Three-level warranty service contract among manufacturer,agent and customer: A game-theoretical approach

A warranty is a service contract between a manufacturer and a customer which plays a vital role in many businesses and legal transactions. In this paper, various three-level service contracts will be presented among the following three participants; a manufacturer, an agent, and a customer. In order to obtain a better result, the interaction between the aforementioned participants will be modeled using the game theory approach. Under non-cooperative and semi-cooperative games, the optimal sale price, warranty period and warranty price for the manufacturer and the optimal maintenance cost or repair cost for the agent are obtained by maximizing their profits. The satisfaction of the customer is also maximized by being able to choose one of the suggested options from the manufacturer and the agent, based on the risk parameter. Several numerical examples and managerial insights are presented and used to illustrate the models presented in this paper.     

Game theoretic analysis of negotiations under bankruptcy

We extend the contingent claims framework for the levered firm in explicitly modelling the resolution of financial distress under formal bankruptcy as a non-cooperative game between claimants under the supervision of the bankruptcy judge. The identity of the class of claimants proposing the first reorganization plan is found to be a key determinant of the time spent under bankruptcy, the likelihood of liquidation and the renegotiated value of claims. Our quantitative results confirm the economic intuition that a bankruptcy design must trade-off the initial priority of claims with the viability of reorganized firms.     

Game theoretic models for climate change negotiations

Negotiations to reduce greenhouse gas accumulation in the atmosphere are modeled as extensive games of perfect information. Various solution concepts, such as Nash equilibrium, reaction function equilibrium, correlated equilibrium and bargaining solutions are applied, analyzed and computed. Special reduction techniques are used when the size of the game tree becomes excessive. A new solution concept, the tree-correlated equilibrium is also introduced. Main features of an Excel add-in designed to compute various solutions are briefly described and a sample policy analysis for a special negotiating scenario is discussed.     

Game theoretic analysis of the bargaining process over a long-term replenishment contract

This paper presents supplier–buyer models to describe the bargaining process between a supplier and a buyer over a long-term replenishment contract. Two different models are developed: one for the situation where the supplier has superior bargaining power over the buyer, and the other for the reverse situation. For each model, a method is derived that employs game theory-based analysis to determine the best strategy for each agent. A computational experiment is conducted to estimate the efficiency of the methods and to determine the economic implications of the results. The result indicates that each algorithm is very efficient compared to other strategies. We also verify that the solutions derived from each model are Nash equilibrium. Significantly improved outcomes are obtained for both agents by agreeing to the terms generated by the algorithms over the terms selected in the usual manner.     

Game theoretic formalization of the concept of sustainable development in the hierarchical control systems

The resolution of numerous ecological problems on different levels must be implemented on the base of sustainable development concept that determines the conditions to the state of ecological-economic systems and impacting control actions. Those conditions can’t be realized by themselves and require special collaborative efforts of different agents using both cooperation and hierarchical control. To formalize the inevitable trade-offs it is natural to use game theoretic models. Unfortunately, the main optimality principles of hierarchical control (compulsion, impulsion) are not time consistent and therefore can’t be recommended as the direct base for collective solutions. The most prospective is the conviction method which is formalized as a transition from hierarchy to cooperation and allows a regularization that provides the time consistency. However, in current social conditions other methods of hierarchical control also keep their actuality. To ensure the time consistency of those optimality principles it is necessary to build cooperative differential games on their base. An example of the approach is considered in this paper.     

A game theoretic model for two types of customers competing for service

Two types of customers arrive at a single server station and demand service. If a customer finds the server busy upon arrival (or retrial) he immediately departs and conducts a retrial after an exponential period of time and persists this way until he gets served. Both types of customers face linear costs for waiting and conducting retrials and wish to find optimal retrial rates which will minimize these costs. This problem is analysed as a two-person nonzero sum game. Both noncooperative strategies are studied.     

