Complementarity demand functions and pricing models for multi-product markets

2009 ◽  
Vol 20 (5) ◽  
pp. 399-430 ◽  
Author(s):  
WANMEI SOON ◽  
GONGYUN ZHAO ◽  
JIEPING ZHANG
Keyword(s):  
Demand Function ◽  
Nonlinear Complementarity Problem ◽  
Decision Makers ◽  
Pricing Models ◽  
Demand Functions ◽  
Product Demand ◽  
Oligopolistic Market ◽  
Best Response ◽  
Product Pricing ◽  
Real Market

In contrast to single-product pricing models, multi-product pricing models have been much less studied because of the complexity of multi-product demand functions. It is highly non-trivial to construct a multi-product demand function on the entire set of non-negative prices, not to mention approximating the real market demands to a desirable accuracy. Thus, many decision makers use incomplete demand functions which are defined only on a restricted domain, e.g. the set where all components of demand functions are non-negative. In the first part of this paper, we demonstrate the necessity of defining demand functions on the entire set of non-negative prices through some examples. Indeed, these examples show that incomplete demand functions may lead to inferior pricing models. Then we formulate a type of demand functions using a Nonlinear Complementarity Problem (NCP). We call it a Complementarity-Constrained Demand Function (CCDF). We will show that such demand functions possess certain desirable properties, such as monotonicity. In the second part of the paper, we consider an oligopolistic market, where producers/sellers are playing a non-cooperative game to determine the prices of their products. When a CCDF is incorporated into the best response problem of each producer/seller involved, it leads to a complementarity constrained pricing problem facing each producer/seller. Some basic properties of the pricing models are presented. In particular, we show that, under certain conditions, the complementarity constraints in this pricing model can be eliminated, which tremendously simplifies the computation and theoretical analysis.

scholarly journals LEARNING TO PLAY BEST RESPONSE IN DUOPOLY GAMES

2004 ◽  
Vol 06 (03) ◽  
pp. 443-459 ◽  
Author(s):  
JAN WENZELBURGER
Keyword(s):  
Demand Function ◽  
Optimal Strategies ◽  
Market Demand ◽  
Response Behavior ◽  
Estimation Errors ◽  
Demand Functions ◽  
Best Response ◽  
Game Theoretic ◽  
Payoff Functions ◽  
Duopoly Market

We consider a quantity-setting duopoly market where firms lack perfect knowledge of the market demand function. They use estimated and therefore misspecified demand functions instead and determine their optimal strategies from the corresponding subjective payoff functions. The central issue of this paper is the question under which conditions a firm can learn the true demand function as well as the response behavior of its competitor from repeated estimations of historical market data. As soon as estimation errors are negligible, a firm is able to play best response in the usual game theoretic sense.

Framework for Deriving Macroscopic Demand Functions from Microscopic Acceleration Models

2017 ◽  
Vol 2623 (1) ◽  
pp. 40-48 ◽  
Author(s):  
Anupam Srivastava ◽  
Wen-Long Jin
Keyword(s):  
Demand Function ◽  
Transmission Model ◽  
Acceleration Process ◽  
Cell Transmission Model ◽  
Traffic Demand ◽  
Macroscopic Models ◽  
Demand Functions ◽  
Integral Role ◽  
Vehicle Acceleration ◽  
Traffic Systems

Vehicle acceleration plays an integral role in determining the operational capacity of roadway sections. Traditional first-order macroscopic models of traffic do not capture the boundedness of vehicle acceleration. In a recent study, it was shown that the cell transmission model could capture critical macroscopic effects of bounded acceleration if one modified the demand function such that traffic demand (sending flow) decreased in density for congested traffic. However, such a modified demand function was calibrated only with data. This paper introduces a framework for deriving such macroscopic demand functions corresponding to well-known microscopic acceleration models. Two mechanisms are explored for deriving the demand function with varying assumptions on how vehicles accelerate within a single discretized cell. The first mechanism is based on the assumption that vehicles within a single cell begin accelerating at the same time and that this information of the trigger of acceleration propagates instantaneously. The second mechanism assumes that the information for the trigger propagates within the cell at a finite speed such that following vehicles begin their acceleration process later than the leading vehicles. The derived demand functions are consistent with those calibrated with data. This study explicitly bridges macroscopic and microscopic models of bounded acceleration and can lead to more efficient evaluation of the effects of bounded acceleration on traffic systems.

