Cobb-Douglas Utility Function Research Articles

Bounded Rational Players in a Symmetric Random Exchange Market

A model of Edgeworthian economies is studied, in which participants are randomly chosen at each period to exchange two goods to increase their utilities, as described by the Cobb–Douglas utility function. Participants can trade deviating from their bilateral equilibrium, provided that the market and the trade follow appropriate symmetry conditions. The article aims to study the convergence to equilibrium in a situation where individuals or small groups of participants trade in a market, and prices are determined by interactions between the participants rather than by demand and supply alone. A dynamic matching and bargaining game is considered, with statistical duality imposed on the market game, ensuring that each participant has a counterpart with opposite preferences. This guaranties that there is sufficient incentive for trade. It is shown that, in each period, the expected logarithm of the trading price in the Edgeworthian economy equals the expected Walrasian price. This demonstrates that, under symmetry conditions, the trading price in the Edgeworthian economy is related to the Walrasian price, indicating convergence of the trading price in the Edgeworthian economy towards the Walrasian price. The study suggests that, under the right conditions, the decentralized trading model leads to price convergence similar to what would be expected in a more classical Walrasian economy, where prices balance demand and supply.

A DRL-based RAQ-GERT dynamic resource allocation algorithm considering utility for multibeam satellite system

With the evolution and popularity of smart devices, the demand and requirement (e.g., communication, file transfer) of satellite users have increased rapidly. Moreover, users have different preferences for services and the quality of service (QoS), like delay and throughput, which leading to user heterogeneity. Facing numerous, time-varying, and heterogeneous users, how to dynamically allocate limited spectrum and on-board power while satisfying user requirements is the major challenge for the multibeam satellite system (MSS). Aiming to seek a solution, firstly, the resource allocation queue graphical evaluation and review technique (RAQ-GERT) network is constructed to describe the service process of the MSS, as well as to compute the channel condition parameters during the whole process. Next, appropriate QoS indicators are selected based on user requirements. Then, QoS indicators are calculated from the results of the RAQ-GERT network, which are combined to form the optimization objective of the MSS by drawing on the Cobb–Douglas utility function. After that, guided by the utility of the MSS, the proximal policy optimization (PPO) algorithm is applied to explore the optimal resource allocation scheme in this heterogeneous user scenario. Finally, the simulation comparisons show that the proposed scheme has enhancements in several performances, up to 42.19 % in service rate, 53.58 % in system capacity, 1.24 % in latency, and 3.42 % in throughput.

Modelling contagious viral dynamics: a kinetic approach based on mutual utility.

The temporal evolution of a contagious viral disease is modelled as the dynamic progression of different classes of population with individuals interacting pairwise. This interaction follows a binary mechanism typical of kinetic theory, wherein agents aim to improve their condition with respect to a mutual utility target. To this end, we introduce kinetic equations of Boltzmann-type to describe the time evolution of the probability distributions of the multi-agent system. The interactions between agents are defined using principles from price theory, specifically employing Cobb-Douglas utility functions for binary exchange and the Edgeworth box to depict the common exchange area where utility increases for both agents. Several numerical experiments presented in the paper highlight the significance of this mechanism in driving the phenomenon toward endemicity.

Optimal job switching and retirement decision

In this paper, we study the effects of two labor flexible features, a job switching opportunity and a retirement option, on the optimal strategies. We assume that the agent’s preferences are represented by a Cobb–Douglas utility function, expressed as a function of consumption and leisure. As long as the agent is working, the agent can choose one of two jobs at any time, and this choice is reversible. However, once the decision to retire is made, the agent is no longer able to work, so this decision is irreversible. We use the martingale method and study the dual problem expressed as an optimal stopping problem. By characterizing two wealth boundaries arising from the labor flexible features, we show that there is job switching during the working time and that the retirement option is exercised under the job with a higher leisure rate. We also show that the presence of the job switching opportunity makes the agent work longer with an increased retirement boundary. Based on a closed-form solution, we discuss some properties of the optimal consumption and risky investment under the proposed labor flexible model.

Research on marine plastic garbage governance in Northwest Pacific Region from the perspective of cooperative game

With the frequent coastal activities of human beings, tens of thousands of tons of floating marine plastics pose a serious threat to marine ecosystems and human survival. This paper studies the feasibility of regional marine plastic garbage management, taking the Northwest Pacific as the research object. According to the Cobb-Douglas utility function of the costs and benefits of plastic processing in China, Japan and South Korea, the Shapley value method was used to analyze it. The study found that the data were substituted into the Shapley value model of cooperative game for calculation, and the results showed that any country joining the triple alliance U would create greater benefits, and obtain higher benefits than the sub alliance. It is a triple win situation for China, Japan and the South Korea to jointly manage marine plastic in the Northwest Pacific. The results of the model confirm that the three countries are willing to maintain long-term cooperation on marine plastic governance, this method can be used to solve the trans-national marine governance innovatively and promote regional ocean cooperation governance. At the same time, by comparing the Northwest Pacific Plan with other action plans, China, Japan and South Korea should abandon political controversy, seeking common ground while putting aside differences, to cooperate fully to curb the growing trend of plastic waste problem in the Northwest Pacific, and contribute to the sustainable development of regional marine.

