Friday, December 23, 2005

SAP: 3 economists in one cab

WSJ Uncut

Thats's a terror, I know, but let's see what happens. Three economists get into a cab, they're each getting off at different places along the route. How will they share the fare?
Assumptions:
(1) There is no rush hour
(2) cabs are plentiful
(3) each one can reach his destination at atleast the same speed, if not faster. So they have come together becuase the total fare would be cheaper than if they had travelled separately.
(4) A and B are allowed to jump out at no cost at their destinations on the way to C's.
(5) Also, say A's usual fare = $1, B's usual fare = $5 and C's usual fare = $9
(so, rather than paying $15, they would pay $9 now)

Now, how do you allocate costs and benefits among 3 people who have come together for mutual benefits. Let us explore the various ways they may think doing this.

(a) Easiest solution, all 3 share A's fare, then B and C share the fare from A's to B's, and C should pay the remaining fare from B's to C's. So, A's fare = $0.33 ; B's fare=$2.33 ; C's fare = $6.33

(b) The benefit of travelling together is the total savings of $6. They can split that up proportionately. A's savings = (1/15)*6 = $.40 ; B's savings = (5/15)*6 = $2 ; C's savings = 6-(0.4+2) = $3.6.
So, A's fare = $0.6 ; B's fare = $3 ; C's fare = $5.4
Here, every passenger pays an amount proportional to what he would have paid w/o the savings. Proportional split up of surplus and debts is a common practice under U.S law, seen mostly in bankruptcy cases

(c) Now, lets introduce the beauty of negotiations. Heard of John Nash? Yeah, the Beautiful Mind guy, some economists dug into his work on negotiation strategies in game theory to propose a solution.
Each passenger would negotiate his best outcome which turns out to be an equal split of the savings. Why? Because this whole deal of travelling together to obtain mutual benefits, would be nullified if any one party walks away. So, A has the highest bargaining power in this case.
So, A is paid $1 to travel along ; B's fare = $3, C's fare = $7

(d) The above solution is problematic because one party is paid to travel. Instead, B and C would negotiate with A and give him a freebie and split up rest of the savings equally.
So, A's fare = $0 ; B's fare = $2.5 ; C's fare = $6.5

(e) The negotiation gets further interesting if B and C form a coalition. They would argue with A that, if they travel without A, they would save $5, so they have to make atleast that now, which means only the remaining $1 of savings is up for equal splitting.
So, A's fare = $0.67 ; B's fare = 5 - (2.5+0.33) = $2.17 ; C's fare = $6.17

The conclusion one would derive, as indicated by Jonathan Gruber, Prof of Economics, MIT, is that there really is no one single solution to this problem, it depends on individual preferences and bargaining power.


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4 Comments:

Blogger kicha said...

If I am one among them, I would not have travelled with guys, who has huge difference b/w their normal fares. if the difference is minimal, then I would go for solution (2).

3:26 PM  
Anonymous Lumbergh-in-training said...

sorry, i forgot my purse today :p

3:58 AM  
Anonymous V. said...

ungala ellam UTA la seat kuduthaa ippadi eludhi SCSE2002 ku anupuveenga... podanga
One thing is, there is no logic with solution (c), paying A money to travel as it adds no value addition to A or B's money.

10:48 PM  
Blogger Padmanaban Kumar (paddu) said...

yes, but thats what happens when each one has the negotiating power or ability to get an equal split of the savings.
It is to overcome this problem anyway that there is solution (d)

11:35 PM  

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