Project 3: Marriage Market

People are dating with a view to marriage. Each person has a profile of characteristics, and a profile of the ideal person that they are seeking. People go on dates, during which time they can sense the profile of the person they're with based on their behavior. During dates, people can also adjust their own behavior to project a profile that is different from their actual profile. At the end of a date, each person describes to the other, honestly or not, the ideal profile they're seeking.

People advertise themselves for dating by posting (a) one of their own characteristics, and (b) one of their desired characteristics. The choices for the advertisement are fixed for the entire simulation, and are not required to be truthful reflections of the player's actual characteristics/desires. Each person looking for a date (that's everybody on the first round) selects a subset of people they would be interested in dating based on the advertisements and past dating experience. It is OK to list somebody you previously dated. The simulator will then randomly assign pairs in which both people are interested in each other. If there are remaining people left, the simulator will choose pairs at random in which one person is interested in dating the other. If there are any people remaining then, they are paired at random. A person X who has previously dated a person Y can mark Y as incompatible, after which the simulator will never match X with Y again. In rare cases, this could lead to a person having no dates for a round.

After a date, a person can request another date with the same person. If both people make this request, the simulator will pair them first, before the random assignment. On second and subsequent dates, people are free to further adjust their behavior to project a different profile, and describe a different ideal partner profile. There is no limit to the number of repeat dates that can happen in this way.

After at least 2 dates with somebody, a person has the option to propose marriage to that somebody. If both people on the same round propose marriage to each other, then the marriage is settled, the pairing is fixed, and the two participants are removed from the dating pool. If only one person proposes marriage, then the simulation proceeds as before. However, the recipient of the proposal now knows that their date wanted to get married to them on that turn.

A person's profile consists of a number d of dimensions that are scored as integers between 0 and 10. For example, if a dimension corresponds to extroversion/introversion then 0 may correspond to very shy, while 10 may correspond to very outgoing. The distribution of values in a dimension is a parameter of the simulation. Some dimensions may be uniformly distributed between 0 and 10 while others may be roughly normally distributed. Some dimensions may be monotonic, i.e., bigger is generally more desirable, all else being equal.

A person p's true profile T_p is a d-dimensional vector of numbers. A person p's desired profile D_p is another d-dimensional vector of numbers, than could be very different from T_p (opposites attract!).

A person's happiness is calculated as follows at the end of the simulation.

• An unmarried person has a happiness of 0, i.e., a neutral happiness.
• A married person accumulates a marriage bonus B, which is a parameter of the simulation. (Question: If B is very high, then what will happen?)
• For monotonic dimensions, if v the partner's true value and w>v is the person's desired value, then there is a happiness decrement of (w-v)²; if $w\leq v$ there is no decrement.
• For the remaining dimensions, if v the partner's true value and w is the person's desired value, then there is a happiness decrement of (w-v)².
• A person also incurs half the happiness decrement incurred by their partner according to the two rules above, since people are happiest when their partners are also happy.

Your primary goal: Achieve a positive happiness score by the end of the simulation as often as possible. Your secondary goal: Maximize your player's average happiness. You will be writing code to make decisions for a single person. Multiple groups' code might be used in a single simulation. Your code may be used for multiple people in a single simulation, perhaps all of them, one code instance per person.

Input parameters include:

• N, the number of people in the simulation. We'll assume N is even.
• d the number of dimensions, and $m\leq d$, the number of monotonic dimensions, which will be the first m of the d dimensions.
• The distribution probability of each value in each dimension. This is a two-dimensional array P where P[i,j] is the probability of having value j (from 0 through 10) for dimension i, and for each i, $\sum_{j=0}^{j=10}P[i,j]=1$. Players' desired and desirable values are both chosen from this distribution at random.
• t the number of turns in the simulation. For example, t=100 would mean everybody has to decide whether to marry within 100 total rounds of dating.
• B, the marriage bonus.

Players also know their own profile and their desired ideal profile, but do not have access to other players' true profiles. Your code should not attempt in any way to bypass these restrictions, e.g., by sharing data structures between different instances of your code. Players do not know the probability distributions for a given simulation: they will need to go on a few dates if they want to gather data about the distributions.

Some things to think about:

• When, if ever, is there an incentive to be dishonest about one's profile or one's desired profile?
• Which attribute do you advertise? Might you be suspicious of an advertisement of a 10 in a monotonic dimension?
• How do you decide if an early match is worth marrying?