Societies are made of trust. Trust is usually substantiated in reputation. Each individual gains reputation by cooperating successively in situations where other counterparties grant trust to that individual.
This reputation "score" can be achieved in 2 ways:
- A peer-to-peer score is stored between each counterparty and the individual, based on their previous interactions
- A common score is shared between all counterparties for a given individual, based on the previous interactions of that individual with all counterparties
The latter was historically decentralised and distributed through rumours, but that only scales up to Dumbar's number. Marketplaces are the scalable solution, a highly trusted entity or protocol that stores and shares the reputation of each party.
The former also only scales up to Dumbar's number, however one can make it scalable by developing trust with middlemen, which add value in 2 ways:
- Facilitating the interaction, when both parties have a higher degree of trust with a third entity than with each other (aka market mediator)
- Decoupling the interaction over time and/or space, by acting as the "buyer" in a point in time/space and later on acting as the "seller" (aka market maker)
Algorithmic trust is the alternative to reputation
In game theory, reputation can be represented as an infinite game between parties. In infinite games you play over and over the same game, and even if there's no incentive to cooperate in any single game, the global optimal strategy can be to cooperate and build reputation.
Algorithmic trust consists of refactoring the unit game, to align incentives on a single game, instead of needing to play the infinite game and build reputation. Which allows the scaling of peer-to-peer transactions without the need of marketplaces or middlemen.
Let's consider the example of a buyer and seller. In this interaction (game), the buyer cooperates if it pays the seller and defects if it doesn't. The seller cooperates if it delivers the product and defects if it doesn't.
Let's assume the product in question costs $10 dollars to produce and is being sold for $15, but the buyer would be willing to pay up to $20, so a successful transaction adds value to both parties by $5. The payoff matrix looks like this:
| Buyer \ Seller | Defects | Delivers |
|---|---|---|
| Defects | 0 \ 0 | 20 \ -10 |
| Pays | -15 \ 15 | 5 \ 5 |
In this case, if the buyer does not care about reputation, the optimal strategy is to defect. Since no matter what is the seller's strategy, defection is always a better outcome for the buyer. From the point of view of the seller, the optimal strategy is also to defect. Since it's the better outcome no matter the buyer's strategy. So the Nash equilibrium is defection, missing the opportunity for both to get value out of the interaction by cooperating.
Let's define the general formula for the above matrix:
- p: Agreed price ($15)
- c: Cost of goods sold ($10)
- v: Perceived added value for the buyer ($20)
| Buyer \ Seller | Defects | Delivers |
|---|---|---|
| Defects | 0 \ 0 | v \ -c |
| Pays | -p \ p | v-p \ -c+p |
Algorithmic trust can be achieved by aligning incentives for cooperation. The protocol starts with the seller taking 2 steps:
- Decide if it delivers the product or not
- Communicate to the protocol if the product was delivered or not
The buyer takes one step: communicate to the protocol if the product was delivered or not. So both have the option to lie to the protocol. However, the payoff matrix is defined in a way that does not require the protocol to know who is telling the truth.
Before taking any decisions, both buyer and seller escrow the maximum amount they may need to pay in the payoff matrix. Then a fourth variable is agreed on:
- t: Truth price (explained later, t << p)
Then the payoff matrix is defined as follows (where P is delivery confirmation and 0 is not confirming delivery):
| Buyer \ Seller | 0 | P |
|---|---|---|
| 0 | 0 \ 0 | -p-t \ -t |
| P | -p/2 \ p/2 | -p \ p |
However, this table does not include the value added to the buyer (v) nor the cost of production to the seller (c). So the actual payoff matrix depends on the first decision of the seller, if it decides not to deliver, then the above matrix is the actual payoff. If it delivers, the actual payoff is as follows:
| Buyer \ Seller | 0 | P |
|---|---|---|
| 0 | v \ -c | v-p-t \ -c-t |
| P | v-p/2 \ -c+p/2 | v-p \ -c+p |
Both payoff matrices have two Nash equilibria, 0,0 and P,P. However, both parties are better off by saying the equilibria which is true (0,0 when the product is not delivered, and P,P when the product is delivered). This incentive to say the truth is because each party can cheaply keep the other in check, if it believes the other will lie:
- Seller did not deliver and buyer believes the seller will play P:
- Buyer plays P: buyer payoff is -p and seller payoff is p
- Buyer plays 0: buyer payoff is -p-t and seller payoff is -t
- Price to stick to the truth: buyer payoff delta from playing P to playing 0 is -t, and inflicts a payoff delta in the seller of -p-t
- Seller delivered and believes the buyer will play 0:
- Seller plays 0: seller payoff is -c and buyer payoff is v
- Seller plays P: seller payoff is -c-t and buyer payoff is v-p-t
- Price to stick to the truth: seller payoff delta from playing 0 to playing P is -t, and inflicts a payoff delta in the buyer of -p-t
Notice that the term used for delivery confirmation is P, since this payoff matrix is the discrete version of a continuous matrix where each party can play a number between 0 and P. The continuous case can be seen as post-transaction negotiation, usually the price of a transaction is negotiated beforehand. This pre-transaction negotiation can still happen to define P, but then the buyer can give a value between 0 and P based on it's satisfaction and the seller can negotiate a "partial refund" in case it agrees standards were not met.
Post negotiating every transaction one does is cumbersome and complex. But not cumbersome for businesses or machines, which also make more rational decisions. B2B can use the protocol, but the potential downside for a large transaction comes with a risk, so the ideal market for this protocol is the AI2AI economy, where agents exchange products and services on micro-transactions between them to create a final output for a consumer.
The first large scale application of the AI2AI economy is the pay-per-crawl, where an AI lab can be negotiating the price to pay for specific open-web content with an AI agent that negotiates on behalf of the content creator.