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.

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.

Discontinuous Demand Functions: Estimation and Pricing

2020 ◽  
Vol 66 (10) ◽  
pp. 4516-4534
Author(s):  
Arnoud V. den Boer ◽  
N. Bora Keskin
Keyword(s):  
Dynamic Pricing ◽  
Demand Function ◽  
Convergence Rates ◽  
Time Varying ◽  
Parametric Function ◽  
Estimation Errors ◽  
Pricing Policy ◽  
Demand Functions ◽  
Dynamic Estimation ◽  
Varying Demand

We consider a dynamic pricing problem with an unknown and discontinuous demand function. There is a seller who dynamically sets the price of a product over a multiperiod time horizon. The expected demand for the product is a piecewise continuous and parametric function of the charged price, allowing for possibly multiple discontinuity points. The seller initially knows neither the locations of the discontinuity points nor the parameters of the demand function but can infer them by observing stochastic demand realizations over time. We measure the seller’s performance by the revenue loss relative to a clairvoyant who knows the underlying demand function with certainty. We construct a dynamic estimation-and-pricing policy that accounts for demand discontinuities, derive the convergence rates of discontinuity- and parameter-estimation errors under this policy, and prove that it achieves near-optimal revenue performance. We also extend our analysis to the cases of time-varying demand discontinuities and inventory constraints. This paper was accepted by Noah Gans, stochastic models and simulation.

Market Demand Functions in the CAPM

1997 ◽  
Author(s):  
Jean-Marc Bottazzi ◽  
Thorsten Hens ◽  
Andreas Löffler
Keyword(s):  
Market Demand ◽  
Demand Functions

scholarly journals A Game Theoretic Look at Life Insurance Underwriting

1980 ◽  
Vol 11 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Jean Lemaire
Keyword(s):  
Cooperative Game ◽  
Life Insurance ◽  
Decision Problem ◽  
Optimal Strategies ◽  
Minimax Criterion ◽  
Game Theoretic ◽  
Optimal Set

The decision problem of acceptance or rejection of life insurance proposals is formulated as a two-person non cooperative game between the insurer and the set of the proposers. Using the minimax criterion or the Bayes criterion, it is shown how the value and the optimal strategies can be computed, and how an optimal set of medical informations can be selected and utilized.

Collective influence maximization for multiple competing products with an awareness-to-influence model

2021 ◽  
Vol 14 (7) ◽  
pp. 1124-1136
Author(s):  
Dimitris Tsaras ◽  
George Trimponias ◽  
Lefteris Ntaflos ◽  
Dimitris Papadias
Keyword(s):  
Diffusion Processes ◽  
Influence Maximization ◽  
Second Phase ◽  
Social Graph ◽  
Practical Applications ◽  
Influence Model ◽  
Best Response ◽  
The Social ◽  
Game Theoretic ◽  
Collective Influence

Influence maximization (IM) is a fundamental task in social network analysis. Typically, IM aims at selecting a set of seeds for the network that influences the maximum number of individuals. Motivated by practical applications, in this paper we focus on an IM variant, where the owner of multiple competing products wishes to select seeds for each product so that the collective influence across all products is maximized. To capture the competing diffusion processes, we introduce an Awareness-to-Influence (AtI) model. In the first phase, awareness about each product propagates in the social graph unhindered by other competing products. In the second phase, a user adopts the most preferred product among those encountered in the awareness phase. To compute the seed sets, we propose GCW, a game-theoretic framework that views the various products as agents, which compete for influence in the social graph and selfishly select their individual strategy. We show that AtI exhibits monotonicity and submodularity; importantly, GCW is a monotone utility game. This allows us to develop an efficient best-response algorithm, with quality guarantees on the collective utility. Our experimental results suggest that our methods are effective, efficient, and scale well to large social networks.

scholarly journals Limitations of modern microeconomic theory of consumer choice: Sociological perspective

Sociologija ◽  
2008 ◽  
Vol 50 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Ognjen Radonjic
Keyword(s):  
Theoretical Model ◽  
Consumer Choice ◽  
Microeconomic Theory ◽  
Market Demand ◽  
Sociological Perspective ◽  
Neoclassical Theory ◽  
Demand Functions ◽  
Sociological Factors ◽  
And Behavior ◽  
Better Than

Neoclassical theory of consumer choice needs to be reformed. Assumption that consumer choice is not influenced by the choice of others is in collision with reality. New and better theory of consumer choice is unimaginable without incorporation of intersubjective factors into the model of derivation of individual and aggregate (market) demand functions. Goal of this study is to underline widely neglected sociological factors that have significant influence on motivation and behavior of consumers. Inclusion of these factors into modern microeconomic theory is of essential importance if we are about to construct theoretical model aimed to describe reality in which we daily exist better than its predecessor did.