Game theoretic approach for fertilizer application: looking for the propensity to cooperate

This paper continues the research implemented in previous work of (Schreider et al. in Environ. Model. Assess. 15(4):223–238, 2010) where a game theoretic model for optimal fertilizer application in the Hopkins River catchment was formulated, implemented and solved for its optimal strategies. In that work, the authors considered farmers from this catchment as individual players whose objective is to maximize their objective functions which are constituted from two components: economic gain associated with the application of fertilizers which contain phosphorus to the soil and environmental harms associated with this application. The environmental losses are associated with the blue-green algae blooming of the coastal waterways due to phosphorus exported from upstream areas of the catchment. In the previous paper, all agents are considered as rational players and two types of equilibria were considered: fully non-cooperative Nash equilibrium and cooperative Pareto optimum solutions. Among the plethora of Pareto optima, the solution corresponding to the equally weighted individual objective functions were selected. In this paper, the cooperative game approach involving the formation of coalitions and modeling of characteristic value function will be applied and Shapley values for the players obtained. A significant contribution of this approach is the construction of a characteristic function which incorporates both the Nash and Pareto equilibria, showing that it is superadditive. It will be shown that this approach will allow each players to obtain payoffs which strictly dominate their payoffs obtained from their Nash equilibria.     

Asymptotic behavior of repairable device systems under warranty and beyond warranty periods

Positivity - In this paper, we present a new mathematical model generalizing the model of a single unit repairable device system, with preventive maintenance under warranty period, and the model of...     

Game theoretic analysis of pricing and vertical cooperative advertising of a retailer-duopoly with a common manufacturer

This paper considers competition of duopolistic retailers, who sell substitutable products supplied by a single manufacturer offering a vertical cooperative advertising program. The price-dependent component of the demand function is derived from the consumers’ utility function in order to avoid logically inconsistent results. Additionally, each supply chain member can increase the costumers’ demand by advertising. By means of game theory, we get the following results: (a) Retailer competition harms all players, but is beneficial to the consumers. (b) Stronger competition is followed by less advertising. (c) Channel-leadership is not always advantageous to the manufacturer, and—likewise—retailers can also be better off when accepting followership. However, as our analysis shows, the increased complexity of the model under consideration reaches the limits of an analytical solution. Therefore, we give a brief outlook on non-nalytical solution methods for Nash and Stackelberg games, that could be used in future research, in the end of our paper.     

POOL — Listing service in Game Theory no.25

POOL — Listing service in Game Theory no.25     

Performance analysis of a batch service queue arising out of manufacturing system modelling

In this paper, we present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite numberS of waiting places and a batch service capacityb. A service period is initialized when a service starting thresholda of waiting customers has been reached. The model is denoted accordingly byM/G ^[a,b] /1–S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.     

The effect of lifetime buys on warranty repair operations

Lifetime buys are a common practice in the electronics and telecommunication industries. Under this practice, manufacturers procure their repair parts inventory in one order to support the spare part needs of a product for the duration of its warranty repair period. In this paper, we consider a repair operation in which defective items under warranty are returned to a manufacturer who either repairs these items using its spare parts inventory or replaces each defective unit with a new product. We show how fixed repair capability costs, variable repair costs, inventory holding costs, and replacement costs affect a firm's optimal repair and replacement decisions. The model is used to gain insights for products from a major mobile device manufacturer in the United States.     

Model theoretic connected components of groups

We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.3). This result extends a theorem of Shelah from [21]. We consider also in this context the multiplicative and the additive groups of some rings (including infinite fields).     

The complexity of recursion theoretic games

We show that some natural games introduced by Lachlan in 1970 as a model of recursion theoretic constructions are undecidable, contrary to what was previously conjectured. Several consequences are pointed out; for instance, the set of all -sentences that are uniformly valid in the lattice of recursively enumerable sets is undecidable. Furthermore we show that these games are equivalent to natural subclasses of effectively presented Borel games.

     

Group theoretic properties of Rijndael-like ciphers

We provide conditions for which the round functions of an ?-bit Rijndael-like block cipher generate the alternating group on the set {0,1}^?. These conditions show that the class of Rijndael-like ciphers whose round functions generate the alternating group on their message space is large, and includes both the actual Rijndael and the block cipher used by the compression function of the Whirlpool hash function. The result indicates that there is no trapdoor design for a Rijndael-like cipher based on the imprimitivity of the group action of its proper round functions which is difficult to detect.