Large Number Of Players Research Articles

English

Consumers around the world vary greatly in age, income, education level, and tastes and understanding how these differences affect consumer buying decision is never easy. However, marketing success largely depends on the ability to anticipate what buyers will do and what they prefer from available products. Today, the highly fragmented Indian edible oil industry with large number of players both from the organized and unorganized sectors has resulted in severe competition and as a result, edible oil businesses in India have shifted their focus to understand consumer choices better on one side and increasingly moving away from products to embracing a structured brand management to achieve competitiveness and profitability in the market place. The present study explores the consumers’ preference for oil brand, oil variants, and factors influencing the purchasing decision. The study highlights that, brand image, price, health consciousness, and quality of a particular brand are the most important factors influencing consumers’ decision making for edible oil purchases.   Key words: Brand image, brand preference, edible oils.

Mechanism Design in Large Games: Incentives and Privacy

We study the design of mechanisms satisfying a novel desideratum: privacy. This requires the mechanism not reveal 'much' about any agent's type to other agents. We propose the notion of joint differential privacy: a variant of differential privacy used in the privacy literature. We show by construction that mechanisms satisfying our desiderata exist when there are a large number of players, and any player's action affects any other's payoff by at most a small amount. Our results imply that in large economies, privacy concerns of agents can be accommodated at no additional 'cost' to standard incentive concerns.

Emergence of Altruistic Behavior Based on Game Involves Reputation and Future Expectation in Complex Networks

We study the altruistic behavior on spatial small-world network and scale-free network in the framework of game theory, by establishing a mechanism based on reputation and future expectation. Each player interacts with his immediate neighbors can follow two strategies: cooperation or defection. Reputation and discount factor are respectively introduced to describe the information of players’ historical behavior and the future expectation of players. Players not only consider current payoff but also care about future payoff when they employ strategy. Simulations and analysis show players choose cooperation voluntarily for the purpose of payoff-maximizing as long as the benefit-to-cost ratio is big enough. The level of convergence average reputation of group does not rely on the level of initial average reputation of group absolutely. Group can converge to full cooperation even though the initial average reputation of group is small. In a certain interval, a slight increase of the initial average reputation of group can effectively enhance the level of cooperation. Although the non-subjective factors prevent cooperation from emerging, complex network has a certain ability to resist the disturbance. The cooperation state in scale-free network is more stable than that in small-world network. Concentrating on the situation of group state changing from cooperative to defective, dynamic spatial patterns of small-world network show long-range connections are the main reason for the emergence of new defective cluster. Reasonable network randomness is in favor of motivating altruistic behavior. In scale-free network, heterogeneity makes players converge to three states: full cooperation, full defection and reputation oscillate in a specific domain with particular mode. A small amount of players with large degree and high reputation and a large number of players with small degree and low reputation restrict each other, which enable group can converge to a state between full cooperation and full defection. In addition, heterogeneity has no effect on promoting behavior spread under the mechanism against the common belief.

Nonasymptotic mean-field games.

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.

Multi-criteria assessment and ranking system of sport team formation based on objective-measured values of criteria set

Basketball is one of the most popular sports games in the world. Professional basketball has become a significant contributor to global economics and business. Considerable funds attracted by the game motivate participants of the sporting process (players, coaches, club owners, administration and etc.) to strive for better athletic results, this way promoting internal and external rivalry. A large number of players and the desire of teams to attract better team members as well as improve the quality of the already available athletes, boost the use of assessment and rating processes. The most popular and widely used player rating systems are based on performance statistics, which reflect situational factors of the game. Most specialists believe that such systems lack objectivity. Meanwhile, the Authors suggest a systematic solution, i.e. an adjusted well-known TOPSIS method and principles for the design of the algorithm based on the method. As a consistent problem solving system, algorithms based on multi-criteria decision-making are regarded to be simple and clear, suitable to substantiate solutions as well as easily applied in practise. Methodologies used by the Authors will help ensuring a greater efficiency of player and team rating, more accurate prognoses of sports results, team formation, and optimisation of the training process considering individualism of team players and encouraging their versatility, i.e. conformity to general physical preparedness norms of the team. The suggested research methods could be used in other sports. Furthermore, these principles could be used in business management for team formation.

