Nostra Market Design

1. Market Structures

Two Main Approaches

5 outcomes at 50% each:
Sum = 250%
(Converges via arbitrage)

5 outcomes at 20% each:
Sum = 100%
(No arbitrage opportunity)

CTF Multi-Outcome vs Grouped Binary

Polymarket's Hybrid Approach (NegRisk CTF)

Super Bowl (NegRisk CTF):
┌────────────┬───────┬───────┬──────────┐
│ Team       │ YES   │ NO    │ YES + NO │
├────────────┼───────┼───────┼──────────┤
│ Chiefs     │ 23¢   │ 77¢   │ 100¢ ✓   │
│ Eagles     │ 19¢   │ 81¢   │ 100¢ ✓   │
└────────────┴───────┴───────┴──────────┘

CFP (Grouped Binary):
┌────────────┬───────┬───────┬──────────┐
│ Team       │ YES   │ NO    │ YES + NO │
├────────────┼───────┼───────┼──────────┤
│ Indiana    │ 93.4¢ │ 99¢   │ 192.4¢   │
│ Ohio State │ 72¢   │ 98¢   │ 170¢     │
└────────────┴───────┴───────┴──────────┘

2. Initial Probability Settings

The Problem with 50% Initial Probability

5 outcomes at 50% each:
Sum = 250%

Arbitrageurs:
- Buy all NO tokens
- Guaranteed profit when one outcome loses
- Creator loses to arbitrageurs

Solution: 100/n% Initial Probability

5 outcomes at 20% each:
Sum = 100%

No arbitrage opportunity at launch.
Creator doesn't lose money to arbitrageurs.

Key Insight

Critical Clarification: 250% Sum is NOT Arbitrage

Grouped Binary (5 outcomes × 50%):

Market 1: Team A  YES (50¢) + NO (50¢) = $1 ✓
Market 2: Team B  YES (50¢) + NO (50¢) = $1 ✓
Market 3: Team C  YES (50¢) + NO (50¢) = $1 ✓
Market 4: Team D  YES (50¢) + NO (50¢) = $1 ✓
Market 5: Team E  YES (50¢) + NO (50¢) = $1 ✓

Sum of YES = 250%... but so what?

Why no arbitrage?
• Each market is INDEPENDENT
• You CANNOT merge tokens across different markets
• Each market individually has YES + NO = $1 ✓

The 250% → 100% convergence is just PRICE DISCOVERY,
not arbitrage. Smart traders normalize it.

What IS Real Arbitrage?

Key: Arbitrage means zero risk, guaranteed profit. The 250% sum doesn't qualify.

Does 100/n% Minimize Creator's Loss?

Comparison: 5 Outcomes, True Probabilities: 60%, 15%, 10%, 10%, 5%

Analysis

The Real Problem: Stuck NO Tokens on Favorites

Conclusion: Neither Solves the Problem

True Solutions Remain:

1. CTF Multi-Outcome - No stuck inventory (can merge)
2. Market Maker - Professional takes inventory risk
3. No initial platform liquidity - Let market discover prices first
4. Accept loss as bootstrap cost - Part of business

3. Liquidity Provision

The Bootstrap Problem

Who Provides Liquidity?

Balanced Position Strategy

For a 5-outcome market with $1000 liquidity:

Split equally: $200 per market

For each market (at 20% YES / 80% NO):
- 200 YES @ $0.20 = $40
- 200 NO @ $0.80 = $160
- Total: $200 → 200 YES + 200 NO (balanced)

If A wins:
- A: 200 YES × $1 = $200
- B: 200 NO × $1 = $200
- C: 200 NO × $1 = $200
- D: 200 NO × $1 = $200
- E: 200 NO × $1 = $200

Return: $1000 ✓ (break even when balanced)

Small Liquidity Problem

4. Stuck Inventory Problem

The Core Issue

Initial: Market A at 20% YES / 80% NO
Creator holds: 200 YES + 200 NO

Time passes... A becomes favorite (80% YES):

Traders: "I want to BUY YES on A!"
Creator: Sells YES, happy 😊

Traders: "I don't want NO on A, A will win!"
Creator: Can't sell NO, stuck 😰

Result:
- YES: 200 → 50 (sold 150, good!)
- NO: 200 → 200 (nobody bought, stuck!)

If A wins:
- 50 YES × $1 = $50
- 200 NO × $0 = $0
Creator started with $200, ends with $50
LOSS: $150 ❌

Why Cross-Market Selling Doesn't Help

Selling NO on losing markets (B, C, D, E) does NOT compensate:

Sell 200 NO on B @ 95¢ = $190 received
But: If A wins, buyer gets 200 × $1 = $200

Creator sold $200 value for $190 = LOSS

Cross-market selling adds MORE losses, not compensation.

CTF Solves This

100 A + 100 B + 100 C + 100 D + 100 E → $100 USDC

No counterparty needed!
Always can exit via merge.
No stuck inventory problem.

Worst Case Scenario for LP

5. Market Makers (MM)

How MMs Make Profit

1. Spread (Buy Low, Sell High)

MM posts orders:
BUY YES @ 49¢
SELL YES @ 51¢

When both sides fill:
- Trader A buys YES @ 51¢ → MM receives 51¢
- Trader B sells YES @ 49¢ → MM pays 49¢

MM profit: 51¢ - 49¢ = 2¢ per share
If 10,000 shares traded: Profit = $200

2. Fee Rebates

Taker (takes order): Pays 2% fee
Maker (provides order): Receives 0.5% rebate

MM always provides orders → earns rebate on every trade

3. High-Frequency Adjustments

Price moving up?
→ Cancel BUY orders (avoid buying expensive)
→ Raise SELL prices (sell higher)

Amateur LP: Updates hourly → Gets run over
Pro MM: Updates every second → Captures spread

4. Hedging Across Markets

Correlated markets:
- "Chiefs win Super Bowl" (YES @ 25¢)
- "Mahomes wins MVP" (YES @ 30¢)

MM sells Chiefs YES, buys Mahomes YES (hedge)
Net exposure: ~zero
But: Keeps spread profit!

