Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

A single buyer-single supplier bargaining problem with asymmetric information : theoretical approach and software implementation

This paper is focused on the coordination of order and production policy between buyers and suppliers in supply chains. When a buyer and a supplier of an item work independently, the buyer will place orders based on his economic order quantity (EOQ). However, the buyer s EOQ may not lead to an optimal policy for the supplier. It can be shown that a cooperative batching policy can reduce total cost significantly. Should the buyer have the more powerful position to enforce his EOQ on the supplier, then no incentive exists for him to deviate from his EOQ in order to choose a cooperative batching policy. To provide an incentive to order in quantities suitable to the supplier, the supplier could offer a side payment. One critical assumption made throughout in the literature dealing with incentive schemes to influence buyer s ordering policy is that the supplier has complete information regarding buyer s cost structure. However, this assumption is far from realistic. As a consequence, the buyer has no incentive to report truthfully on his cost structure. Moreover there is an incentive to overstate the total relevant cost in order to obtain as high a side payment as possible. This paper provides a bargaining model with asymmetric information about the buyer s cost structure assuming that the buyer has the bargaining power to enforce his EOQ on the supplier in case of a break-down in negotiations. An algorithm for the determination of an optimal set of contracts which are specifically designed for different cost structures of the buyer, assumed by the supplier, will be presented. This algorithm was implemented in a software application, that supports the supplier in determining the optimal set of contracts

Cooperation in an HMMS-type supply chain: A management application of cooperative game theory = Kooperáció egy HMMS-típusú ellátási láncban: A kooperatív játékelmélet egy menedzsment alkalmazása

We apply cooperative game theory concepts to analyze a Holt-Modigliani-Muth-Simon (HMMS) supply chain. The bullwhip effect in a two-stage supply chain (supplier-manufacturer) in the framework of the HMMS-model with quadratic cost functions is considered. It is assumed that both firms minimize their relevant costs, and two cases are examined: the supplier and the manufacturer minimize their relevant costs in a decentralized and in a centralized (cooperative) way. The question of how to share the savings of the decreased bullwhip effect in the centralized (cooperative) model is answered by the weighted Shapley value, by a transferable utility cooperative game theory tool, where the weights are for the exogenously given “bargaining powers” of the participants of the supply chain. = A cikkben a kooperatív játékelmélet fogalmait alkalmazzuk egy Holt-Mogigliani-Muth-Simon-típusú ellátási lánc esetében. Az ostorcsapás-hatás elemeit egy beszállító-termelő ellátási láncban ragadjuk meg egy kvadratikus készletezési és termelési költség mellett. Feltételezzük, hogy mindkét vállalat minimalizálja a releváns költségeit. Két működési rendszert hasonlítunk össze: egy hierarchikus döntéshozatali rendszert, amikor először a termelő, majd a beszállító optimalizálja helyzetét, majd egy centralizált (kooperatív) modellt, amikor a vállalatok az együttes költségüket minimalizálják. A kérdés úgy merül fel, hogy a csökkentett ostorcsapás-hatás esetén hogyan osszák meg a részvevők ebben a transzferálható hasznosságú kooperatív játékban a költség megtakarítást, exogén módon adott tárgyalási pozíció mellett

Household Models: An Historical Perspective

This paper is a survey of the literature on theoretical models of the household, paying particular attention to some of the earlier contributions, and using them to place the current state of the theory in perspective. One of its aims is to suggest that the literature’s neglect of Samuelson’s proposal, that households can be modelled as if they maximised a form of social welfare function, was a mistake. However, the idea following directly from the Nash bargaining models, that the household’s preference ordering over the utility profiles of its members depends on exogenous variables, in particular wage rates and non-wage incomes, is an important one. Combined with Samuelson’s proposal, it can be made the basis for a general approach to modelling household decision taking, flexible enough to encompass non-cooperative behaviour and Pareto inefficiencies arising out of the inevitable incompleteness and unenforceability of domestic agreements. We also point out the importance of household production and some of the implications of its neglect in modelling households. Above all, the aim is to provide a deeper understanding of the current theoretical literature on household economics by means of a survey of its history.household behavior, family economics, household welfare, time allocation, labor supply, household production, child care, gender, discrimination, cooperative models, non-cooperative models, trade models, microeconomic history

