Incentivization

Related work. Given cryptoeconomic systems work solely on the basis of incentives with nopresence of a centralized court to punish delectors, it is important that transaction and blockpropagation in blockchains be incentive compatible. A significant body of work with respect tothe incentive compatibility problem of blockchains has been on withholding attacks and selfishmining. Babaioff et al. l propose an incentive mechanism for a very specific topology -a forest of d-ary trees. Abraham et al.argue that when a node is part of multiple propagationpaths, nodes at the same distance from the source wouldn't be able to charge more than an amountTmin designated by the system. This analysis has two issues - (i) a system designated minimumpayment can't work in practice due to the possibility of a side-channel payment mechanism undercutting the minimum (ii) it does not take into account the fact that a node that forwards packetaster has a higher value than a slower one. Ersoy et al. provide an incentivization scheme thatis forwarding-dominant and Sybil-resistant as defined below.

Requirements. We thus arrive at the requirements we expect from a forwarding scheme

1. Forwarding-dominant: It should be a dominant strategy for nodes to forward transactionsand blocks instead of withholding them.

2. Sybil-resistant: Nodes should not have an incentive to not create sybil identities in thepropagation path in order to capture a larger share of the fee.

3. Performance rewarding: Nodes should have a continuous incentive to improve their performance and forward packets to their children faster.

Fee distribution function. showthe existence of a fee sharing strategy that achieves desirable properties in certain settings, werelrain from imposing a lee sharing structure into the system and rather leave it to the marketparticipants to decide. We do so primarily because of the following reasons:

1. Side-channel atacks: Nodes can bypass any system imposed restrictions by creating off-bandpayment channels where they reallocate fees.

2. Service diferentiation: Two nodes at the same level of the propagation path can have diflerentcosts due to usage of diflerent service providers providing diflerent levels of performanceguarantees.

3. Orphaning parents: A node that is part of multiple propagation paths might choose a latecoming though cheaper fee history transaction as compared to a faster more expensive oneThe premium that a child node is willing to pay for speed depends on what his children arewilling to pay and his risk associated with not being in the path by not choosing the fastertransaction.

The values of these risks and rewards will be determined by market participants over time. Any sortof system imposed restriction will lead to nodes acting suboptimally or finding ways to circumventthe restriction.

Fee distribution mechanism, In order for nodes that are part of the propagation path to getpaid their due share, there should be a mechanism for them to claim their share. Such a feedistribution mechanism should satisfy the following properties:

1. Orphaning-resistant: Nodes further down the propagation path have an incentive to removesome of their parents from the path history and thus claim a larger share for those thatremain (including themselves).

2. Order-preserving: A fee distribution mechanism in which not all nodes in the propagation path are rewarded unilormly, say in a decreasing order from the source, nodes lfave anincentive to rearrange the nodes in the path so to put themselves (or their allies) at higherpaying positions.

In order to satisly the above two properties, a transaction and a block is modified to contain awitness which is appended to the original content body.

The witness can be implemented in the following two ways:

1. Signature chaining: In this approach, every node in the propagation path appends the publickey of the node it is forwarding the content to and signs the body with its private key. Letn; be the ith node in the propagation path, n.pub and n.priv be node n's public and privatekey respectively and f; be some fee metric claimed by node n;, then the witness forwardedby ni to ni+i is as follows:

However, this scheme requires a node to have knowledge of not only its children's IP addressesbut public keys too. The schemel described next resolves this issue.

1. Key list: A node appends a newly created key pair < Kpub, Kpri > to the witness andsigns the witness not including Kpriy. The receiving node removes Kpriv from the witnessand uses it to sign the witness after appending its own public key and a new key pair. Thetransmitting node uses a unique key pair for every node it forwards packets too.

Listed below are some notations used in the discussion that follows:

1. Si,s:The set of subscribers of node ni including downstream PerfBloc nodes when the originasource is s.

2. S'i,s:The set of subscribers of node ni excluding downstream PerfBloc nodes when the originasource is s. Since S, . is independent of s we simply denote it as S'i.

3. Ri,s:The revenue earned by node ni including its share from the revenue of downstream PerfBloc nodes when the original source is s.

4. R'i,s:The revenue earned by node ni excluding its share from the revenue of downstream PerfBloc nodes when the original source is s.