Calculate probabilities using LMSR

db/schema.sql

@@ -42,34 +42,19 @@ CREATE TABLE markets(
     end_date TIMESTAMP WITH TIME ZONE NOT NULL,
     settled_at TIMESTAMP WITH TIME ZONE,
     user_id INTEGER NOT NULL REFERENCES users(id),
-    invoice_id INTEGER NOT NULL UNIQUE REFERENCES invoices(id)
+    invoice_id INTEGER NOT NULL UNIQUE REFERENCES invoices(id),
+    lmsr_b FLOAT NOT NULL
 );
 
-CREATE TABLE shares(
-    id SERIAL PRIMARY KEY,
-    market_id INTEGER NOT NULL REFERENCES markets(id),
-    description TEXT NOT NULL,
-    win BOOLEAN
-);
-
-CREATE TYPE order_side AS ENUM ('BUY', 'SELL');
-
 CREATE TABLE orders(
     id SERIAL PRIMARY KEY,
-    created_at TIMESTAMP WITH TIME ZONE NOT NULL DEFAULT CURRENT_TIMESTAMP,
+    market_id INTEGER NOT NULL REFERENCES markets(id),
-    deleted_at TIMESTAMP WITH TIME ZONE,
-    share_id INTEGER NOT NULL REFERENCES shares(id),
     user_id INTEGER NOT NULL REFERENCES users(id),
-    side ORDER_SIDE NOT NULL,
     quantity BIGINT NOT NULL,
-    price BIGINT NOT NULL,
+    outcome INTEGER NOT NULL,
-    invoice_id INTEGER REFERENCES invoices(id),
+    invoice_id INTEGER REFERENCES invoices(id)
-    order_id INTEGER REFERENCES orders(id)
 );
 
-ALTER TABLE orders ADD CONSTRAINT order_price CHECK(price > 0 AND price < 100);
-ALTER TABLE orders ADD CONSTRAINT order_quantity CHECK(quantity > 0);
-
 CREATE TABLE withdrawals(
     id SERIAL PRIMARY KEY,
     created_at TIMESTAMP WITH TIME ZONE NOT NULL DEFAULT CURRENT_TIMESTAMP,

server/router/handler/market.go

@@ -3,9 +3,11 @@ package handler
 import (
 	"database/sql"
 	"fmt"
+	"math"
 	"net/http"
 	"time"
 
+	"git.ekzyis.com/ekzyis/delphi.market/lib/lmsr"
 	"git.ekzyis.com/ekzyis/delphi.market/server/router/context"
 	"git.ekzyis.com/ekzyis/delphi.market/server/router/pages"
 	"git.ekzyis.com/ekzyis/delphi.market/server/router/pages/components"
@@ -30,7 +32,14 @@ func HandleCreate(sc context.Context) echo.HandlerFunc {
 			endDate        = c.FormValue("end_date")
 			hash           lntypes.Hash
 			paymentRequest string
-			cost           = lnwire.MilliSatoshi(1000e3)
+			cost           = lnwire.MilliSatoshi(10_000e3) // creating a market costs 10k sats
+
+			// The cost is used to fund the market.
+			// Maximum possible amount of money the market maker can lose is b*ln2.
+			// This means if we can only payout as many sats as we paid for the market,
+			// we need to solve for b: b = cost / ln2
+			b = float64(cost) / math.Log(2)
+
 			expiry         = int64(600)
 			expiresAt      = time.Now().Add(time.Second * time.Duration(expiry))
 			invoiceId      int
@@ -62,10 +71,10 @@ func HandleCreate(sc context.Context) echo.HandlerFunc {
 		}
 
 		if err = tx.QueryRowContext(ctx, ""+
-			"INSERT INTO markets (question, description, end_date, user_id, invoice_id) "+
+			"INSERT INTO markets (question, description, end_date, user_id, invoice_id, lmsr_b) "+
-			"VALUES ($1, $2, $3, $4, $5) "+
+			"VALUES ($1, $2, $3, $4, $5, $6) "+
 			"RETURNING id",
-			question, description, endDate, u.Id, invoiceId).Scan(&marketId); err != nil {
+			question, description, endDate, u.Id, invoiceId, b).Scan(&marketId); err != nil {
 			return err
 		}
 