scholarly journals Demand functions and demand manifolds

2021 ◽  
Author(s):  
Alan Beggs
Keyword(s):  
Demand Function ◽  
Firm Behavior ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Static Properties ◽  
Demand Functions ◽  
Necessary And Sufficient ◽  
The Relationship

AbstractMrázová and Neary (2017) introduce the notion of the Demand Manifold which expresses the relationship between the elasticity and curvature of a demand function. They argue that this determines many important comparative static properties of firm behavior. This paper gives necessary and sufficient conditions for two demand functions to have the same demand manifold and so to have similar comparative static properties.

scholarly journals Consistent Conjectural Variations Equilibrium in a Mixed Duopoly

2011 ◽  
Vol 15 (4) ◽  
pp. 425-432 ◽  
Author(s):  
Nataliya I. Kalashnykova ◽  
◽  
Vladimir A. Bulavsky ◽  
Vyacheslav V. Kalashnikov ◽  
Felipe J. Castillo Pérez ◽  
...  
Keyword(s):  
Demand Function ◽  
Market Price ◽  
Mixed Duopoly ◽  
Demand Functions ◽  
Interior Equilibrium ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Influence Coefficients ◽  
Conjectural Variations ◽  
Conjectural Variations Equilibrium

In this paper, we consider a model of mixed duopoly with Conjectured Variations Equilibrium (CVE). The agents’ conjectures concern the price variations depending on the increase or decrease in their production outputs. We establish existence and uniqueness results for the conjectured variations equilibrium (called an exterior equilibrium) for any set of feasible conjectures. To introduce the notion of an interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures). To prepare the base for the extension of our results to the case of non-differentiable demand functions, we also investigate the behavior of the consistent conjectures in dependence upon a parameter representing the demand function derivative with respect to the market price.

scholarly journals USING THE SELECTION GUIDE FOR SPILL COUNTERMEASURES TECHNOLOGIES IN RESPONSE DECISION MAKING AND PLANNING

2001 ◽  
Vol 2001 (2) ◽  
pp. 797-803 ◽  
Author(s):  
Debra Scholz ◽  
John Boyd ◽  
Ann Hayward Walker ◽  
Jacqueline Michel
Keyword(s):  
Work Group ◽  
Technical Information ◽  
Decision Makers ◽  
Response Strategy ◽  
Effective Response ◽  
Product Categories ◽  
Additional Information ◽  
Best Response ◽  
Response Team ◽  
Pre Treatment

ABSTRACT As part of national response priorities, On-Scene Coordinators (OSCs) and Incident Commanders should use all appropriate containment and removal tactics, including the use of products listed on the National Contingency Plan (NCP) Product Schedule, in a coordinated manner to ensure a timely, effective response that minimizes adverse impacts to the environment (40 CFR § 300.317). To facilitate greater understanding of these products and technologies, a Selection Guide was developed to evaluate their potential benefits and identify appropriate situations for their use. Although the NCP Product Schedule and Notebook provide information on regulated spill response products, the decision maker needs additional information presented clearly in a concise format that clarifies how these products can affect the spilled oil and the environment once applied. The Selection Guide provides a spill response tool that gives OSCs and other decision makers an easy-to-use source of technical information on spill response countermeasures that are regulated by the NCP, including alternate sorbents, bioremediation agents, dispersants, elasticity modifiers, emulsion treating agents, in situ burning on land and on water, shoreline pre-treatment agents, solidifiers, surface-collecting agents (herders), surface-washing agents, and firefighting foams, as well as potential response strategies for “unusual” spill response conditions (i.e., fast-water booming strategies, non-floating oil strategies, and water intake monitoring). The Selection Guide facilitates easy comparison among product categories, as well as aids decision makers in determining the best response strategy or product for a particular issue that “traditional” response tools do not seem to address completely. The Selection Guide has been developed under the Work Plan of the Region III Spill Response Countermeasures Work Group, in cooperation with the Region IV Regional Response Team (RRT). This document is applicable for inland and coastal areas and is intended for use during actual spill incidents and pre-spill planning efforts. This information also assists decision makers in evaluating vendor requests to use their products.

