Implement LMSR cost function

lib/lmsr/lmsr.go

@@ -0,0 +1,51 @@
+package lmsr
+
+import "math"
+
+// Robin Hanson's Logarithmic Market Scoring Rule (LMSR) market maker
+// https://mason.gmu.edu/~rhanson/mktscore.pdf
+
+// "The market maker keeps track of how many shares have been purchased by
+// traders in total so far for each outcome: that is, the number of shares
+// outstanding for each outcome. Let q1 and q2 be the number (“quantity”)
+// of shares outstanding for each of the two outcomes. The market maker also
+// maintains a cost function C(q1,q2) which records how much money traders
+// have collectively spent so far, and depends only on the number of shares
+// outstanding, q1 and q2. For LMSR, the cost function is [this]:
+//
+// <see code>
+// ...
+//
+// The parameter “b” controls the maximum possible amount of money the market
+// maker can lose (which happens to be b*ln2 in the two-outcome case). The
+// larger “b” is, the more money the market maker can lose. But a larger “b”
+// also means the market has more liquidity or depth, meaning that traders can
+// buy more shares at or near the current price without causing massive price swings."
+//
+// -- David Pennock, http://blog.oddhead.com/2006/10/30/implementing-hansons-market-maker/
+func binaryLMSRcost(b float64, q1 float64, q2 float64) float64 {
+	return b * math.Log(math.Pow(math.E, q1/b)+math.Pow(math.E, q2/b))
+}
+
+func Quote(b float64, q1 int, q2 int, dq1 int) float64 {
+	// q1 must always be the quantity of shares that are bought / sold.
+	// If you want to change q2, you need to swap q1 and q2 as input arguments.
+	fq1 := float64(q1)
+	fq2 := float64(q2)
+	fdq1 := float64(dq1)
+	return binaryLMSRcost(b, fq1+fdq1, fq2) - binaryLMSRcost(b, fq1, fq2)
+}
+
+func Price(b float64, q1 int, q2 int) float64 {
+	//
+	// q1 must always be the quantity of shares that are bought / sold.
+	// If you want to change q2, you need to swap q1 and q2 as input arguments.
+	//
+	// An infinitesimal share would cost this much:
+	//
+	//   p = e^{q1/b} / ( e^{q1/b} + e^{q2/b} )
+	//
+	// However, to find the price of buying one full share
+	// we need to use the cost function.
+	return Quote(b, q1, q2, 1)
+}