The next topic of Decon’s simulation series is the commission system design problem.

Let’s say a wholesaler offers a three day deal of selling 1,000 shoes for 10,000 KRW a pair. Retailers who find this deal attractive would place their order and make a deposit.

If the deal is concluded with enough buyers (retailers), the buyers would receive a certain amount of commission points based on their order quantity and time. If the deal falls apart, orders are cancelled and deposits are returned.

Buyers would want to get attractive products and at the same time maximize their gains from commission points. How commission points are provided could either stimulate deals or lead to a catastrophic result that renders commission points meaningless.

While each buyer is acting strategically to maximize gains, how should commission points be distributed to ensure successful deals?

# The Commission System Design Problem

The easiest method that comes to mind is giving out points proportional to the quantity purchased. Regardless of the purchased time, buyers who bought considerable amounts would be given commission points proportional to their order.

If we set the x axis to reflect remaining goods until the deal is completed (inventory) and the y axis to reflect commission points, the function table would look something like the following:

Because the function ends up to be y=t, we will call it the ‘uniform’ type.

#### Ways to Distribute Commission Points

With the uniform type, buyers would buy as much goods to acquire more commission points. At a glance, this seems ideal.

However, the uniform type does not give benefits in commission points based on time of purchase. Because a deposit equal to the total cost of the amount purchased is made as soon as the order is placed, buyers are met with opportunity costs of giving up interest profit or liquidity. Therefore, it is advantageous for the buyers to hop on as late as possible.

At a different perspective, if commission points are different based on time of purchase, you could effectively adjust the time point when buyers take the deal. Wholesalers would want their deals to be concluded as soon as possible.

In the decreasing type, the amount of commission points a buyer would receive decreases over time. In other words, the more remaining goods, the more commission points a buyer gets. Consequently, it is expected that buyers would want to jump in on the deal early on.

On the other hand, what would the increasing type look like? In this case, the later you buy, the more commission points you get. Based on such effect, one could think about two possibilities in the increasing type:

- While more people wait for the last moment to enter the deal, the deal could be nullified by being timed out.
- By giving people a reason to buy at the last moment, many people will join in on an incomplete deal, which means they will contribute to conclusion of deals. Additionally, it is reasonable to give more incentives to those who contributed to closing a deal.

What about a convex or concave quadratic function?

In our simulation report, Decon aims to assess various commission point distribution methods through simulation and find out which is optimal.

# Simulation Environment Setting

Let’s look into the simulation environment setting.

- Number of agents: Refers to the number of network users (simply put, buyers)
- Episode: Each episode starts from the beginning of a deal, agents’ decisions, distribution of commission points, and closure or timeout of a deal.
- Mechanism: The simulation was conducted with different kinds of commission point distribution methods (random, uniform, decreasing, increasing, convex, and concave types).
- Commission pool: Refers to the total amount of commission points to drive buyer participation.
- Sales quantity: Refers to the total amount of goods. Early on, this would be seen as inventory.
- Price: Refers to the price of each item.
- Purchasing unit: Refers to the unit of goods a buyer can purchase. For instance, if the purchasing unit is 5, buyers can buy in increments of five (5, 10, 15, and so on).
- Maximum purchasing quantity: The maximum amount of goods a buyer can purchase. In this simulation, each buyer can only buy once per deal, meaning that if a buyer wants to buy a total of 20ea, they have to place an order of 20ea, not two orders of 10ea.
- Deal time: The duration of which a deal is in progress and ends with a timeout

Buyers would want to maximize their gains by subtracting their opportunity cost of making a deposit from the commission points they will receive. As episodes progress, we programmed the agents (buyers) to learn how many goods to buy at what point in time.

#### Commission Point Distribution Method

As mentioned above, we used random, uniform, decreasing, increasing, convex, and concave types of commission point distribution. Details of each type is as follows:

*Random*

The ratio of commission points a buyer can receive at a certain amount of remaining goods is set as random in the beginning of the simulation.

For instance, let’s say the number of sales (N) is 10 and the commission point ratio is allocated like [0.1, 0.2, 0.4, 0.5, 0.9, 0.3, 0.3, 0.3, 0.8, 0.2]. If a buyer purchases 3ea at 10 remaining goods, the calculation for commission points would be:

**Uniform**

Commission points are proportional to the number of purchased goods. If the number of sales is N and an agent bought M, the benefit can be calculated as follows:

*Decreasing and Increasing*

The decreasing type distributes commission points based on a increasing function with the amount of remaining goods as the x axis. The linear increase can be considered a linear function. The current remaining goods is S and the number of purchased goods is M.

The angle (a) and y-intercept (b) all have positive values. The more remaining goods, the more more commission points you can receive. As the deal progresses — as goods are sold — the number of commission points you can get decreases gradually.

The increasing type can be seen as a decreasing function. The basics are the same as an increasing function but the angle (a) takes a negative value. Also, for the x value in between 0 and the number of sales (N), the y value has to be bigger than 0.

*Convex and Concave*

The convex and concave types display a quadratic function that is symmetrical of half of the sold goods (N/2). Yet, in the convex type, the curvature (a) is larger than 0 whereas the concave type has a curvature (a) smaller than 0. In every possible x value, the y value has to be larger than 0.

The gain can be calculated with the following formula:

#### Cost

The opportunity cost is determined based on how interest rates are calculated. Committing to a deal early and depositing tokens renders more cost. Additionally, each agent have different interest rates.

Each agent is assigned to a credit rating from 1 to 10 based on statistical data regarding credit scores (December 2018). Five top banks based on total asset holdings were chosen based on the September 2018 Financial Supervisory Service’s financial information statistics system. The average rate of the loan interest rates of these banks was used.

#### Reward

The reward that an agent receives is equal to benefit subtracted by cost. Each agent studies to maximize their reward.

# Wrapping Up

In this article, we looked through what the commission system design problem is and introduced multiple commission point distribution methods. We also explained the simulation setting, agents, and simulation environment.

In our next article, we will analyze the results of the actual simulation.