Merchants

Merchants are NPCs found throughout Kamigotchi World who buy or sell items.

Players can interact with merchants to exchange for their hard-earned MUSU for items. These are often commonly used items like food for Kamigotchi and the Player. Some merchants will also purchase items from players.

Characters

Mina

Mina is likely the first merchant you'll encounter. Her humble storefront is accessible through a portal found along the northern edge of the first map. Many players have reportedly fallen in love at first sight. But be warned. Mina only loves money. Spend more at her shop to earn her favor and a place in her wallet heart. She keeps track, you know.

The lovely red haired ribbon mogul is acutely aware of her regional monopoly over new players and adjusts her prices according to player demand.

Ugajin has wares if you have coin.

Listings

Listings are the items a merchant hold in stock. Listings are priced in different ways and are unique to each merchant. For example, just because Mina stocks Ice Cream does not mean other merchants will stock it as well. And if they do, there is no guarantee the they will price them the same way Mina does.

Mina's store boasts a wide selection for new players to choose from.

Fixed Pricing

Fixed listings are those with prices that stay consistent. Regardless of player demand for the items, these listings will be offered at a set price.

Dynamic Pricing

Dynamic listings are those with prices that fluctuate according to demand. Merchants track the number of sales for these listings and adjust the price if that sales volume deviates from their projections. These prices even fluctuate in the middle of a purchase. Players should always double check the total price of their cart to confirm they are indeed willing to pay any premiums resulting from the demand they themselves generate.

Merchants use a Discrete Gradual Dutch Auction (dGDA) to calculate the prices for any dynamic listings. The price of the n-th item purchased from a listing is calculated by:

$$p_n(t) = k \alpha^n e^{-\lambda t}$$

where

$$k:= initial\ price \\\alpha := scale\ factor\ (multiplier\ per\ purchase) \\\lambda := decay\ constant \\t := time\ elapsed\ since\ listing\ launched$$

This formula can extend to the purchase of quantities > 1. However, in the name of gas efficiency, Kamigotchi World uses the aggregate formulation to support purchases of items in bulk:

$$P(q) =\frac{k\alpha^m(\alpha^q-1)}{e^{\lambda T}(\alpha-1)}$$

where

$$k:= initial\ price \\\alpha := scale\ factor\ (multiplier\ per\ purchase) \\\lambda := decay\ constant \\T := time\ elapsed\ since\ start\ of\ listing \\m := total\ historically\ purchased \\q := current\ purchase\ quantity$$

Derivations for the latter can be found in this lovely blog article by Frankie et al of Paradigm.

Dynamic Pricing in Action

For an example of Dynamic Pricing in the world of Kamigotchi, consider a situation in which a particularly strong Predator Kami has just liquidated a large number of other Kamis in a short period of time. As a result demand for Red Gakki Ribbons - which can be used to revive Kamis - increases.

Let's assume that, post-murderous rampage, the first buyer comes to purchase a single Red Gakki Ribbon for 95 MUSU. Let's also assume a scale factor of 1.02 and a decay constant of .01 for dynamic pricing of Ribbons. Exactly one minute after the initial buyer pays 95 MUSU for their Ribbon, a second buyer arrives and buys a Ribbon. What price do they pay? Putting our assumptions together, we get:

95 (initial price) * 1.02 (scale factor) * (e^-(.01 (decay factor) *1 (minutes elapsed)))

This resolves to just shy of 96 MUSU. Not much of a difference! But what if we iterate over ten players each needing to buy one Ribbon and buying one minute apart? The third buyer will pay 97 MUSU. The fourth will pay 98 MUSU. The tenth will pay....a little less than 104 MUSU.

As long as buyers keep buying at this same interval, the rate of growth of the price will increase, though only slightly under an assumed 1.02 scale factor. But what happens when players stop buying for, say, ten minutes? Let's return to the equation:

103.72 (Price at 10th buy) * 1.02 (scale factor) * (e^-(.01 (decay factor) *10 (minutes elapsed)))

This resolves to 95.77 MUSU. We are nearly back at our starting price! In this way the market price of Ribbons is responsive to buyers, both when demand is increasing and when it abates.