On channel coordination through revenue-sharing contracts with price and shelf-space dependent demand

This paper deals with the problem of coordinating a vertically separated channel under a consignment contract with revenue sharing. We consider the demand of the downstream player, e.g., the retailer, being price and shelf-space sensitive. Under such a setting, the retailer decides on the revenue-sharing percentage and the slotting fee. And the upstream player, e.g., the manufacturer, decides on the retail price and the size of shelf-space. For each item sold, the retailer deducts an agreed-upon percentage from the selling price and remits the balance to the manufacturer. We model the decision-making of the two firms as a Stackelberg game, and carry out equilibrium analysis for both the centralized and decentralized regimes of the channel, with and without cooperation. In addition, a profit sharing scheme through a two-part slotting allowance is proposed, which leads to Pareto improvements among channel participants. Our analysis reveals that the non-cooperative game tends to set a higher revenue-sharing percentage and lower slotting fee by the retailer, and a higher retail price and less display space by the manufacturer, which leads to a lower channel profit. The consistent bias can be perfectly rectified by the cooperative game through the proposed two-part contractual agreement.     

Optimal coalition formation and surplus distribution: Two sides of one coin

A fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them, as opposed to the treatment as a binary choice in the non-fuzzy (crisp) game. Building on the property - not made use of so far in the literature of fuzzy games - that a fuzzy game can be represented as a convex program, this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players, two sides of one coin. Furthermore, this program is seen to provide a unifying framework for representing the core, the least core, and the (fuzzy) nucleolus, among others. Next, we derive conditions for uniqueness of core rewards and to deal with non-uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well-known concepts for selection from the core, including the Dutta-Ray solution (Dutta and Ray, 1989), the equal sacrifice solution (Yu, 1973), the equal division solution (Selten, 1972) and the tau-value (Tijs, 1981). We also generalize the concept of the Grand Coalition of contracting players by allowing for multiple technologies, and we specify the conditions for this allocation to be unique and Egalitarian. Finally, we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus.     

Centralized and decentralized management of groundwater with multiple users

In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems.     

Equilibrium analysis of supply chain structures under power imbalance

This paper investigates the implications of channel power on supply chain stability in a setting where multiple suppliers sell substitutable products through a common retailer. Such supply chains have been traditionally analyzed as one- or two-stage Stackelberg non-cooperative games with all suppliers sharing balanced (equal) decision-making power. In this paper, we relax this assumption and formulate game-theoretic models to examine scenarios where one supplier can act as the Stackelberg leader. Consequently, we analyze new supply chain structures and introduce the notion of structure dominance, a novel approach to analyze the performance of supply chains that has practical implications. Thus, a decision maker can employ the concepts of structure dominance to determine whether there exist supply chain scenarios that are more stable than others, i.e., less prone to power reconfigurations, at both agent and group level. We find that power imbalance causes significant declines in supply chain profits, and the more balanced the agents are the higher their profits when demand is linear, regardless of product competition. It develops that neither the Manufacturer Stackelberg nor the Retailer Stackelberg supply chains are stable structures in our generalized setting, but that structures where power is equally split between agents provide for best stability and performance.     

Interaction indices for games on combinatorial structures with forbidden coalitions

The notion of interaction among a set of players has been defined on the Boolean lattice and Cartesian products of lattices. The aim of this paper is to extend this concept to combinatorial structures with forbidden coalitions. The set of feasible coalitions is supposed to fulfil some general conditions. This general representation encompasses convex geometries, antimatroids, augmenting systems and distributive lattices. Two axiomatic characterizations are obtained. They both assume that the Shapley value is already defined on the combinatorial structures. The first one is restricted to pairs of players and is based on a generalization of a recursivity axiom that uniquely specifies the interaction index from the Shapley value when all coalitions are permitted. This unique correspondence cannot be maintained when some coalitions are forbidden. From this, a weak recursivity axiom is defined. We show that this axiom together with linearity and dummy player are sufficient to specify the interaction index. The second axiomatic characterization is obtained from the linearity, dummy player and partnership axioms. An interpretation of the interaction index in the context of surplus sharing is also proposed. Finally, our interaction index is instantiated to the case of games under precedence constraints.     

Stackelberg equilibria in managerial delegation games

Managerial compensation packages do not only influence managers’ behavior, but also have an impact on competing firms. In a managerial delegation game investigating the latter aspect, it is shown that the inherent prisoner’s dilemma situation can be resolved (without changing the normally studied setup or timing). In the first stage, owners choose an incentive function for their managers, in the second stage they choose the weights assigned to that function besides profits and in the third stage managers play a Cournot game. Solving this continuous optimization problem with the implicit function theorem shows that choosing an incentive from the set of “multiplicative incentives”, i.e. any generalized affine transformation of the product of both firms’ quantities, which includes e.g. relative profit, ensures that the Stackelberg outcome is among the set of equilibrium outcomes. Furthermore, it is the unique outcome if the rival owner opts for one of the well-known incentives like sales, revenue or market share. The general approach used allows demonstrating that with no other linear incentive a Stackelberg outcome results and that incentives like profit-to-cost ratio should be avoided. Selecting a multiplicative incentive is a dominant strategy of the game.     

Efficient promotion strategies in hierarchical organizations

The Peter principle has recently been investigated by means of an agent-based simulation, and its validity has been numerically corroborated. It has been confirmed that, within certain conditions, it can really influence in a negative way the efficiency of a pyramidal organization adopting meritocratic promotions. It was also found that, in order to bypass these effects, alternative promotion strategies should be adopted, as for example a random selection choice. In this paper, within the same line of research, we study promotion strategies in a more realistic hierarchical and modular organization, and we show the robustness of our previous results, extending their validity to a more general context. We also discuss why the adoption of these strategies could be useful for real organizations.     

Diversity of scales makes an advantage: The case of the Minority Game

We use the Minority Game as a testing frame for the problem of the emergence of diversity in socio-economic systems. For the MG with heterogeneous impacts, we show that the direct generalisation of the usual agents’ profit does not fit some real-world situations. As a typical example we use the traffic formulation of the MG. Taking into account vehicles of various lengths it can easily happen that one of the roads is crowded by a few long trucks and the other contains more drivers but still is less covered by vehicles. Most drivers are in the shorter queue, so the majority win. To describe such situations, we generalised the formula for agents’ profit by explicitly introducing a utility function depending on an agent’s impact. Then, the overall profit of the system may become positive depending on the actual choice of the utility function. We investigated several choices of the utility function and showed that this variant of the MG may turn into a positive sum game.     

Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach

We present a game-theoretic approach to optimize the strategies of toll enforcement on a motorway network. In contrast to previous approaches, we consider a network with an arbitrary topology, and we handle the fact that users may choose their Origin-Destination path; in particular they may take a detour to avoid sections with a high control rate. We show that a Nash equilibrium can be computed with an LP (although the game is not zero-sum), and we give a MIP for the computation of a Stackelberg equilibrium. Experimental results based on an application to the enforcement of a truck toll on German motorways are presented.