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On the Gas Routing via Game Theory

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DOI: 10.4236/ajor.2015.54022    1,948 Downloads   2,296 Views   Citations
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ABSTRACT

The delivery of the natural gas obtained by drilling, fracking and sending the product to consumers is done usually in two phases: in the first phase, the gas is collected from all wells spread on a large area, and belonging to several companies, and is sent to a depot owned by the city; then, in the second phase, another company is taking the gas on a network of ducts belonging to the city, along the streets to the neighborhoods and the individual consumers. The first phase is managed by the gas producing companies on the ducts owned by each company, possibly also on some public ducts. In this paper, we discuss only this first phase, to show why the benefits of these companies depend on the cooperation of the producers, and further, how a fair allocation of the total gas obtained, to the drilling companies, is computed. Following the model of flow games, we generate a cooperative transferable utilities game, as shown in the first section, and in this game any efficient value gives an allocation of benefits to the owners of ducts in the total network. However, it may well happen that the chosen value is not coalitional rational, in the game, that is, it does not belong to the Core of the game. By using the results obtained in an earlier work of the author, sketched in the second section, we show in the last section how the same allocation may be associated to a new game, which has the corresponding value a coalitional rational value. An example of a three person flow game shows the game generation, as well as the procedure to be used for obtaining the new game in which the same value, a Shapley Value, will give a coalitional rational allocation.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Dragan, I. (2015) On the Gas Routing via Game Theory. American Journal of Operations Research, 5, 288-292. doi: 10.4236/ajor.2015.54022.

References

[1] Kalai, E. and Zemel, E. (1982) On Totally Balanced Games and Games of Flow. Mathematics of Operations Research, 7, 476-478.
http://dx.doi.org/10.1287/moor.7.3.476
[2] Owen, G. (1995) Game Theory. 3rd Edition, Academic Press, San Diego.
[3] Dragan, I. (2014) On the Coalitional Rationality of the Shapley Value and Other Efficient Values. American Journal of Operations Research, 4, 328-334.
http://dx.doi.org/10.4236/ajor.2014.44022
[4] Dragan, I. (1991) The Potential Basis and the Weighted Shapley Value. Libertas Mathematica, 11, 139-146.
[5] Dragan, I. and Martinez-Legaz, J.E. (2001) On the Semivalues and the Power Core of Cooperative TU Games. International Game Theory Review, 3, 127-139.
http://dx.doi.org/10.1142/s0219198901000324
[6] Dragan, I. (2005) On the Inverse Problem for Semivalues of Cooperative TU Games. International Journal of Pure and Applied Mathematics, 22, 545-561.

  
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