Game Theory · Lesson 10 · ← Lesson 09

Splitting the pie: BATNA is power

Your leverage in any deal is your best alternative to it.

~14 min · one sitting Skill: bargaining, BATNA, ZOPA Builds on: commitment, sequential reasoning
First — 20-second recall from Lesson 09

For a signal to separate the types, it must be…

01 · EVERY DEAL IS A SPLITThe question isn't what you want — it's what happens if you don't agree

Most people walk into a negotiation asking "how much can I get?" That's the wrong first question. Bargaining isn't a competition for a fixed pile — it's the problem of dividing a surplus that only materialises if you both say yes.

The skull-base course needs a sponsor. There is no deal without a willing buyer — and if there's no deal, each side gets its outside option, not this surplus. So the correct first move is: what happens if we DON'T agree?

Before you name a number, name your outside option. That's your floor, your fallback, your true source of power.

That outside option — your best alternative to the negotiated agreement — is what economists and negotiators call a BATNA. It sets the minimum you'd accept. It's the only number that really matters before talks start.

The BATNA framework is developed in Fisher & Ury, Getting to Yes (1981). The formal game-theoretic grounding is in Nash bargaining theory; see SEP — Game Theory §4.

02 · BATNA · RESERVATION VALUE · ZOPAThe sponsorship worked out

Let's build the full picture with your real situation. You're seeking a corporate sponsor for the skull-base course at HSJ Porto Alegre.

Worked example — the R$10k / R$25k figures below are illustrative, chosen to teach the mechanics cleanly. Your real ask (D1 in DECISIONS.md) has its own numbers; you'll plug those into your own rep at the end of this lesson, not these.

You (course organiser)
R$10,000
Your BATNA: another sponsor has offered exactly this. So R$10k is your reservation value — the minimum you'd accept from this sponsor before you'd rather take the other offer.
The sponsor
R$25,000
Their BATNA: sponsoring a rival conference buys them equivalent exposure at this price. So R$25k is their reservation value — the maximum they'd pay before they'd rather go elsewhere.

A deal is possible only when your floor is below their ceiling. Here, R$10k < R$25k. The gap between them is the ZOPA.

The ZOPA — Zone Of Possible Agreement
R$0
R$10k
Your floor
R$25k
Their ceiling
R$40k ← ZOPA: R$15k of surplus to divide →

Every price from R$10k to R$25k beats both sides' outside options. The R$15k of surplus is what the negotiation is really fighting over. Where you land inside that band determines who captures how much of the pie.

Model read: ZOPA = R$10k–R$25k — any price in that band beats both outside options. Surplus = R$25k − R$10k = R$15k, which is exactly what the negotiation divides.
The core insight

Negotiation doesn't create value by itself — it divides existing surplus. Finding the ZOPA tells you whether a deal is possible. Positioning within the ZOPA is the strategic game.

Same math, your own chair Knowing your genuine walk-away (BATNA) before a coverage or referral negotiation — your slice of the surplus moves with your outside option, not with how badly you need the deal.

03 · QUICK CHECKIs there a deal?

Your floor is R$10k; the sponsor's ceiling is R$25k. Is there a deal, and what's the surplus?

The ZOPA is R$10k–R$25k. Any price in that range is mutually beneficial — better for both than walking away. The question shifts from whether to make a deal to what price within the ZOPA, and that's where the interesting strategy lives.

04 · MOVING THE PRICEFive levers inside the ZOPA

Once you've established there's a surplus to divide, five forces pull the settlement price toward you or away from you.

BATNA strength
Your outside option sets your floor. Line up a second sponsor and your BATNA rises from R$10k to, say, R$15k — your floor moves up and you capture more surplus. This is the most powerful lever because it changes the game's structure, not just your rhetoric.
Patience
The side that can wait longer gets more. In alternating-offers bargaining, the player with a lower cost of delay captures a larger slice. If the course date is fixed and you're negotiating one week before the brochure prints, you've given up most of your patience advantage — they know you'll fold first.
Anchoring
A credible, well-reasoned first offer pulls the settlement toward it. Opening at R$30k (above their ceiling but with a clear rationale — audience size, competitor benchmarks) creates a psychological reference point. Counter-offers tend to stay closer to a confident anchor than to the true midpoint.
Information
Protect your floor; probe theirs. If they learn your BATNA is only R$10k, they'll push to R$10,001. If you learn their ceiling is R$25k, you can hold out confidently near R$24k. Information asymmetry is a real advantage — be professionally vague about your minimum.
Commitment
A credible "best and final" can claim more — but risks no deal. From Lesson 07: a commitment works only if the other side believes you'll walk. Use sparingly and only when your BATNA genuinely supports the walk. Bluffing a commitment is the classic way to destroy a deal that should have happened.

The alternating-offers model (patience as leverage) is due to Rubinstein (1982); for intuition see Open Yale ECON 159, Lecture 18. Anchoring effects are documented across many negotiation experiments; see Dixit & Nalebuff, The Art of Strategy (Norton, 2008), Ch. 11.

05 · LEVERAGEWhat actually moves your share?

Which single move most increases YOUR share of the sponsorship surplus?

Bargaining power flows from your willingness and ability to walk away — which is exactly what a strong BATNA gives you. The other options either signal desperation (need), anchor you low (drop price first), or hand them your floor (reveal minimum). A second sponsor offer changes the structural math: your floor rises, your credibility rises, and their ability to extract surplus falls.

06 · KNOW THE LIMITSWhen bargaining logic breaks

BATNA and ZOPA explain how a deal gets divided once a deal is possible. They say nothing about situations where the bargaining frame itself doesn't apply — forcing it there produces false confidence, not insight.

Contraindications — don't force bargaining logic here

  • No ZOPA, no deal. If there's no ZOPA (your floor sits above their ceiling), there's no deal to split — walk to your BATNA rather than negotiate against nothing.
  • An unverifiable BATNA is a weak one. A strong BATNA you can't credibly show does little — it has to be believable to move your slice.
  • Both sides must be able to walk. Bargaining assumes both sides can walk away — a captive counterparty is a different game.

Check the ZOPA and the credibility of both BATNAs before you spend effort on anchoring or patience — those levers only move a settlement that's already possible.

07 · LOCK IT INThe bargaining prep routine

Bring it back. Take a real upcoming negotiation — the course sponsorship, a vendor contract, a hospital arrangement, a co-surgeon deal.

① What is your BATNA right now? ② What is your reservation value? ③ What do you estimate theirs to be? ④ Sketch the ZOPA — does a deal exist? ⑤ What is the ONE move that most improves your slice? Write these down before the conversation starts. That prep is the whole game.

Use the real ask. Open DECISIONS.md and work row D1 — the real skull-base course sponsorship ask (course Jul 13–15 HSJ/Moov → SBCBC Jul 16–17 Gramado; roughly R$41k gap left to close). The R$10k / R$25k figures earlier in this lesson were a teaching example — for your rep, fill in your own floor, reservation value, and BATNA. Don't invent specific sponsor numbers; use what you actually know or can find out.

Copy learning-records/REP-TEMPLATE.md to learning-records/REP-D1-sponsorship.md and fill Phase 1, using this lesson's five questions above applied to D1.

The gate: this lesson isn't "done" when you finish reading — it's done when one REP-*.md exists with Phase 1 filled. Delivered ≠ learned. One honest rep beats reading the next three lessons.

Primary sources: Open Yale ECON 159 (Polak) · SEP — Game Theory · Fisher & Ury, Getting to Yes (1981) · Dixit & Nalebuff, The Art of Strategy (Norton, 2008).