Equilibrium strategy for mean–variance–utility portfolio selection under Heston’s SV model

This paper considers a mean–variance–utility portfolio problem in which the investor manages her/his wealth by consuming and investing in a financial market consisting of a risk-free bond and a risky asset whose price process follows Heston’s stochastic volatility (SV) model. The objective of the investor is to obtain an equilibrium investment and consumption strategy by maximizing the terminal wealth and the accumulated binary utility function incorporating consumption and income. The semi-closed form expressions for the equilibrium investment and consumption strategy as well as the corresponding value function are derived by solving an extended Hamilton–Jacobi–Bellman system within the game-theoretic framework. Moreover, some numerical experiments are provided to show the effects of model parameters on the equilibrium strategy by adopting the Cobb–Douglas utility function.

The improved model of incentive-pricing of internet schemes for Cobb-Douglas utility function by using LINGO 13.0

In this paper, an improved model of the incentive-pricing scheme was designed. Previous research only shows the incentive model with the disadvantages of no considering the utility function to measure the satisfaction of the user. Then, the models are improved by deriving from the incorporation of bundling and reverse charging models obtained from previous studies, as well as taking into account the quality of service to users by using the Cobb-Douglas utility function. Optimal pricing schemes applied to the local data server, which is mail traffic data. The model used is the nonlinear optimization problem and solved by LINGO 13.0 to get the optimal solution. The results show that optimal results in the form of pricing schemes by applying flat fee, usage-based, and two-part tariff for homogeneous consumer’s schemes and the improved models show better performance in achieving the profit than the previous incentive pricing models.

Dynamic Effects Arise Due to Consumers' Preferences Depending on Past Choices.

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game’s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game’s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game’s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.

Investigations to the price evolutions of goods exchange with CES utility functions

The price evolutions of goods exchange in multi-agent market are investigated by employing the kinetic theory. Assume that a closed market consists of two groups (A and B) of agents, who have the same preferences for goods. The constant elasticity of substitution (CES) utility function which contains Cobb–Douglas utility function and Leontief utility function, is used to describe the agent’s preferences. A system of linear Boltzmann type equation is given to describe the probability distributions of goods for agents of the two groups, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth conditions. We assume that agents in group A put all their goods into the market for maximum utility, while agents in group B aim to acquire maximal utility from goods exchange by suitably selecting the percentage of goods which are exchanged. The effects of different trading strategies on commodity price and wealth distribution are discussed. The results show that the trading strategies of agents in group B have effectively improved their wealth status under certain assumptions. Also, a general system of nonlinear Boltzmann equation for the probability distributions of goods is given to describe the pricing issues of goods exchange for agents. The numerical experiments of nonlinear Boltzmann equations demonstrate how the trading strategies and preferences of agents modify the price of goods.

A refined utility function for modeling “me” vs. “us” allocation in a sequential group decision process

Considering the psychological aspects of altruism and reciprocity in strategic interactions, we propose using the Cobb–Douglas utility function to refine standard utility functions as a weighted product of the player’s utility (“me” factor) and the jointly utility of players (“us” factor). We model an altruism willingness function to define the strategic allocation within “me” vs. “us” based on perceived kindness of the counterparts during the past agreements and unconditional altruism. Numerical examples are presented to show how the model represents the sequential group decision process of players with heterogeneous altruism profiles.

Improved cloud computing model of internet pricing schemes based on Cobb-Douglas utility function

In this research, cloud computing model on internet pricing scheme based on Cobb-Douglas utility function was formed. The model formed is a combination of cloud computing model, consumer problem model by using Cobb-Douglas utility functions. These model considers the level of customer satisfaction on the sale of a service product and the service quality of the service provider company. The model used is solved by using LINGO 13.0 program to get the optimal solution result. Based on the calculation, the optimal solution was obtained for two types of cases, for the first case is 217.76 and for the second case is 206.97 which is on cloud computing model with usage based pricing scheme and flat fee, respectively. Based on the result of each cases, both Internet Service Provider (ISP) and internet users will get maximum benefit when ISP applied models with utility function compared to the original model.

Approximating Walrasian Equilibria

This paper proposes a price adjustment process that converges globally for a set of pure exchange economies, in which each agent has a Constant Elasticity of Substitution utility function. In this process, the auctioneer approximates demand schedules by assuming that each trader has a Cobb–Douglas utility function. The process generates prices that cannot be represented by linear combinations of previous prices, and hence precludes cycles. In the so-called unstable Scarf economies, prices spiral towards the Walrasian equilibrium in the same direction as found by Scarf. Simulation in large scale Scarf economies suggests that the speed of convergence may be polynomial in the size of the economy.