Compensations in the Shapley value and the compensation solutions for graph games

We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give an interpretation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph. Firstly, we consider cooperative games with a forest (cycle-free graph). We extend the compensation vector by considering all rooted spanning trees of the forest (see Demange 2004) instead of orderings of the players. The associated allocation rule, called the compensation solution, is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component. Secondly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively.

Bargaining, Coalitions and Externalities: a Comment on Maskin

We first observe that two of Maskin’s results do not extend beyond three players: we construct a four-player partition function with nonpositive externalities whose unique solution is inefficient, as well as a four-player characteristic function that has a unique efficient solution for each ordering of the players, but for which the payoff vector obtained by averaging these solutions over the different orderings does not coincide with the Shapley value. On the other hand, we reinforce Maskin’s insight that externalities may play a crucial role in generating inefficiency. Many existing solutions on how to share profits assume or derive the property of efficiency. Yet we argue that players may have an interest to choose with whom to bargain. We illustrate how this may trigger inefficiency, especially in the presence of externalities, even if bargaining among any group of agents results in an efficient distribution of the surplus they can produce. We also provide some sufficient conditions for efficiency.externalities; coalition formation; Shapley value

Efficiency in Family Bargaining: Living Arrangements and Caregiving Decisions of Adult Children and Disabled Elderly Parents

In this paper, we use a two-stage bargaining model to analyze the living arrangement of a disabled elderly parent and the assistance provided to the parent by her adult children. The first stage determines the living arrangement: the parent can live in a nursing home, live alone in the community, or live with any child who has invited coresidence. The second stage determines the assistance provided by each child in the family. Working by backward induction, we first calculate the level of assistance that each child would provide to the parent in each possible living arrangement. Using these calculations, we then analyze the living arrangement that would emerge from the first stage game. A key assumption of our model is that family members cannot or will not make binding agreements at the first stage regarding transfers at the second stage. Because coresidence is likely to reduce the bargaining power of the coresident child relative to her siblings, coresidence may fail to emerge as the equilibrium living arrangement even when it is Pareto efficient. That is, the outcome of the two-stage game need not be Pareto efficient.

Collective Household Models: Principles and Main Results.

In the traditional approach to consumer behaviour it is assumed that households behave as if they were single decision making units. This approach has methodological, empirical and welfare economic deficiencies. A valuable alternative to the traditional model is the collective approach to household behaviour. The collective approach explicitly takes account of the fact that many person households consist of several members which may have different preferences. Among these household members, an intrahousehold bargaining process is assumed to take place. Next to providing an introduction to the collective approach, this survey intends to show how different collective household models, each with their own aims and assumptions, are connected.collective household models, household bargaining, intrahousehold allocation, consumption behaviour, labour supply.

Efficiency in Family Bargaining: Living Arrangements and Caregiving Decisions of Adult Children and Disabled Elderly Parents

In this paper, we use a two-stage bargaining model to analyze the living arrangement of a disabled elderly parent and the assistance provided to the parent by her adult children. The first stage determines the living arrangement: the parent can live in a nursing home, live alone in the community, or live with any child who has invited coresidence. The second stage determines the assistance provided by each child in the family. Working by backward induction, we first calculate the level of assistance that each child would provide to the parent in each possible living arrangement. Using these calculations, we then analyze the living arrangement that would emerge from the first stage game. A key assumption of our model is that family members cannot or will not make binding agreements at the first stage regarding transfers at the second stage. Because coresidence is likely to reduce the bargaining power of the coresident child relative to her siblings, coresidence may fail to emerge as the equilibrium living arrangement even when it is Pareto efficient. That is, the outcome of the two-stage game need not be Pareto efficient.