MM Profit Formula

MM Profit = Spread Income
          + Fee Rebates
          + Arbitrage Gains
          - Inventory Losses
          - Operating Costs

How to Attract MMs to Nostra

Key Insight: Polymarket Model

6. Fee Structure

Fee Distribution Model

Proposed Fee Structure

Trade: $100
Fee: 2% = $2.00

Distribution:
├── LP (liquidity provider): $1.50 (75%)
└── Platform (Nostra):       $0.50 (25%)

LP Yield Calculation

LP provides: $1,000 liquidity
Market volume: $50,000/month
Fee rate: 2%
LP share: 75%

LP earnings:
$50,000 × 2% × 75% = $750/month

LP yield:
$750 / $1,000 = 75% monthly APY 🔥

(High yield compensates for inventory risk)

The Tradeoff

Can Fees Cover Losses?

7. AMM vs Order Book

Fundamental Difference

AMM Example: World Cup

LMSR AMM for 8 teams:

Initial pool ($5000 liquidity):
┌─────────────┬────────┬───────┬──────────────┐
│ Team        │ Tokens │ Price │ Implied Odds │
├─────────────┼────────┼───────┼──────────────┤
│ Brazil      │ 5000   │ 12.5¢ │ 12.5%        │
│ France      │ 5000   │ 12.5¢ │ 12.5%        │
│ Argentina   │ 5000   │ 12.5¢ │ 12.5%        │
│ ...         │ 5000   │ 12.5¢ │ 12.5%        │
└─────────────┴────────┴───────┴──────────────┘

Trader buys $100 Brazil:
→ Gets ~700 Brazil tokens
→ Pool Brazil: 5000 → 4300
→ Brazil price: 12.5% → 25% (automatic!)

Comparison Table

Key Insight

8. Platform Economics

The Unavoidable Bootstrap Cost

Budget Example

Nostra Year 1 Plan:

Launch 50 markets
Initial liquidity: $500 per market = $25,000
Expected loss rate: 20%
Expected loss: $5,000

Think of it as:
"$5,000 marketing spend to build a prediction market"

Compare to:
- Google Ads: $10,000
- Influencer marketing: $20,000
- Traditional marketing: $50,000+

$5,000 liquidity loss = CHEAP customer acquisition

Growth Path

Polymarket's Business Model

9. Recommendations for Nostra

Initial Probability

Market Structure

Liquidity Strategy

- Platform provides $500-1000 per market
- Accept 20% loss as marketing cost
- Focus on few markets with deeper liquidity
- No public LP UI needed (like Polymarket)

- Partner with small MM ($2-5K/month)
- Offload inventory risk to MM
- Predictable cost structure

- Volume attracts more MMs naturally
- Platform becomes fee-based business
- Consider adding public LP feature

Trading System

Fee Structure

Distribution:
├── Platform: 25% ($0.50 per $100 trade)
└── Liquidity Providers: 75% ($1.50 per $100 trade)

Or if platform provides liquidity:
└── Platform keeps 100% of fees

10. Implementation Considerations

Code Changes for 100/n% Pricing

Database Schema (No Change Needed)

// Prisma schema - currentPrice default doesn't matter
// Price is set at market creation time
model Outcome {
  currentPrice Decimal @default(0.5)  // Can keep default
  probability  Decimal @default(50)   // Set at creation
}

Market Creation Logic

// When creating market with N outcomes
const totalOutcomes = outcomes.length;
const initialPrice = 1 / totalOutcomes;  // 100/n%
const initialProbability = 100 / totalOutcomes;

for (const outcome of outcomes) {
  await outcomeRepository.create({
    ...outcome,
    currentPrice: initialPrice,      // 0.20 for 5 outcomes
    probability: initialProbability, // 20% for 5 outcomes
  });
}

Price Update Options

Buy A → A price up
Others unchanged
Sum drifts from 100%
Arbitrage corrects

Buy A → A price up
Others auto-decrease
Sum stays at 100%
Requires more logic

MM Bot Architecture (Optional)

// Auto-rebalancing market maker bot
const MM_CONFIG = {
  maxImbalance: 50,       // Max YES/NO difference
  spreadBps: 400,         // 4% spread
  rebalanceThreshold: 25  // Rebalance at 25 token imbalance
};

async function onTrade(market, side, amount) {
  const position = getPosition(market);
  const imbalance = Math.abs(position.yes - position.no);

  if (imbalance > MM_CONFIG.rebalanceThreshold) {
    await rebalance(market, position);
  }

  // Adjust spreads based on inventory
  await adjustSpreads(market, position);
}

async function checkToxicInventory(market) {
  const yesPrice = market.yesPrice;

  // If YES is winning big, NO is toxic
  if (yesPrice > 0.70) {
    const noTokens = getPosition(market, 'NO');
    if (noTokens > 0) {
      // Sell at ANY price before it goes to zero
      await placeSellOrder(market, 'NO', noTokens, yesPrice * 0.5);
    }
  }
}

UI Considerations

Risk Disclosure (Required)

For any LP feature (if built):

⚠️ RISK WARNING

Providing liquidity involves significant risk.

• You may lose 30-80% of deposited funds
• Fee income may NOT cover losses
• Worst case: lose almost everything

Only deposit what you can afford to lose.

Summary: Key Decisions for Nostra