# Optimal pricing for Crypto-Currency Exchanges

I have a general understanding of game theory, and want to try to apply it to crypto-currency exchanges, which are completely decentralised systems. I come from a finance background so I will define some key terms.

BID Price: Price at which the exchange is willing to buy an asset from you.

ASK Price: Price at which the exchange is willing to sell an asset from you.

ASK>BID, so as a trader, you will always pay the higher ASK price when buying and will get the lower BID price when selling.

Consider the following autonomous Bitcoin exchanges with the following prices on a certain date:

As you can see each exchange quotes its own price and spread.

In a frictionless world, a trader can buy Bitcoins at the cheapest ASK price (in this case exchange B at 1477) and sell the coins on the exchange with the highest BID price (exchange A at a BID price of 1603). This arbitrage opportunity is also found on the other exchanges as long as the ASK price paid by the trader is less than the BID price on the other exchange.

Now let's say I want to create my own exchange. If I want to eliminate all arbitrage opportunities, I would quote a BID price equal to the lowest BID (exchange B: 1475) and an ASK price equal to the highest ASK (exchange A: 1604). While this eliminates arbitrage on my exchange, it also makes me very uncompetitive given that my spread will equal 129. As such, no one will trade on my exchange.

Given that I want to keep my spread competitive, with a goal of minimising arbitrage opportunities. What is the best course of action to take for quoting Bitcoin prices?

This is a real case, and the figures in the table are actual Bitcoin\USD prices taken on a particular date for these anonymised exchanges.

• Perhaps I am missing something but what does this have to do with game theory? Commented May 8, 2017 at 19:42
• Well the idea is that I want to set the prices on my exchange such that they are considered competitive compared to others, but at the same time discourage traders from arbitraging my price. Commented May 8, 2017 at 19:54
• But the other prices are set. You are the only actor with a decision. This does not seem to need require game theory. Commented May 8, 2017 at 19:59