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Bitcoin: exploring behavior on the block chain

Bitcoin gained popular notoriety because of its rapid price appreciation and volatility, but its block chain also represents a self-recording and detailed account of users’ behavior. Theoretically, the block chain preserves aspects of that behavior, and how it changes as as people learn about this tech and develop individual sophistication and group-level norms.

The first step in this analysis is extraction of behavioral data from the block chain - creating a transaction digraph, then an entity digraph. Then I can explore entity activity patterns related to price peaks in Bitcoin’s history.

Data extraction

Users interact with each other through Bitcoin using supposedly anonymous bitcoin addresses (Note that I’m considering anonymity in the block chain, isolated from other data ;)). Each address is associated with the public part of a public-private key pair, and a user can create new addresses at will. Users transfer funds from one address to another using an atomic data structure: the transaction.

Visualization of a bitcoin transaction.

Transactions are collections of inputs and outputs, where inputs reference the outputs of transactions already in the block chain. New transactions redeem collections of existing, unredeemed outputs in the block chain, then reassign portions of their total value to addresses in newly created outputs. New BTC is injected into the block chain as a reward to miners for adding transactions. Rewards come in the form of special generating, or “coinbase”, transactions which assign reward BTC to addresses specified by the miner. This BTC is then available to be reassigned to other addresses through successive transactions. The net worth of a particular address \(a_i\) at a given time is the sum of all reassignments bestowing BTC to \(a_i\), less the reassignments from \(a_i\) to other addresses, where all reassignments occur before the specified time.

The transaction graph

The block chain is essentially a digraph of transaction nodes, where every arc is an output-input pair with address and value attributes. Transactions are validated and added in blocks, so each transaction in a block has the same timestamp. A toy example of transactions in the block chain is presented below.

Toy transaction graph example. Each transaction \(T_{ij}\) occurs at time \(t_i\). Since \(T_{00}\) and \(T_{01}\) were both added to the block chain in the same block, they occur at the same time \(t_0\). Generator transaction \(T_{00}\) assigns a reward of 50 BTC to address \(a_1\). \(T_{20}\) splits the value assigned to \(a_2\) and \(a_1\) from previous transactions into equal parts and reassigns one part each to \(a_2\) and \(a_4\), though the output assigning to \(a_2\) has not been referenced by another transaction. \(T_{01}\) splits the 2 BTC assigned to \(a_0\) from a previous transaction, reassigning 1 BTC to \(a_2\), whose output has not been redeemed, and 1 BTC to \(a_1\). \(T_{10}\) reassigns 1 BTC from \(a_1\) to \(a_3\).

Because the input addresses of a transaction must be controlled by a single source, I can scan the transaction graph and aggregate addresses into entities. Entities are one step closer to representing actual users, but could be individuals or groups or bots: whatever exerts control over the aggregated addresses. Each transaction then represents one or more fund reassignments from entity to entity, creating an entity network.

To make the entity network, I must do the following:

  1. Create the transaction graph from the stored block chain.
  2. Extract the address and timing information in the transaction graph.
  3. Deanonymize by collapsing the input address sets of transactions with commonly held addresses into entities.
  4. Extract timestamp and value attributes for arcs between entities from transactions in the transaction graph.

Below, we see the creation of the entity graph from our toy transaction graph.

Because \(a_2\) and \(a_3\) are both collected into transaction input sets with \(a_1\), we can infer that the same entity controls all three addresses. Given only this toy transaction network, we can then make the entity network at right, where the collected entity \(\{a_1, a_2, a_3\}\) sends and receives Bitcoin at different times to itself and to other entities.

Fun with BTC price spikes and user behavior

Up until early 2014, there were three Bitcoin price spikes. These are marked below, in regions lasting 20 days before to 20 days after each price peak.

Bitcoin price from mid-2010 to early 2014, in US dollars. The three price spikes are highlighted below, from 20 days before to 20 days after each peak.

These price peaks are natural points to examine user behavior. Below, I visualize change of BTC wealth vs. initial holdings per entity during the first price peak. Importantly, the x-axis shows the rank of entities’ BTC wealth 20 days before the peak, while the y-axis shows entities’ net wealth change over the period. The vertical lines indicate intervals of actual BTC worth, as opposed to the entity worth rank shown on the x-axis.

First price peak: entity initial wealth rank vs. wealth change during peak time region.

This scatter plot shows some interesting behavior! High rollers essentially emptied their accounts, or at least transferred most of their wealth to other entities (aggregated to early 2014). At the other extreme, BTC-poor entities increased their holdings, perhaps reacting to the price appreciation before the peak.

There are many more avenues to explore with this data (hint: deanonimization) but this was a fun first look!


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