Game Theory and the Mate-Searching Game (Mathematical Framework)

[unnamed user]

You may know, or maybe you don’t, but many things in life, especially in our social lives, operate according to the rules of a mathematical field called game theory. Personally, I've dabbled a bit in the mathematics of this (I don’t know much, but still), and I believe that interesting, or perhaps even surprising, results can emerge from it.

PRELIMINARY SETUP

First, we will define two sets. One of them is the set of Men (denoted as M), and the other is the set of Women (denoted as F). The union of these two sets, M ∪ F, will give us the set N, which represents the set of players. I think we’re in agreement up to this point.

Game: The Competition Space

The Cartesian product of all the players (the set N) is called the game space or the competition space. For example, the Cartesian product of the Men set (M) and the Women set (F), denoted as F × M, gives all possible pairings, and this space is called the matching space.

Functions

Now, we will define some functions, so remember your high school math! One of the functions we will define is called the Sexual Market Value function (smv).

Definition: smv: N → [0,10] is a function where each player has a positive smv value. (Here, F ∪ M = N and [0,10] is a closed interval, containing all real numbers between 0 and 10. So, the smv function is essentially a mapping from the player set to the closed interval [0,10].)

Time-dependent SMV Function

If the smv function is assigned as a constant value for each player, meaning it doesn’t change, then looksmaxing would be impossible and meaningless. In order for looksmaxing to make sense, we must introduce a time dimension to the smv function. This means the function should be two-variable and should change according to the time (the player’s state at time t).

Missing: We need to define how the function changes over time (for example, linearly, logarithmically, or depending on an external variable).

So,

Definition (time-dependent smv): smv(x,t) is a time-dependent smv function that shows the smv value of player x at time t.

Utility Function

U: S × [0,10] × [0,10] → ℝ

STRATEGY SET

Each player in the matchmaking game has four choices in their strategy: propose, not propose, accept, or reject. Now let’s define a set S as the strategy set: S = {propose, not propose, accept, reject}.

Matching Rules

• One-to-one Matching Rule: Each player can only match with one person in a given game.
• SMV Difference: Whether a player will make a proposal depends on the difference between their own smv and the smv of the target player. For example:
  Δsmv(x,y) = |smv(x,t) - smv(y,t)|
  If Δsmv(x,y) is below a certain threshold value ε, player x will propose to player y.

Matching Strategies

Each player can choose one strategy from the set S = {propose, not propose, accept, reject}. The strategies are defined as follows:

• Propose: The player makes a proposal to another player.
• Not Propose: The player does not make any proposals during that round.
• Accept: The player accepts a proposal they received.
• Reject: The player rejects a proposal they received.

Transitions between these strategies depend on the player’s utility function.


So far, I’ve set up this mathematical framework. What do you think?

 

[Soter]

I think that Pythagoras might have been right when he said that even God can be abstracted and understood by numbers but this shit you wrote is way too simple even for a basic model. No original or fresh insight either. All this post did was to make you look like a geek.