Existence Of Unique Nash Equilibrium Research Articles

The order and transshipment decisions in a two-location inventory system with demand forecast updates

To improve profitability and reduce demand uncertainty, lateral transshipment is employed in this study to reallocate inventory with updated demand information. A decentralized inventory system with two retailers ordering from one common supplier is analyzed. Each retailer places the order independently before the selling season begins based on original demand forecast. As lead time elapses, more information is collected to update the demand forecast and transshipment is examined. This study constructs a two-stage model and applies backward induction to solve the problem. A threshold transshipment policy is proposed at stage 2. The existence of unique Nash equilibrium is proven at stage 1. Both the centralized system with transshipment and the newsvendor-like system without transshipment are studied as benchmarks to evaluate the performance of transshipment in the decentralized system. Extensive numerical examples are conducted to provide some valuable management implications. The results show that transshipment can lead to profit increase, especially in the system with high informative value of demand forecast updates.

Evaluation of two transshipment policies in a two-location decentralized inventory system under partial backordering

This research investigates the replenishment and transshipment decisions in a two-retailer inventory system with a single selling season. Both emergency lateral transshipment (ELT) and preventive lateral transshipment (PLT) are investigated. ELT satisfies partial backordering. We prove the existence of unique Nash equilibrium for the system under each policy. The results show that the ELT solution is independent of the transshipment price while the PLT solution converges to the newsvendor solution as the transshipment price increases. Numerical analysis is presented to illustrate the advantage of each policy. This study assists retailers in deciding which transshipment policy should be preferred.

Managing Television Commercial Inventory under Competition: An Equilibrium Analysis

ABSTRACTWe develop a game theoretic model for managing prime time on‐air ad inventory in the television industry. The ad inventory in this industry is priced based on rating points or the number of viewers that watch a commercial. The rating points are sold through two distinct processes: the upfront, which occurs before the broadcast season, and the scatter, which occurs throughout during the broadcast season. Television networks need to allocate their total rating points inventory to these two markets before knowing either the performance rating of their shows or the scatter market price, both of which are ex ante uncertain. The television networks offer performance guarantees on the inventory that is sold in the upfront market while such guarantees are not offered in the scatter market. We consider the inventory competition between two television networks under such a setting. To the best of our knowledge, ours is the first article to consider competition in media revenue management. We establish the existence of unique Nash equilibrium under quantity competition and describe the sensitivity of the equilibrium outcome with respect to various problem parameters. We show that choosing quantity over price during the upfront is a dominant strategy for a television network. We compare our competitive model with a centralized system and discuss the managerial implications for our work.

Game based incentive mechanism for cooperative spectrum sensing with mobile crowd sensors

Mobile crowd sensing emerges as a new paradigm where widespread personal sensors can help to collect information beyond the previously possible scale. Existing spectrum sensing papers consider only secondary users in a cognitive system as the cooperative nodes. While if there are not enough secondary users exist, the cooperative detection performance will be degraded,and which will incur to a low spectrum efficiency or an inevitable interference to primary users. Hence in this paper, we take advantage of the Mobile Crowd Sensing to study the cooperative spectrum sensing where the sensing users are not only the secondary users but also a crowd of mobile users equipped with personal spectrum sensors (such as smartphones, vehicle sensors and tablets). Since spectrum sensing will incur costs for sensing users, an incentive mechanism is necessary to motivate adequate participation. In this paper, a Stackelberg game based incentive mechanism is proposed where the fusion center is leader and mobile sensing users are followers. In Leader game, the fusion center provides an optimal reward to incentive sensing users. And in Follower game, mobile sensing users adjust their own detection probabilities for obtaining more profits when given the reward published by the fusion center. Furthermore, the strategy adjusting process for each sensing user is modeled as a Coalition game where sensing users decide whether join in a coalition based on its utility maximization. We prove the existence of unique Nash Equilibrium in both Follower game and Leader game. Extensive simulations evaluate the feasibility and practically of proposed incentive mechanism. And the results show that a better detection performance can be obtained by the fusion center in our algorithm.

Subcarrier Allocation and Cooperative Partner Selection Based on Nash Bargaining Game for Physical Layer Security in OFDM Wireless Networks

SummaryMost orthogonal frequency division multiplexing (OFDM) cooperative schemes in wireless communication system are poor in secure transmission. Based on the Nash bargaining game (NBG), this paper presents a method of OFDM system cooperative scheme restricted in physical layer security. In the model, each wireless node can act as not only a source node, but also a potential relay node. The sub‐carrier allocation problem among selfish nodes is formulated as a two‐persons bargaining game to guarantee fairness. It is proved that the Nash bargaining solution (NBS) of sub‐carriers allocation is existence of unique Nash equilibrium. Based on the bargaining algorithm and the Hungarian method, a multiple‐users partner selection algorithm is proposed in this paper. Simulation results indicate that the subcarrier allocation fairness is dependent on how much rate increase its partner can make. The proposed partner selection algorithm based on the Hungarian method can improve the overall secrecy rate of the network. Copyright © 2016 John Wiley & Sons, Ltd.

IMPACT OF RETAILER COMPETITION ON MANUFACTURER'S DECISIONS AND PROFITS AT EQUILIBRIUM

As most of the supply chains in practice are decentralized, a key issue in supply chain management is to study the coordination of supply chain. The interactions among players are typically of two types, viz. vertical competition and horizontal competition. We use a game theoretic framework to analyze a two-stage supply chain. The supply chain is modeled as a Stackelberg game with a manufacturer as leader and multiple retailers as followers. We consider multiple retailers competing on quantities (Cournot competition) and study its impact on manufacturer's equilibrium decisions and profits. We show that the wholesale price contract does not achieve Nash equilibrium when retailers offer uniform pricing. On the other hand, in case of perfect price discrimination we prove the existence of unique Nash equilibrium in both deterministic and stochastic demand set-up. Under stochastic demand set-up, we consider information asymmetry between the manufacturer and retailers with respect to demand signal. Furthermore, we show the retailers' selling effort boost up the sales. As variance of sales can hurt the manufacturer's production decisions badly, we conjecture that the manufacturer can offer a retailer incentive contract which can manipulate retailers' equilibrium decision.

Analysis of a simple capacity game

AbstractWe study a two‐player two‐fare‐class static single‐period capacity allocation game with complete information. Nonnested (partitioned) booking limit policies are investigated in both noncooperative and cooperative situations. We show the existence of unique Nash equilibrium in the noncooperative situation. In the cooperative game, we analyze the cost saving of the two players and investigate the concavity of the objective function. For both noncooperative and cooperative settings, we assume the demands to be a truncated normal distribution and provide a comprehensive sensitivity analysis to discover the effects of unit revenue, rejection cost, and transfer rate on the equilibrium solution. Our numerical experiments show that the nonnested model can be a good approximation to the nested booking limit model. For the cooperative setting, we identify conditions that give rise to improvements in the total system revenue. Finally, under each game‐theoretic setting, we present the managerial implications of our solutions along with numerical examples.