scholarly journals A Guaranteed Deterministic Approach to Superhedging—The Case of Convex Payoff Functions on Options

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1246 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
A Priori ◽  
Contingent Claim ◽  
Mixed Strategies ◽  
Deterministic Approach ◽  
Deterministic Problem ◽  
History Of ◽  
Game Theoretic ◽  
Payoff Functions ◽  
Special Case ◽  
Problem Setting

This paper considers super-replication in a guaranteed deterministic problem setting with discrete time. The aim of hedging a contingent claim is to ensure the coverage of possible payoffs under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compacts that depend on the history of prices. The increments of the price at each moment in time must lie in the corresponding compacts. The absence of transaction costs is assumed. The game–theoretic interpretation of pricing American options implies that the corresponding Bellman–Isaacs equations hold for both pure and mixed strategies. In the present paper, we study some properties of the least favorable (for the “hedger”) mixed strategies of the “market” and of their supports in the special case of convex payoff functions.

scholarly journals Income elasticity of demand within individual consumer groups and the level of income elasticity of the entire market demand 

2012 ◽  
Vol 52 (No. 9) ◽  
pp. 412-417
Author(s):  
P. Syrovátka
Keyword(s):  
Consumer Behaviour ◽  
Income Elasticity ◽  
Meat Products ◽  
Market Demand ◽  
Demand Functions ◽  
Elasticity Of Demand ◽  
Income Elasticities ◽  
Aggregation Equation ◽  
Application Potential ◽  
Income Elasticity Of Demand

The paper is focused on the derivation of the mathematical relationship among the income-elasticity level of the entire market demand and the income-elasticity values of the demand functions of the consumers’ groups buying on the defined market. The determination of the mathematical term was based on the linearity of the relevant demand functions. Under the linearity assumption, the income elasticity coefficient of the entire market demand equals the weighted sum of the income-demand elasticities of the differentiated consumer groups buying on the given market. The weights in the aggregation formula are defined as the related demand shares, i.e. as the proportions of the groups’ demands to the entire market demand. The derived aggregation equation is quite held if no demand interactions (e.g. the snob or fashion effect) are recorded among differentiated consumers’ groups. The derived formula was examined by using empirical data about the consumer behaviour of Czech households in the market of meat and meat products (Czech Statistical Office). However, the application potential of the achieved term for the income-elasticity aggregations is much broader within the consumer-behaviour analysis. In addition to the subject aggregations of the demand functions, we can also apply the derived formula for the analysis and estimations of the income elasticities within the demand-object aggregations, i.e. the multistage analysis of the income elasticity of consumer demand. Another possibility of the use of the aggregation equation is for the evaluations and estimations of the income elasticity of the region-demand functions in relation to the subregions’ demands or reversely.

scholarly journals Supply Chain Decision-Making and Coordination considering Anticipated Regret under Price Discount

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jie Jian ◽  
Huipeng Li ◽  
Nian Zhang ◽  
Jiafu Su
Keyword(s):  
Supply Chain ◽  
Sensitivity Coefficient ◽  
Pricing Strategy ◽  
Market Demand ◽  
Anticipated Regret ◽  
Consumer Heterogeneity ◽  
Price Discount ◽  
Demand Functions ◽  
Homogeneous Product ◽  
The Impact

The increasing homogeneous product market has made more competition among companies to focus on improving customers’ experience. In order to get more competitive advantages, companies often launch discount products to attract consumers. However, stimulated by discount products, the perception of anticipated regret is becoming stronger, which is an inevitable issue in front of companies with price discount strategy. Considering the impact of anticipated regret for discount products, this paper quantitatively describes the utility functions and deduces the demand functions of original price products and discount products. The theoretical analysis and numerical simulation are used to analyze centralized and decentralized models of supply chain for discount products. On its basis, the revenue-sharing contract is designed to optimize the profits of supply chain. This paper finds that the price of products increases first and then decreases with the increase of regret sensitivity coefficient and consumer heterogeneity. When the regret sensitivity coefficient and consumer heterogeneity are lower, companies in the supply chain can adopt the “skimming pricing” strategy in order to obtain more profits. When the regret sensitivity coefficient and consumer heterogeneity increase, companies in the supply chain can adopt “penetrating pricing” strategies to stimulate market demand. For high regret consumers, manufacturers can adopt a “commitment advertising” strategy to promise price and quality, and retailers can adopt a “prestige pricing” strategy to reduce consumer perception of regret. In response to products with higher differences in consumer acceptance, manufacturers can adopt a “differentiated customization” strategy to meet different types of consumer demand and retailers can adopt a “differential pricing” strategy for precise marketing.

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