[Token Economics] Series Ⅰ: Mechanism Design, Incentive Compatibility and VCG Mechanism

Token Economy is broadly divided into three main research directions:

1. Topic on Private Money represented by bitcoin in the ear of blockchain 1.0;
2. Direction of Game Theory—Mechanism Design—New Institutional Economics—Incentive Compatibility, which is derived from game theory and is used to study the game theory problems of all parties in the system of Token economy.
3. Direction of Coase Theory—Contract Theory—Property Rights Theory—Transaction Cost Theory, which is based on Coase Theory and is used to study the transformation of smart contract to commercial society. (Yuan Yuming and Yan Si, 2018)

This article only makes a brief discussion on the second direction, hoping to be able to attract jade by throwing out a brick and initiating discussion.
In the design of Token system win-win situation can be achieved through three ways:

1. “win-win” can be achieved through improving production relations and promoting production efficiency and production growth, which enlarges the “cake” of whole economy.
2. “win-win” can be achieved through reducing the trust cost of execution layer and transaction cost, which reduces economic losses and save total social cost.
3. “win-win” can be achieved through mechanism design theory, which can make all participants reach incentive compatibility, share common goals and work hard for them.
   The first two points have already been systematically discussed (Yuan Yuming, 2018). Moreover, incentive compatibility is also an indispensable part when considering multi-party repeated games in the process of designing Token system. In short, incentive compatibility is just one constraint in the mechanism design. That means that the principal and the agent’s objective function are compatible, and the individual rationality is compatible with the collective rationality. Subjectively “selfish and self-interested” while it objectively benefits others and the collectives. In another word, while everyone is thinking for themselves, the overall goal of optimal and sub-optimal is achieved, namely motivation for yourself and incidentally for others. This theory is very suitable for the design of Token system and community governance. Another constraint is the individual rationality derived from the most basic hypothesis of rational man, namely participation constraint. In total, your mechanism will be more beneficial with other’s participation than without them.

Mechanism Design

Mechanism design is a sub-area of microeconomics and game theory. It considers how to solve the problem of multiple self-interested participants who prefer to have private information. Mechanism design was first proposed by Leonid Hurwicz, the Russian-American economist who was the winner of the 2007 Nobel Prize in Economics, and he is therefore known as the "father of mechanism design theory." The goal of mechanism if defined by a social choice function. Given the type of participation, this function chooses the best result. The mechanism design problem is to try to implement a game rule to achieve the solution of the social choice function, regardless of the selfish tendency of the participants. In 1973, Hervitch published a paper entitled "The Design of Mechanisms for Resource Allocation" in the top economic journal of the American Economic Review, which explains Two core problems in the theoretical framework of mechanism design — the incentive compatibility principle and the revelation principle, laying the framework of mechanism design theory. Incentive compatibility is a situation in mechanism design theory, entering the model in the form of constraints.
Internet technology has greatly reduced the information transmission cost in transaction costs while blockchain technology has made the execution cost in smart contract almost zero. But neither of them can solve the problem of information asymmetry thoroughly. Information asymmetry is one of the important reasons that affect the market's function and cause market failure. At present, there is no technology that can completely eliminate information asymmetry. Therefore, at this stage, mechanism design theory can be used to design an incentive mechanism to encourage economic people to display real information. This involves the revelation principle in the theory of mechanism design.
Therefore, in the Token system designing, all the designs that are conducive to eliminating information asymmetry are good.

The Revelation Principle

The revelation principle was proposed by Roger B. Myerson in the paper "Optimal Auction Design" published in the journal of Mathematics of operations research in 1981. “The revelation principle: Given any feasible auction mechanism, there exists an equivalent feasible direct revelation mechanism which gives to the seller and all bidders the same expected utilities as in the given mechanism.”
The revelation principle refers to make participants under the constraint of incentive compatibility revel personal information spontaneously via mechanism design, as so to eliminate information asymmetry. How to make the participants do that spontaneously? The answer will be related to another mechanism which is Vickrey-Clarke-Groves Mechanism, namely VCG Mechanism.

VCG Mechanism

VCG Mechanism refers to a series of mechanism formed from the three articles of Vickrey (1961), Clarke (1971) and Groves (1973) respectively. The process of forming VCG mechanism is divided into three steps:
Vickrey auction
W.Vickrey presented the “Vickery auction” in an article entitled “Counterspeculation, Auctions and Competitive Sealed Tenders” published in the Journey of Finance in 1961. One’s real demand is hard to “revel”. For an instance, Tom has special favorites for singer Eminem while Jerry don’t. Assuming that one ticket of his concert values 500 RMB, then it is very likely that Tom and Jerry’s psychological price is 800 RMB and 600 RMB respectively. If all tickets are sold at a uniform price as 500 RMB, the real demand cannot revel in that the consumer surplus of Tom and Jerry are (800-500=)300 RMB and (600-500=)100 RMB. A more common method in economics is auction, through which everyone’s real price in their mind can be revealed. And different effects can be achieved through designing different auction rules.
Auctions can be divided into open and sealed auctions in general classification. Here are a few common auction methods:

1. English Auction
2. Dutch Auction
3. The first-price sealed auction
4. The Second Price Sealed Auction
   English auction is a common type of open ascending price auction, Dutch auction is known as an open descending price auction and the third auction is a common type of sealed auction. I would like to introduce the fourth kind, The Second Price Sealed Acution, namely Vickrey auction which belongs to the K-price sealed-bid auction and is a practical application of the VCG mechanism in the auction. That means, in sealed-bid auction, the highest bidder will actually pay the second highest price. For example, A, B and C three people participate in one auction, in which A bids 10 RMB, B bids 8 RMB and C bids 6 RMB. Because it is a sealed auction in which one has no means to know other’s biding price, the successful bidder is A whose actual payment is the second highest price 8 RMB. Under this mechanism it is easier for bidders to reveal their real price comparing with the mechanism of paying the highest price. This is conducted under the condition of repeated games. Supposing that A bid is 10 RMB and B will mark 8 RMB, A will win the bid. And if charging according his bid, A will be charged 10 RMB. When this auction (ie. game) repeats, A will adjust his bid until 8.01 RMB (assuming down to the second decimal point), which may not be possible at this time. Then another participant C join in, and so on, C will continue to adjust bid to 8.02 RMB. At that time, the market income is 8.02 RMB. In order to avoid such probing behavior, another method can be taken: when A bids 10 RMB while B bids 8 RMB, we charge the successful bidder A 8 RMB, the second highest price instead of his own bid of 10 RMB. Then A has no incentive to lower his bid. When D joins, D needs to bid more than 10 RMB to win the bid, and the market income will become 10 RMB (regardless of the D bid, we will charge according the second highest bid, A’s bid). Such an auction is called Vickrey auction (namely the second highest price auction). In real world, the logic of VCG mechanism is often used in auctions of search engineers and social advertising fields.

Clarke Tax

Clarke Tax was proposed by Clarke, E.H. in the article entitled “Multipart Pricing of Public Goods” published in Public Choice in 1971. Clark tax refers to a tax system that levies on key person who influence social decision-making. The amount of tax collected is equal to the net loss caused by the participation of the key person in the decision-making process. Although it is mainly used to deal with the sustainability of public goods and free-riding, its mechanism can also enable participants to reveal their true Types spontaneously.
Take the above example again, but the distinction is that Clarke tax is used to solve problems concerning public goods. In other words, it shall become the situation that Tom and Jerry contribute money together to invite Eminem to open a concert, so it is obvious that the Clarke tax can also be used for crowdfunding. Still, for the concert ticket Tom is willing to pay 800 RMB and Jerry 600 RMB. If each contributes 500 RMB, for Tom the utility is 800-500=300 RMB while for Jerry 600-500=100 RMB. But if Tom quotes first and is willing to give 800 RMB, Jerry only needs to quotes 200 RMB or even gives no money. That is a question of hitchhiking. It is time for Clarke tax to work. The public or government (or community in blockchain field) informs Jerry that her low price causes failure of the concert and she shall be levied on tax which is equal to Tom’s utility 300 RMB. Obviously, Jerry is unwilling to pay. (when the real utility of Jerry is -300 RMB, she is willing to pay this tax. But considering that Eminem’s concert is still good, so this situation basically does not exist.)
Grove mechanism was proposed by Theodore Grives in an article entitled “Incentive in Teams” published in Econometrica. Groves mechanism solved such a problem: that the target is to choose a result from a disperse set of results to maximize the total value of all participants. Grove mechanism is efficient and strategy-proof.
Review of the general logic
Through the revelation principle information asymmetry could be fetched up so as to meet the constraints of participation and incentive compatibility at the same time. Thereby moral hazard and adverse selection could be reduced and the situation of bad money expelling good money could be avoided. The revelation principle is the method of meeting incentive compatibility constraint and reducing information asymmetry. VCG mechanism is the way to achieve the revelation principle.
As we all know, auction is often a good way to reveal real demand without leaving any consumer surplus. In Token system, it is often necessary to reveal the real demands of all participants, such as the real demand for transaction speed, how to avoid dust attack, the setting of Gas charges, the real demand for EOS RAM and the real demand for bandwidth and storage space in IPFS, etc. The designers of Token system often think of the way of auction, but may tend to use a simple Dutch auction. In this case, if trying to integrate into VCG mechanism with much consideration, we may receive unexpected results.

Terms Explanation

Deceit: basically, it can be simplified to “hide the real information” or “substitute false information for real information”. So, the so-called “credit” can be simplified to “provide real information completely”. In US courts, witnesses are required to read a vow before giving testimony: “……the truth, the whole truth and nothing but the truth”. In other words, as long as all the facts are provided and there is no information other than the facts, it is fundamentally difficult to deceive.
Budget balance: refers to the fact that in one mechanism, the budget paid by participants meets all the requirements and there is no surplus in the whole system.
Future research direction
How to explore solutions to prevent collusion for a theoretical level can be one research direction in the future. VCG mechanism is very fragile in the presence of the “collusion” problems, and the problem of collusion is widespread in reality.
An interesting finding is that what if we research with public chain as public goods, or with the charges of ETH’s Gas (or EOS’s RAM) as tax, such as Tobin tax and Clarke tax. Under the constraint of budget balance, new ideas could be provided for pricing Gas and RAM. Public chain, even the blocks scooped out by miners, can be regarded as a kind of public goods. In fact, it is a kind of Common Goods. Transfer of Gas can be viewed as a sort of Clarke tax. Through Clarke tax or the transformation of Gas users’ real demands will be revealed, which is a manifestation through revelation principle under the incentive compatibility constraint.

Reference:

1. 田国强. 经济机制理论:信息效率与激励机制设计[C]// 经济学. 2003:271-308.
2. 袁煜明. 我们现在处于区块链经济的1776年. http://www.huobiresearch.com/
3. Clarke, E., 1971, “Multipart pricing of public goods”, Public Choice, 11:17-33.
4. Groves, T., 1973, “Incentives in teams”, Econometrica, 41, 617-663.
5. Myerson R B. Optimal auction design[J]. Mathematics of operations research, 1981, 6(1): 58-73.
6. Vickrey, W., 1961, “Counterspeculation, auctions and competitive sealed tenders”, Journal of Finance, 16, 8-37.