The Fine Picture

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Demand Function ◽  
Terms Of Trade ◽  
Exchange Model ◽  
Full Measure ◽  
Revealed Preferences ◽  
Trade Intensity ◽  
Demand Functions ◽  
Regular Economies ◽  
Uniqueness Of Equilibrium ◽  
Weak Axiom

This chapter restricts the m-tuple (fi) of demand functions defining the exchange model to belong to ε‎c. In addition to the assumptions made in the previous chapters (recall that ε‎c is a subset of ε‎r), the demand function fi satisfies the weak axiom of revealed preferences for every consumer, and the slightly stronger negative definiteness of the Slutsky matrix for the consumer whose demand function satisfies desirability (A). These stronger assumptions are aimed at giving more economic flesh to the exchange model. As a consequence, the natural projection inherits much stronger properties that give a specificity of its own to the exchange model. The most important properties of the exchange model with (fi) ɛ ε‎c are the regularity of the no-trade equilibria, the openness and full measure (a.k.a., the genericity) of the set of regular equilibria as a subset of the equilibrium manifold, the inclusion of the set of equilibrium allocations in one and only one connected component of the set of regular economies, the uniqueness of equilibrium for all economies belonging to that component, and the interpretation of that property in terms of trade intensity.

Effects of app pricing structures on product evaluations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Marcus Renatus Johannes Wolkenfelt ◽  
Frederik Bungaran Ishak Situmeang
Keyword(s):  
Machine Learning ◽  
Online Reviews ◽  
Machine Learning Algorithms ◽  
Future Research ◽  
Product Reviews ◽  
Pricing Models ◽  
Data Set ◽  
Content Type ◽  
Product Pricing ◽  
Google Play

Purpose The purpose of this paper is to contribute to the marketing literature and practice by examining the effect of product pricing on consumer behaviours with regard to the assertiveness and the sentiments expressed in their product reviews. In addition, the paper uses new data collection and machine learning tools that can also be extended for other research of online consumer reviewing behaviours. Design/methodology/approach Using web crawling techniques, a large data set was extracted from the Google Play Store. Following this, the authors created machine learning algorithms to identify topics from product reviews and to quantify assertiveness and sentiments from the review texts. Findings The results indicate that product pricing models affect consumer review sentiment, assertiveness and topics. Removing upfront payment obligations positively impacts the overall and pricing specific consumer sentiment and reduces assertiveness. Research limitations/implications The results reveal new effects of pricing models on the nature of consumer reviews of products and form a basis for future research. The study was conducted in the gaming category of the Google Play Store and the generalisability of the findings for other app segments or marketplaces should be further tested. Originality/value The findings can help companies that create digital products in choosing a pricing strategy for their apps. The paper is the first to investigate how pricing modes affect the nature of online reviews written by consumers.

scholarly journals TEAM REASONING AND A MEASURE OF MUTUAL ADVANTAGE IN GAMES

2017 ◽  
Vol 34 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Jurgis Karpus ◽  
Mantas Radzvilas
Keyword(s):  
Multiple Solutions ◽  
Decision Makers ◽  
Common Goal ◽  
Team Reasoning ◽  
Best Response ◽  
Mutual Advantage ◽  
Game Theoretic ◽  
Formal Representations

Abstract:The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interacting players in games may sometimes reason as members of a team – a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximum mutual advantage in the games they play.

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