Nikolay A. Zenkevich

Conditions for sustainable cooperation

There are three important aspects to-be-taken into account when the stability problem of a long-term cooperative agreement is investigated: time consistency (dynamic stability) of the cooperative agreement, strategic stability and irrational behavior proofness. The mathematical results based on imputation distribution procedure (IDP) are developed for dealing with the above-mentioned aspects of cooperation. The authors prove that, for a special class of differential games, a time-consistent cooperative agreement can be strategically supported by a Nash equilibrium. An example is also considered, where all the three conditions are satisfied.

COALITIONAL SOLUTION OF A GAME-THEORETIC EMISSION REDUCTION MODEL

In this paper the problem of allocation over time of total cost incurred by coalitions of countries in a coalitional game of pollution reduction is considered. The Nash equilibrium in the game played by coalitions is computed and then the value of each coalition is allocated according to some given mechanism between its members.

STRONG EQUILIBRIA IN THE VEHICLE ROUTING GAME

This paper introduces an extension of the vehicle routing problem by including several distributors in competition. Each customer is characterized by demand and a wholesale price. Under this scenario a solution may have unserviced customers and elementary routes with no customer visits. The problem is described as a vehicle routing game (VRG) with coordinated strategies. We provide a computable procedure to calculate a strong equilibrium (SE) in the VRG that is stable against deviations from any coalition. Following this procedure, we solve iteratively optimization subproblems for a single distributor, reducing the set of unserviced customers at each iteration. We prove that strong equilibria of one type exist for a VRG, and we provide conditions for another type to exist. We also introduce a semi-cooperative SE that helps reduce a set of strong equilibria in the VRG. Our methodology is suited for parallel computing, and could be efficiently applied to routing vehicles with a few compartments. It also calculates a numerical example for a three person VRG with six cars and twelve customers.

Stable Cooperation Under Environmental Constraints

A game-theoretic model of territorial environmental production under Cournot competition is studied. The process is modeled as cooperative differential game. The stable distribution mechanism of the common cooperative benefit among players is proposed. We proved that the cooperative total stock of accumulated pollution is strictly less then the pollution under Nash equilibrium for the whole duration of the game. We design a stable Shapley value as a cooperative solution, which is time-consistent. The Shapley value is also strategic stable and satisfies the irrational-behavior-proofness condition. The numerical example is given.

Comparison of two Economic Models for a Business-to-Business Exchange

We model business-to-business (B2B) exchange as intermediary within the principal-agent framework. As the principal, the exchange chooses the trading mechanism. As agent, sellers and buyers voluntarily play deal-formation games according to the rule specified by the trading mechanism Participations in the exchange is endogenized by allowing sellers and buyers to possess outside options. We examine two trading mechanisms in detail, Perry’s bargaining model, and Chatterjee and Samuelson’s bilateral double auction with sealed bids. A two-part-tariff charge system, entry fee plus commission percentage, is imposed on sellers and buyers. We find that individual behaviours in the deal-formation game vary drastically with the exact form of trading mechanism, relative bargaining power between sellers and buyers, and the existence of outside options. On the other hand, the optimal commission percentages are found to be remarkably insensitive to these micro-level details. Entry fees, though as the effective as commission percentages in raising revenue, strongly discourage participations.

Auction Games and Pricing Process

Abstract Its considered a multi-item first price closed auction with asymmetric bidders and one seller under competition. This base auction can be modeled as a non-zero sum game with discontinuous payoff functions. Its shown that in this game exist unique Nash equilibrium in mixed strategies when antimonopoly and competition conditions are accomplished. Then its investigated also a multistage repeated auction with described base auction as a single step. Its derived sufficient conditions when a cooperative cartel solution is time consistent. To construct the imputation in models of profit allocation and to compute transaction (cost allocation as a dual problem) is used the solution of the base auction game.

Improvement of Operational Performance of Internationalized Companies through Collaboration in Distribution Networks

Abstract The purpose of this paper is to provide theoretical insights on the impact of supply chain collaboration on the operational performance of firms and collaborative advantage as an intermediate variable in the context of the supply networks of internationalized firms. The research is based on a case study of a distribution network constituting Russian and international firms. The obtained results indicate that supply chain collaboration improves operational performance of internationalized firms and firms in domestic market. Moreover, the study advocates that collaboration in distribution networks can be considered as driving factor for international firms to enter the emerging markets through supply networks.

Strong coalitional equilibrium in a transportation game

This paper introduces an extension of the vehicle routing problem by involving several decision makers in competition. Each customer is characterized by demand and distance to the warehouse. The problem is described in form of a cooperative transportation game (CTG). We consider customers as players in the game. Their strategies are the routes for a vehicle they should rent in a coalition to deliver goods subject to their demand with minimal transportation costs, under the assumption that transportation costs are allocated between the players according to the Nash arbitration scheme. For each profile in coalitional strategies, we define a coalitional structure of players and the costs of each player. A strong equilibrium is found for the cooperative transportation game. In addition, we develop a procedure to calculate the strong equilibrium. This procedure is illustrated by a numerical example.

Strong Coalitional Structure in an Open Vehicle Routing Game

In the chapter it is investigated a special case of one-product open vehicle routing game, in which there is a central warehouse or wholesaler, several customers, who are considered to be players. Each player is placed in a node of the transportation network and is characterized by demand and distance to the warehouse. For such a problem a coalitional transportation game (CTG) is formalized. In such a game each customer (player) should rent a track to deliver goods from the central warehouse. It is assumed that all tracks have the same capacity. The players tend to minimize their transportation costs and totally supply their demands. A player may rent a vehicle alone, or chose a coalition of players to cooperate. In cooperation the players of coalitions find the shortest path form the central depot to all the player of coalition. Transportation costs are allocated between players according to the Nash arbitration scheme. Strong equilibrium which is stable against deviations of any coalition of players is found in a CTG. A computation procedure for strong equilibrium construction is proposed. Implementation of procedure is illustrated with a numerical example.

Price Competition on the Market of Counterfeiting Software

In this paper, the market of software products is considered. Regularly this market is suffering from existence of counterfeit or pirate products which causes problems and challenges for original software developers. Taking this fact into account the paper is trying to solve the problem of price competition on this market. The software company set the price and the quality of the software product while the counterfeit or pirate company suggests the consumers the product of the lower quality. First the general model is analyzed and price equilibrium is defined. Second, the monopoly case is considered separately and optimal software price is defined. Finally, it is supposed that there are two companies that produce original software on the market who compete and differentiate in product quality, and there are two pirate companies who produce the same type of software. The duopoly case is analyzed and equilibrium prices for competing companies are obtained in the explicit form.