A Mean Field Game Theoretic Approach for Security Enhancements in Mobile Ad hoc Networks

Game theory can provide a useful tool to study the security problem in mobile ad hoc networks (MANETs). Most of existing works on applying game theories to security only consider two players in the security game model: an attacker and a defender. While this assumption may be valid for a network with centralized administration, it is not realistic in MANETs, where centralized administration is not available. In this paper, using recent advances in mean field game theory, we propose a novel game theoretic approach with multiple players for security in MANETs. The mean field game theory provides a powerful mathematical tool for problems with a large number of players. The proposed scheme can enable an individual node in MANETs to make strategic security defence decisions without centralized administration. In addition, since security defence mechanisms consume precious system resources (e.g., energy), the proposed scheme considers not only the security requirement of MANETs but also the system resources. Moreover, each node in the proposed scheme only needs to know its own state information and the aggregate effect of the other nodes in the MANET. Therefore, the proposed scheme is a fully distributed scheme. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

Nonasymptotic Mean-Field Games

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.

On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players

In this paper, we investigate the mean field games of N agents who are weakly coupled via the empirical measures. The underlying dynamics of the representative agent is assumed to be a controlled nonlinear diffusion process with variable coefficients. We show that individual optimal strategies based on any solution of the main consistency equation for the backward-forward mean filed game model represent a 1/N-Nash equilibrium for approximating systems of N agents.

Approximate Variational Inference for a Model of Social Interactions

This paper proposes approximate variational inference methods for estimation of a strategic model of social interactions. Players interact in an exogenous network and sequentially choose a binary action. The utility of an action is a function of the choices of neighbors in the network. I prove that the interaction process can be represented as a potential game and it converges to a unique stationary equilibrium distribution. However, exact inference for this model is infeasible because of a computationally intractable likelihood, which cannot be evaluated even when there are few players. To overcome this problem, I propose variational approximations for the likelihood that allow approximate inference. This technique can be applied to any discrete exponential family, and therefore it is a general tool for inference in models with a large number of players. The methodology is illustrated with several simulated datasets and compared with MCMC methods.

Improved gravitational search algorithm for loadability enhancement of transmission lines using UPFC

In competitive electricity market, transmission system need to handle increased power transfers due to presence of large number of players. This increased volume of traffic causes network congestion in some of the lines. If the congestion is not relieved, line outage may take place. In order to improve system load ability and remove network congestion, UPFC can act as a tool for line loadability enhancement. The proposed method uses improved gravitational search algorithm to analyse maximum power transfer capability of UPFC. This is tested on IEEE-57 bus system on MATLAB platform. The location of UPFC is determined by real power variation of the system and maximum power transfer capability is evaluated. The performance of improved gravitational search algorithm is compared with traditional gravity search algorithm.

Delay and information aggregation in stopping games with private information

We consider equilibrium timing decisions in a model with a large number of players and informational externalities. The players have private information about a common payoff parameter that determines the optimal time to invest. They learn from each other in real time by observing past investment decisions. We develop new methods of analysis for such large games, and we give a full characterization of symmetric equilibria. We show that the equilibrium statistical inferences are based on an exponential learning model. Although the beliefs converge to truth, learning takes place too late. Ex-ante welfare is strictly between that without observational learning and that with full information.

Disturbance and Delay Robustness Guarantees of Gradient Systems Based on Static Noncooperative Games With an Application to Feedback Control for PEV Charging Load Allocation

This paper investigates robustness of gradient-type dynamical systems derived from static noncooperative games with a large number of players. The control objective is to drive state variables to the vicinities of Nash equilibria in the presence of disturbance and time-delay. The framework of integral input-to-state stability for large-scale systems is employed for verifying such global robustness. Several robustness criteria are presented, and Lyapunov-Krasovskii functionals are constructed. The developed theory is applied to the plug-in electric vehicle charging problem of allocating the charging load to the overnight demand valley to reduce the impact on the electric grid. Securing robustness of the dynamic load allocation is important, since eliminating uncertainties in demand predictions would become harder due to energy storage integration coupled with various energy-aware technologies. Introducing feedback, this paper guarantees stability and achieves robustness of the allocation dynamics subject to communication delay when demand predictions are not accurate. The usefulness of the proposed decentralized scheme is illustrated by numerical simulations.

