Nowadays, online taxi has become a major transportation choice of many urban workers in Jakarta not only they provide fair mechanism of pricing, but also customer can enjoy other facilities such as ride sharing. Ride sharing is the situation where groups of people would use the same vehicle (car) when they are heading to the same direction. By the street goes by, the A can arrive first, then B, then C. They would depart onto different point, but the taxi goes along the same way.

Sharing a Cab phenomenon can be done by anyone including students going to campus, workers going to work, or friends going to mall. When they share a cab, the most possible way to pay is to averagely divide the fare on each individual. But the main questions arise; since each individual would depart or come from different point, Is it really fair to apply such method?

Sharing a taxi is an example of* Cooperative Game Theory* in Economics. It is one of the two counterparts of game theory that studies the interactions among coalitions of players. The description of a *cooperative game* is still in terms of a characters function which specifies for every group of players the total payoff that the members of S can obtain by signing an agreement among themselves; this payoff is available for distribution among the members of the group. In order to obtain the fairness principle within cooperative game theory, there are three principles that must be met. First, the contribution of each player is calculated based on the marginal contribution. Second, each individual who have contributed, must receive equal benefit. Third, if there is player who is not able to contribute, he/she won’t get benefit.

Based on the above model, we can say that averagely divide the taxi fare into each individual is actually not the best model.

**So, how much should individual pay when they share a cab?**

*Shapley value* can answer such question. Shapley value is often viewed as a good normative answer to the question posed in cooperative game theory. That is, those who contribute more to the groups that include them should be paid more. Shapley value, has a nice interpretation in terms of expected marginal contribution. It is calculated by considering all the possible orders of arrival of the players into a room and giving each player his marginal contribution

Let us see the illustration below :

Amber, Bieber, and Charlie are an employee of X Corporation based in Pancoran. From Pancoran, Amber is going home to Tanjung barat that will cost her Rp 10,000. At the same time, Bieber is also going to Lenteng Agung that will cost him Rp 20,000. Charlie also is going to campus located in Depok that will cost him Rp 50,000. They decided to share a taxi and the payment will be given to those who ride the longest haul, Charlie.

Tabel 1 Margin Contribution of Each Player

Based on table above, it appears that the amount of contributions paid by first person will affect the contribution of the next player. It is proven that each individual (player) would pay different cost, based on the length of travel.

If Amber is the first person to pay, then she will contribute some travel expenses of herself, which is Rp 10,000. Furthermore, Bieber will only pay the contribution of some travel expenses minus Amber’s contributions (Rp20,000 – Rp10,000). Finally, Charlie only needs to pay the rest of the unopened costs which is Rp30,000 (Rp50,000 – (Rp10,000+Rp10,000)). However, if Bieber decides to be the first to pay, Amber will not pay her contribution. This is because the cost of Amber’s travel already be done by Bieber; making the coalition system seem to work only with Bieber and Charlie. Especially if Charlie decides to be the first to pay, all the travel expenses of Amber and Charlie have been done by Abby, so no cooperative game is created.

Finally, The total contribution of each player then is multiplied by the probability in this case is 1/6. As a result, Amber only needs to pay Rp 3,333; Bieber only pay Rp 8,333; and Charlie contributes Rp38,333. The total is Rp50,000.

Hope this help guys!

Reference:

Bonanno, G., 2015. Cooperative Games: The Shapley Value. [Online] Available at: http://faculty.econ.ucdavis.edu/faculty/bonanno/teaching/122/Shapley.pdf [Accessed May 1, 2017]

Ferguson, T., 2014. Game Theory – UCLA Department of Mathematics, Los Angeles: UCLA.