# The Problem of Choice

Stable Marriage Allocation Problem

This is a classic problem of an arranged marriage.

Let us assume that there are three prospective grooms and bridegrooms for the system of arranged marriages in India. Let us denote the male prospects as A, B and C, while let us denote the female prospects as X, Y and Z.

 Males Females Person 1 A X Person 2 B Y Person 3 C Z

Let us assume that the prospective grooms and brides are talking to each other. Then , from the choice from the male prospects, we have the following table.

 Male Female A X A Z B Z C None Four matches Three choices

Similarly, for the first choice of the female prospects, we have the following choices.

 Female Male X A X C Y None Z C Four prospect Three choices

The first choices for the prospective brides and bride-grooms are given below.

 Choices for the marriage Choice(s) Total number of Choice(s) A X, Z 2 B Z 1 C None 0 X A, C 2 Y None 0 Z C 1

Then, with the trade-offs, we get a 3-dimensional pay-off matrix as given below.

 Choices X Y Z A (1,1) (1,-1) (0,0) B (0,0) (0,-1) (1,1) C (-1,1) (-1,-1) (-1,1)

There are a few codes. The codes are as follows, for the pay-off matrix.

‘-1’ – No Search Found

‘0’ –  No Choices Matched

‘+1’ – Prospective Choice

‘2’  –  Exact Choice

The assumptions that are taken are given as below:

1. Choices from the male side is preferred
2. The female side do not choose a groom, but suggest
3. The strategy is dominant from the groom’s side
4. This is based on the traditional Indian value system
5. If there is no choice, no marriage takes place in the finite possibilities