Best-reply dynamics in large binary-choice anonymous games

We consider small-influence anonymous games with a large number of players n where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most cnlogn steps for some constant c>0). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least 1−e−c′n for some constant c′>0.

Continuous Time Finite State Mean Field Games

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study the $N+1$-player problem, which the mean field model attempts to approximate. Our main result is the convergence as $N\to \infty$ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.

Best-Reply Dynamic in Large Aggregative Games

We consider small-influence aggregative games with a large number of players n. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most cn log n steps for some constant c>0). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least 1-e-c'n for some constant c'>0.

Introduction: Effects of Global Developments on Gender and the Legal Practice

The selected papers in this symposium were presented at the 2012 Annual Meeting of the Law and Society Association in Honolulu, Hawaii as part of two panels organized by the International Research Collaborative (IRC) on gender and global legal practice. This emerging research initiative brings together legal scholars and sociologists who examine the relationship between gender and the legal profession in a national and cross-national framework. The purpose of the IRC initiative is to create a dialogue among scholars and professionals both nationally and internationally. The papers in this symposium provide a snapshot of current issues and developments in legal practice, focusing in particular on women’s legal work and their status and experience in a globally transforming legal profession. To date, global analyses still remain quite local and continue to measure and predict developments without stepping outside of domestic settings and familiar research approaches. The contributions to this symposium reflect on these ongoing challenges in local and cross-national research, addressing both opportunities and inequalities that global processes have created for women and men in the legal profession. They serve as a preliminary attempt to underscore the significance of global and local approaches and to further our understanding of emerging changes in the legal profession in various cultures, in an era of globalization. Globalization more generally implies interdependency among economies around the world, heightens intensity of competition among a large number of players, fosters multinational trading and investment activities, and increases the prevalence of cross-border transactions.1

Probabilistic Analysis of Mean-Field Games

The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games with mean field interactions. We implement the Mean-Field Game strategy developed analytically by Lasry and Lions in a purely probabilistic framework, relying on tailor-made forms of the stochastic maximum principle. While we assume that the state dynamics are affine in the states and the controls, and the costs are convex, our assumptions on the nature of the dependence of all the coefficients upon the statistical distribution of the states of the individual players remains of a rather general nature. Our probabilistic approach calls for the solution of systems of forward-backward stochastic differential equations of a McKean--Vlasov type for which no existence result is known, and for which we prove existence and regularity of the corresponding value function. Finally, we prove that a solution of the Mean-Field Game problem as formulated by Lasry and Lions, does indeed provide approximate Nash equilibriums for games with a large number of players, and we quantify the nature of the approximation.

Best-Reply Dynamics in Large Anonymous Games

We consider small-influence anonymous games with a large number of players n where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most c*n*logn steps for some constant c > 0). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least 1-e^{c'n} for some constant c'>0.

On Rationalizability and Beliefs in Discrete Private-Value First-Price Auctions

We extend Dekel and Wolinsky's (2003) result on private-value first price auctions by providing different sufficient conditions under which each player has a unique rationalizable bid conditional on her value. Unlike Dekel and Wolinsky's, our result does not necessarily require a large number of players. If values are independently distributed, (i) our conditions are weaker than Dekel and Wolinsky's, and (ii) our conditions require a large number of players only if the distributions on values has a low reverse hazard rate for some value. Our result holds for the cases where players' utility functions are concave or values are not identically distributed.

Video-based training to improve umpire decision-making

Introduction: Umpires are responsible for maintaining the flow, control and safety of a game by applying the laws of the game in a fair and consistent manner. Australian Football (AF) is arguably the most difficult football game to adjudicate, given the large number of players on the field (n=36) combined with the physically combative nature and hectic speed of the game. This dynamic game environment is visually complex requiring umpires to utilise refined perceptual-cognitive skills to make correct and timely decisions.