Skill: quochungto/bookforge-negotiation-strategist (version 1.0.0)

--- name: negotiation-strategist description: "Apply the complete game-theoretic bargaining framework to any negotiation. Use this skill when a user needs to structure a negotiation, determine who has leverage, calculate the fair split, or decide whether to make a concession or walk away. Triggers include: user is preparing for a salary negotiation, contract renegotiation, partnership deal, M&A term sheet, or labor negotiation and wants to know what number to open with and why; user wants to determine the 'pie' — the true surplus that is actually at stake between the two parties, not the headline dollar figures; user needs to identify and quantify their Best Alternative to a Negotiated Agreement (BATNA) or the other side's BATNA before entering talks; user wants to know how to improve their bargaining position before the negotiation starts (raise your BATNA, lower theirs); user must decide whether to bundle multiple issues together or separate them; user is weighing whether to actually strike, walk out, or threaten to do so, and wants to understand the cost-benefit calculation; user wants to propose a virtual-strike or escrowed-revenue arrangement to eliminate collateral damage while preserving negotiating pressure; user is in an alternating-offer negotiation and wants to calculate the equilibrium split given relative patience levels; user suspects they are negotiating over the wrong number (confusing total value with incremental value above no-deal); user faces brinkmanship — escalating risk of breakdown — and wants to calibrate how far to push. This skill does NOT cover simultaneous-move games (use nash-equilibrium-analyzer), one-shot ultimatum games without iteration, or multi-party coalition bargaining beyond two principal parties." version: 1.0.0 homepage: https://github.com/bookforge-ai/bookforge-skills/tree/main/books/the-art-of-strategy/skills/negotiation-strategist metadata: {"openclaw":{"emoji":"📚","homepage":"https://github.com/bookforge-ai/bookforge-skills"}} status: draft source-books: - id: the-art-of-strategy title: "The Art of Strategy" authors: ["Avinash K. Dixit", "Barry J. Nalebuff"] chapters: [11] tags: [game-theory, negotiation, bargaining, BATNA, deal-structuring] depends-on: [backward-reasoning-game-solver] execution: tier: 1 mode: full inputs: - type: document description: "Description of the negotiation situation: the parties, what is being negotiated, what each side can do if no deal is reached (their outside options or BATNAs), the timeline, any multi-issue dimensions, and the current state of talks" tools-required: [Read, Write] tools-optional: [] mcps-required: [] environment: "Any agent environment; user describes the negotiation context in text; agent produces a structured strategy with explicit numbers, leverage analysis, and recommended moves" discovery: goal: "Measure the pie correctly, identify each party's BATNA, calculate the equilibrium split, diagnose the leverage imbalance, and produce a concrete negotiation strategy with specific opening positions, concession logic, and walk-away thresholds" tasks: - "Identify both parties and what they are negotiating over" - "Establish each party's BATNA: what each gets with zero agreement" - "Calculate the pie: total agreement value minus sum of BATNAs" - "Apply the equal-split principle: each party gets BATNA plus half the pie" - "Assess impatience asymmetry using the delta formula to adjust the split" - "Diagnose BATNA improvement opportunities: raise yours, lower theirs" - "Evaluate whether to bundle or unbundle multiple issues" - "Assess brinkmanship and strike dynamics if talks have or may break down" - "Evaluate virtual-strike option if a real disruption would cause collateral damage" - "Deliver: pie calculation, each party's fair-split number, BATNA improvement moves, recommended opening position, and walk-away threshold" audience: "Business negotiators, HR and labor relations teams, corporate development professionals, lawyers structuring deals, partnership managers, procurement teams, and anyone entering a bilateral negotiation where the stakes are explicit and the goal is an optimal, durable agreement" when_to_use: - "User needs to calculate what number to open with in a salary or contract negotiation" - "User suspects they are being asked to split total value instead of incremental value — the pie-measurement trap" - "User wants to know how their BATNA or the other side's BATNA affects who gets what" - "User must decide whether to take actions before negotiating that will change the BATNAs" - "User is structuring a multi-issue deal and wants to know whether to bundle or separate issues" - "User is in or approaching a strike, lockout, or deal-collapse situation and wants a clear cost-benefit view" - "User wants to propose a virtual-strike mechanism to preserve negotiating credibility without collateral harm" --- # Negotiation Strategist ## When to Use Use this skill any time two parties are negotiating over value that only exists if they reach agreement. The framework applies whether the context is labor-management, commercial contracts, partnership terms, M&A deal points, or international trade negotiations. The two foundational questions this skill answers: 1. **How much value is actually at stake?** (The pie — not the headline number) 2. **Who gets how much, and why?** (BATNA-based equal split, adjusted for patience and leverage) ## Core Framework ### Step 1: Establish the BATNAs Before calculating anything, identify what each party gets with no deal. **BATNA = Best Alternative to a Negotiated Agreement.** It is the best outcome each side can secure on its own without the other party's cooperation. - Ask: "If talks break down completely, what does each side do and what does that earn them?" - BATNAs are not aspirations. They are concrete fallback outcomes. If a union can earn $300/day in outside work during a strike, that is their BATNA. If management can operate with replacement workers at $500/day profit, that is theirs. - BATNAs can be improved strategically (see Step 5). ### Step 2: Calculate the Pie **The pie is not the total value of the agreement. It is the additional value created by agreement above what both parties would get anyway.