precautionary premium embodies a tradeoff between risk and downside risk. It is the size of a mean-preserving spread for thish the strength of aversion to risk just offsets the strength of aversion to downside risk. Using this result, decreasing absolute prudence can be interpreted as meaning that the amount of exposure to risk (as measured by a spread) for which aversion to risk just offsets aversion to downside risk decreases as wealth increases. This happens when an increase in wealth causes a smaller percentage change in absolute downside risk aversion than in absolute risk aversion.

Published under the new title On the Risk-Downside Risk Tradeoff, The Manchester School, 72(2), (2004), pp. 179-187.

p>WP 00-02
Income and Substitution Effects of Increases in Risk when Payoffs are Linear in the Random Variable
Carmen F. Menezes and X. Henry Wang

Payoff functions that are linear in the random variable arise in a wide variety of decision models under uncertainty. The decomposition of the effect of increased risk on decisions into income and substitution terms for such models has received much attention in the literature. This paper provides a Hicks-Slutsky decomposition of the effect of Rothschild-Stiglitz increases in risk on the optimal decision. Two measures of aversion to additional risk are introduced. Their behavior is shown to control the signs of the income and substitution effects.