@@ -94,16 +103,77 @@ func HandleMarket(sc context.Context) echo.HandlerFunc {
 			id  = c.Param("id")
 			m   = types.Market{}
 			u   = types.User{}
+			l   = types.LSMR{}
 			err error
 		)
 
 		if err = db.QueryRowContext(ctx, ""+
-			"SELECT m.id, m.question, m.description, m.created_at, m.end_date, "+
+			"SELECT m.id, m.question, m.description, m.created_at, m.end_date, m.lmsr_b, "+
 			"u.id, u.name, u.created_at, u.ln_pubkey, u.nostr_pubkey, u.msats "+
 			"FROM markets m "+
 			"JOIN users u ON m.user_id = u.id "+
 			"JOIN invoices i ON m.invoice_id = i.id "+
 			"WHERE m.id = $1 AND i.confirmed_at IS NOT NULL", id).Scan(
+			&m.Id, &m.Question, &m.Description, &m.CreatedAt, &m.EndDate, &l.B,
+			&u.Id, &u.Name, &u.CreatedAt, &u.LnPubkey, &u.NostrPubkey, &u.Msats); err != nil {
+			if err == sql.ErrNoRows {
+				return echo.NewHTTPError(http.StatusNotFound)
+			}
+			return err
+		}
+		m.User = u
+
+		if err = db.QueryRowContext(ctx, ""+
+			"SELECT "+
+			"COUNT(o.quantity) FILTER(WHERE o.outcome = 0) AS q1, "+
+			"COUNT(o.quantity) FILTER(WHERE o.outcome = 1) AS q2 "+
+			"FROM orders o "+
+			"JOIN markets m ON o.market_id = m.id "+
+			"JOIN invoices i ON o.invoice_id = i.id "+
+			// QUESTION: Should unpaid orders contribute to quantity or not?
+			//
+			// The answer is relevant for concurrent orders:
+			// If they do, one can artificially increase the price for others
+			// by creating a lot of pending orders.
+			// If they don't, one can buy infinite amount of shares at the same price
+			// by creating a lot of small but concurrent orders.
+			// I think this means that pending order must be scoped to a user
+			// but this isn't sybil resistant.
+			//
+			// For now, we will ignore pending orders.
+			"WHERE o.market_id = $1 AND i.confirmed_at IS NOT NULL", id).Scan(
+			&l.Q1, &l.Q2); err != nil {
+			if err == sql.ErrNoRows {
+				return echo.NewHTTPError(http.StatusNotFound)
+			}
+			return err
+		}
+
+		return pages.Market(m, types.MarketP{
+			Pyes: lmsr.Price(l.B, l.Q2, l.Q1),
+			Pno:  lmsr.Price(l.B, l.Q1, l.Q2), // prices
+
+		}).Render(context.RenderContext(sc, c), c.Response().Writer)
+	}
+}
+
+func GetPrice(sc context.Context) echo.HandlerFunc {
+	return func(c echo.Context) error {
+
+		var (
+			db  = sc.Db
+			ctx = c.Request().Context()
+			id  = c.Param("id")
+			m   = types.Market{}
+			u   = types.User{}
+			err error
+		)
+
+		if err = db.QueryRowContext(ctx, ""+
+			"SELECT m.id, m.question, m.description, m.created_at, m.end_date, "+
+			"u.id, u.name, u.created_at, u.ln_pubkey, u.nostr_pubkey, msats "+
+			"FROM markets m JOIN users u ON m.user_id = u.id "+
+			"WHERE m.id = $1", id).Scan(
 			&m.Id, &m.Question, &m.Description, &m.CreatedAt, &m.EndDate,
 			&u.Id, &u.Name, &u.CreatedAt, &u.LnPubkey, &u.NostrPubkey, &u.Msats); err != nil {
 			if err == sql.ErrNoRows {
@@ -114,6 +184,6 @@ func HandleMarket(sc context.Context) echo.HandlerFunc {
 
 		m.User = u
 
-		return pages.Market(m).Render(context.RenderContext(sc, c), c.Response().Writer)
+		return nil
 	}
 }

server/router/pages/market.templ

@@ -4,11 +4,13 @@ import (
     "git.ekzyis.com/ekzyis/delphi.market/server/router/pages/components"
 	"git.ekzyis.com/ekzyis/delphi.market/types"
 	"github.com/dustin/go-humanize"
+	"strconv"
+	"fmt"
 )
 
 // TODO: Add countdown? Use or at least show somewhere precise timestamps?
 
-templ Market(m types.Market) {
+templ Market(m types.Market, p types.MarketP) {
     <html>
 		@components.Head()
 		<body class="container">
@@ -33,4 +35,13 @@ templ Market(m types.Market) {
 			@components.Footer()
 		</body>
 	</html>
+}
+
+func formatPrice(p float64) string {
+	return fmt.Sprintf("%v msats", strconv.FormatInt(pToPrice(p), 10))
+}
+
+func pToPrice(p float64) int64 {
+	// 0.513 means 513 msats
+	return int64(p * 1e3)
 }

types/types.go

@@ -37,3 +37,15 @@ type Market struct {
 	CreatedAt   time.Time
 	EndDate     time.Time
 }
+
+type LSMR struct {
+	B  float64
+	Q1 int
+	Q2 int
+}
+
+type MarketP struct {
+	// probability of outcomes
+	Pyes float64
+	Pno  float64
+}