This paper presents an application of co-operative transferable utility game as a case study of public transport in the city of Asmara. It is shown that allocation of core concepts like nucleon and nucleolus, can also be computed by a different approach. Players in a co-operative transferable utility game have been interpreted as route numbers, and total number of trips that can be operated in a day as the value. Implementation of solutions is also discussed.

Co-operative n-person transferable utility games have been studied extensively [1]-[3]. In co-operative game theory, the main problem is to provide fair allocation to all the players in a game. Transferable utility in n-person co-operative games can be represented in a characteristic form, i.e., {(N,v) where N={1,2,3,....,n}, n being the total number of players participating}.These players form coalitions S  N in an arbitrary way. Each coalition S can achieve a value, v(S) (assuming that the players in S ‘co-operate’). The value v(N) of the grand coalition N can thus be interpreted as the total profit arising from the co-operation of all players. An allocation is a vector xN having component sum equal to v(N). The desired allocations should be fair in the sense that they should assess the strength of the individual players relative to (N, v) in an acceptable way. The solution of the co-operative game is to find an allocation vector that is unique. Recently, there has been a lot of interest in studying and using the allocation concepts like Nucleolus, Nucleon, F-Nucleolus, etc. [1], [3]-[4].

The core of the co-operative game was introduced by Von Neumann and Morgernstern [5]. This may have an empty core and hence, many allocation (solution) concepts like Nucleolus, Nucleon, F-Nucleolus, etc., have been introduced and considered as relaxations to the concept of the core. To get a unique allocation vector, one should look into single point solutions. Nucleolus, Nucleon and F-Nucleous are all single point solutions. Considering a two player example, if Player 1 has Re. 1 to invest and Player 2 has Rs. 2 to invest, then both together invest Rs. 3 to purchase a lottery ticket and win a prize of Rs. 1000. Since they could not invest individually, they pooled up their resources to invest jointly.

Public Transport and Co-operative Games: A Case Study of Asmara City, co-operative transferable utility, Nucleolus, Implementation of solutions, Nucleon, F-Nucleolus, unique allocation vector.