This whitepaper describes a novel, multi-dimensional, infinitely inclusive market model. The described model yields infinite types of new market dynamics and traditional markets as special cases, based on very few parameters. As the market allows any supply of arbitrarily small or large value to be traded in any currency, incl. subjective value currencies, any resulting liquid market must then find the fairest value of the supply.
Assume we have a seller with a finite supply
A market
where
More generally, we add a parameter to the market
This then allows for an ordering of the bids
In this paper, we will define a partial ordering and a total ordering that is fairest, most inclusive and accomodates all types of markets, as well as innovating new types of markets with a generic framework.
The seller sets the following parameters
The importance
Each bid
The amount
Let
Then
$$\mathcal{C} = \mathcal{C}\text{obj} \text{ } \dot{\cup} \text{ } \mathcal{C}\text{sub}$$
that is, any currency either has objective value xor subjective value.
We choose some
$$\text{ccy}\text{base} \in \mathcal{C}\text{obj}$$
as the base currency and we define
as the fair exchange rate between
and
Before we categorize the bids, let's simplify them. First, we call a bid
if it is of an objective value currency.
The amount
This means, without loss of generality, we can assume all objective bids to be denominated in the base currency.
Assuming that the min value
We can denote a bid
The seller defines the importance per bid category
$$\mathcal{I} = (\mathcal{I}\text{\bf{C\bf{HR}}}, \mathcal{I}\text{\bf{HR}}, \mathcal{I}\text{\bf{LURK}}, \mathcal{I}\text{\bf{SUBJ}})$$
where each importace is a natural number
$$\mathcal{I}\square\in\mathbb{N}{\ge 0}, \square\in\{\text{\bf{C\bf{HR}}}, \text{\bf{HR}}, \text{\bf{LURK}}, \text{\bf{SUBJ}}\}$$
the market is activated
and the lurkers never get serviced
Amongst every subsequence of the ordered bids
E.g. if
$$\mathcal{I} = (\mathcal{I}\text{\bf{C\bf{HR}}} = 2, \mathcal{I}\text{\bf{HR}} = 3, \mathcal{I}\text{\bf{LURK}} = 0, \mathcal{I}\text{\bf{SUBJ}} = 1)$$
then, on average, any subsequence of 6 bids serviced should contain 2 chrony, 3 highroller bids and 1 subjective bid.
We want to create a market function such that:
-
importance is respected
-
order of objective bids is objectively deterministic
-
internal category order is maintained
-
worst case rank for chrony bids is finite
-
the seller can use it's own subjective value function to value subjective bids
Chrony bids are time ordered, highroller bids are value ordered, subjective bids are ordered by each seller subjectively and lurker bids live in the projective infinity, never serviced.
$$\mathcal{I} = (\mathcal{I}\text{\bf{C\bf{HR}}} = 1, \mathcal{I}\text{\bf{HR}} = 0, \mathcal{I}\text{\bf{LURK}} = 0, \mathcal{I}\text{\bf{SUBJ}} = 0)$$
$$\mathcal{I} = (\mathcal{I}\text{\bf{C\bf{HR}}} = 0, \mathcal{I}\text{\bf{HR}} = 1, \mathcal{I}\text{\bf{LURK}} = 0, \mathcal{I}\text{\bf{SUBJ}} = 0)$$
$$\mathcal{I} = (\mathcal{I}\text{\bf{C\bf{HR}}} = 0, \mathcal{I}\text{\bf{HR}} = 0, \mathcal{I}\text{\bf{LURK}} = 0, \mathcal{I}\text{\bf{SUBJ}} = 1)$$
We can almost surely assume
that the bids can be sorted chronologically.
Given this chronological ordering, let's group the bids by creating subsequences of constant parameters:
$$\underbrace{B_1, \ldots, B_{i_1}}{\mathcal{P}1}, \underbrace{B{i_1+1}, \ldots, B{i_2}}{\mathcal{P}2}, \ldots, \underbrace{B{i{G_N}+1}, \ldots, B_N}{\mathcal{P}{G_N}}$$
that is, changing the parameters
We are left with the task of ordering the bids given constant parameters
The importance
We also know that
which means that
Given the previous max
First, we choose the next bid category as the category that brings our realized importance closest (
To that end, calculate the realized importance
$$\hat{\mathcal{I}}=\begin{pmatrix} \hat{\nu}\text{\bf{C\bf{HR}}} \ \hat{\nu}\text{\bf{HR}} \end{pmatrix}$$
$$\hat{\nu}\square = \frac{\#\{\text{BC}(B_i)==\square\}{i=n\ldots m+1}}{m-n+1}$$
and choose
If the next category should be
If the next category should be
If the next category should be
-
$B_\text{next}$ is the chronogically next$\text{\bf{SUBJ}}$ bid available. However, the seller can choose to decline the bid, using it's subjective value function. -
Let the seller choose one xor none from all the existing
$\text{\bf{SUBJ}}$ bids.
Either case results in a total, deterministic and objective ordering of all the objective bids and a total subjective ordering of all the subjective bids, both interwoven according to the chosen importance
$\mathcal{I}$ .
A discussion of the choices is found here.
Note the next category can never be
Any bid can always choose to cancel, thereby improving the rank of all bids behind it. Hence we only need to talk about the worst case.
Worst case rank is deterministic if we allow it to be
The above algorithm keeps the worst case rank for CHR bids deterministic and finite.
This is mainly because each
We can assume that any possible supply
Using a chain of CFS, defined below, we can transact arbitrarily small (or large) values.
Hence, every kind and quantity of any supply is supported. This market model is infinitely inclusive.
Smart contracts are autonomous, decentralized apps. The described market model is implemented as a smart contract for the following reasons: infinite inclusivity, zero credit risk, perfect transparency, ability to use any kind of currency.
A currency is called fungible if it is available in varying units.
We can define the fungability
E.g.
A CFS is a simple, permissionless smart contract that exchanges the minimal unit of a currency
A CFS never rounds and only makes exact exchanges.
Using a CFS, we have increased the fungability of any currency
Assume the value of the supply
By chaining CFS, we can keep increasing the fungability until
A chain of CFS can achieve arbitrary fungability.
Consider:
- We accomodate any supply of arbitrarily small or large value.
- We allow any currency, whether those of objective value xor subjective value.
- We define currency as an arbitrarily fungible bundle of arbitrary energy and information.
- We accomodate the entire region of objective value currencies possible (below, at and above the min value).
- We create the desired (according to importance) sequence of servicing the demand.
- We allow for infinite types of dynamics incl. traditional markets as special cases, set via simple parameters.
All these superlatives make this market model the most open possible.
Assuming liquidity, this market model thus provides the fairest valuation of any supply.
By changing the parameters, minimum
An economy is a set of trades. The event of a bid getting serviced is a trade. If this market model provides the fairest valuation and with it the fairest trade, then the resulting economy is fairest economy possible.
Micro-economics teaches us that (specilization and) fair trading improves the value of all parties.
If this paper is correct in that the described market model results in the fairest valuation, then it should be used for all markets. Especially the most valuable market: time
- Everyone has time
- Everyone knows that time is most valuable.
When supply=time, all currencies are per