Network Connectivity Game

We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point.

Dynamic Shapley Value in the Game with Perishable Goods

The paper investigates two-stage stochastic minimum spanning tree games with perishable goods. The cooperative behaviour of the players is defined. At each stage, all players jointly take action to construct a network with a cost matrix. At the second stage, a particular player may leave the game, and the probability of this leaving depends on the cooperative behaviour of all players at the first stage. At each stage game, the total cost of the spanning tree is calculated to include the sum of the costs of the contained edges and the cost of the loss of perishable goods expended on that edge of the spanning tree. The characteristic functions in the game are considered, and the dynamic Shapley values are modified. The time consistency of the dynamic Shapley values is studied.

TO BUILD A HOUSE TOGETHER – INTEREST GROUP ACTIVITY FOR ALL-DAY ORGANIZATION OF THE EDUCATIONAL DAY

The presented report offers development of activity by interests, conducted in a group for all-day organization of the educational day, 5th grade, First primary school „St. Cyril and St. Methodius“, Gotse Delchev. The topic „How to build a house together – ours group, school, society – where all the differences are being respected and feels like home“ selection is based on the specific features of the school group. The group aim is to focus the students attention to themselves and further through precised class organization provided by the teacher to reach realization of the goals is being used game working approach. „The Plot“ of the student’s group is compared to building a house. Playing consequently tree games, the students build their „house“. In the game process attention is given to the respect and tolerance based in the personality of the students. Moreover, the process of skill development of the students is being provoked through discussion regarding „National symbols“ where the aim is to build a common sense related to the social norms of behavior. Game working approach is being used as a reliable tool in order to increase the students activity in all organization forms of education and socialization.