A General Equilibrium Evolutionary Model with Generic Utility Functions and Generic Bell-Shaped Attractiveness Maps, Generating Fashion Cycle Dynamics

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are possibly characterized by heterogeneous preference structures. With respect to the classical Walrasian framework, in our setting the definition of equilibrium, in addition to utility functions and endowments, depends also on population shares, which affect the market clearing conditions. We prove that, despite such difference with the standard framework, for every economy and for each population shares there exists at least one equilibrium and we show that, for all population shares, generically in the set of the economies, equilibria are finite and regular. We then introduce the dynamic law governing the evolution of the population shares, and we investigate the existence and the stability of the resulting stationary equilibria. More precisely, we assume that the reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is described via a generic bell-shaped map, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model may reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts in the agents’ consumption choices, and in the groups’ attractiveness and population shares. We illustrate the emergence of fashion cycle dynamics in the case of Stone-Geary utility functions, which generalize the Cobb-Douglas utility functions, and for different formulations of the attractiveness maps, already considered in the literature.

Representations of preferences with pseudolinear utility functions

We provide an axiomatization of preferences that are representable by pseudolinear utility functions on product spaces C×R. A set of necessary and sufficient axioms that a binary relation must fulfill to be representable by a pseudolinear utility function is given. Our framework gives axiomatic foundations to the “money in the utility function” approach in monetary economics. Axiomatizations of quasilinear utility functions, of separable pseudolinear utility functions, of group separable pseudolinear utility functions are derived. A particular attention is given to additive separable pseudolinear utility functions. Extensions to C×I with I a non-degenerate open interval of R are given. An axiomatization of Cobb–Douglas utility functions is obtained.

Stochastic inequalities based on Cobb-Douglas utility functions

The authors are indebted to the Spanish Ministry of Science and Innovation and Principado de Asturias since this research is financed by Grants MTM2013-45588-C3-1-P, MTM2015-63971-P, FC-15-GRUPIN14-101 and FC-15-GRUPIN14-142

Investigations of Nonlinear Triopoly Models with Different Mechanisms

This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3‐dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3‐dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism (LMA) while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable.

Borrowing constraints, effective flexibility in labor supply, and portfolio selection

We study optimal job switching and consumption/investment policies of an economic agent under the borrowing constraints against future labor income in a continuous and infinite time horizon. The agent’s preference is given by the Cobb–Douglas utility function whose arguments are consumption and leisure, and the jobs are characterized by the trade-off between labor income and leisure. We obtain a closed-form solution to the optimization problem by using the martingale and duality method, and investigate theoretical implications of it. The most interesting finding for the optimal job switching policy is that the borrowing constraints in the financial market can decrease the effective flexibility in labor supply of the agent in the labor market. Thus, an environment of the financial market can affect an agent’s decision making in the labor market. We also show how the effects of the borrowing constraints on the optimal consumption/investment policy reinforce or compete with those of the job switching opportunities.

IPV model with Cobb–Douglas and reference-dependent utility functions

The optimal allocation of land resources using auctions is beneficial for rational land use. This paper introduces the Cobb–Douglas utility function and reference-dependent utility function into the original independent private value model to study the effect of bidders’ preferences for winning probability in different auction schemes. This preference has an obvious influence on the seller’s expected revenue in the first price auction. When the buyer demonstrates a relatively large preference for the probability of winning, selecting the second-price auction is helpful for seller to obtain high expected revenue. On the other hand, when this preference is relatively small, a favorable choice for the seller is the first-price auction with the reserve price publicly announced. The comprehensive coupling effect of different parameters can be analyzed by using the improved auction model, which considers the reference and preference situations simultaneously. This model would be useful in the design of a land auction scheme.

Notes on income heterogeneity and number of contributors: Public goods model

AbstractThis paper proves that a large degree of income heterogeneity increases the number of free riders under the noncooperative Nash equilibrium of voluntary contributions to public goods with a Cobb–Douglas utility function. We prove this by investigating an algorithm structure that identifies free riders. We also support this proof by showing the numerical simulation results based on this algorithm.

When Students Become “Prisoners”: A Game Theory Analysis of Internship by Beijing College Students

Purpose —The oversupply of college graduates and increasing competition in the Chinese urban labor market have forced college students to undertake internships much earlier and to a greater intensity in the hope of boosting their employment prospects. It may be argued that the considerable time and energy thus spent on internships is deleterious to their university studies. The paper considers the factors that determine the intensity of an internship experience. Design/Approach/Methods —Building on a Cobb-Douglas utility function, the paper constructs a Prisoners’ Dilemma game to model the internship behavior of Chinese college students, and then examines the determinants of internship using data from a 2011 survey of approximately 10,000 Chinese college students from 47 higher education institutions in the Beijing metropolitan area and multivariate regression analysis. Findings —Empirical results confirm three key hypotheses derived from our model: first, students’ perceptions of higher differentials across available jobs in the labor market entice them to intern excessively; second, the improving quality of college teaching and the consequent benefit for knowledge acquisition mitigates the need for excessive internship; third, student preferences for fundamental knowledge acquisition also tilts the balance towards more study and less internship. Originality/Value —These findings suggest that in the context of a tight graduate labor market, improving the quality of college teaching provides a viable alternative to excessive internship by students.