** Formula: ``` Pie = (Agreement Value) - (Party A BATNA) - (Party B BATNA) ``` Example: Hotel earns $1,000/day when open. Union BATNA = $300/day (outside work). Management BATNA = $500/day (scab operation). ``` Pie = $1,000 - $300 - $500 = $200/day ``` The parties are not negotiating over $1,000. They are negotiating over $200. This matters enormously — anchoring on the wrong number leads to systematically wrong expectations. **The Talmud principle traces this insight to ancient fairness norms:** when two parties dispute a garment each claims, the portion each concedes to the other is split evenly. The logic is exactly the BATNA-based pie calculation applied to physical division of cloth. ### Step 3: Calculate the Equal Split With equal patience and equal bargaining position: ``` Party A receives: A's BATNA + Pie/2 Party B receives: B's BATNA + Pie/2 ``` From the hotel example: ``` Union receives: $300 + $100 = $400/day Management receives: $500 + $100 = $600/day ``` The equal split of the pie is the baseline. It is "equal" not in the sense of equal total receipts, but in the sense that each party gains the same increment above their no-deal fallback. **Why this is the right number:** Both parties contribute equally to the existence of the pie. Neither can claim a larger share of the surplus simply because their outside option happens to be higher. The BATNA is already theirs — it is not a bargaining chip to be divided. ### Step 4: Adjust for Impatience (Rubinstein Equilibrium) When the two parties alternate making offers and delays are costly, impatience breaks the 50/50 split of the pie in favor of the more patient party. **Impatience factor δ (delta):** The fraction of value that remains after one round of delay. If a dollar next week is worth $0.99 today, then δ = 0.99 (patient). If a dollar next week is worth $0.33 today, then δ = 1/3 (very impatient). **Rubinstein equilibrium split of the pie:** ``` Proposer's share of pie = 1 / (1 + δ) Responder's share of pie = δ / (1 + δ) ``` Key cases: - δ = 1 (no cost to waiting): split is 1/2 and 1/2. Pure 50/50. - δ = 1/2 (each delay loses half the pie): proposer gets 2/3, responder gets 1/3. - δ → 0 (extreme impatience, like ultimatum game): proposer gets essentially everything. **Backward induction logic (from the backward-reasoning-game-solver framework):** The proposer's advantage arises because each round the proposer can claim the portion of pie that would be lost if the responder said no. The responder only gets the δ-discounted value of their next turn. Working backward from the terminal condition produces the δ/(1+δ) formula for the responder's share. **Practical implication:** If your counterpart is under more time pressure than you are (public media coverage, quarterly earnings, expiring option, cash crunch), you are effectively the more patient party and should capture more than 50% of the pie. Conversely, if your organization faces political pressure to settle quickly, expect to concede more. ### Step 5: Improve the BATNAs — "This Will Hurt You More Than It Hurts Me" BATNAs are often not fixed. Before or during negotiations, both parties can take actions that shift the BATNA landscape. **General rule:** You will do better in the negotiation if your BATNA improves relative to your counterpart's BATNA — even if both BATNAs get worse in absolute terms, as long as theirs gets worse by more. **Calculation:** If an action costs you X but costs the other party Y, and Y > X, the action is worth taking even though it hurts you, because it improves your relative bargaining position by (Y - X)/2 after the pie is re-split. Example: - Baseline: Union BATNA $300, Management BATNA $500. Pie = $200. Union share = $400. - Union intensifies picketing: costs union $100/day in outside income, reduces management's scab profit by $200/day. - New BATNAs: Union = $200, Management = $300. Pie = $500. New union share = $200 + $250 = $450. - Net gain to union: +$50/day despite the self-imposed cost. **MLB 1980 case study:** Players struck during the exhibition season (players received no salary, but owners collected gate revenue from vacationers). Players returned for the regular season but threatened another strike on Memorial Day weekend — when owner revenues spike sharply. The players had no salary at stake during the exhibition season, so their cost was low. Owner revenue loss was highest precisely when the strike threat loomed. The players identified the timing that maximized the asymmetry between their cost and the owners' cost. **BATNA improvement tactics:** - **Raise your BATNA:** Develop credible outside alternatives before negotiating. Competing offers, alternative suppliers, internal capability development, coalition formation. - **Lower their BATNA:** Actions that reduce the other side's ability to walk away or operate without you. Intensified competition for their customers, public commitments that make their fallback position more visible or more costly. - **Both simultaneously:** If both BATNAs drop but theirs drops more, you gain. ### Step 6: Multi-Issue Bundling When multiple issues are on the table, the choice to bundle or unbundle them strategically affects outcomes. **Bundle when:** - You value different issues differently than your counterpart does. - Bundling allows a package trade where you concede on issues you care less about in exchange for wins on issues you care more about. - Example: A company values group health coverage at $1,000/worker while an individual worker would pay $2,000 for the same coverage. The company can offer health coverage instead of an equivalent wage increase — both parties prefer the bundle. - Broad negotiations (like GATT/WTO trade rounds) succeed more than narrow sector-by-sector talks for exactly this reason: the larger the bundled package, the more room for issue-swapping. **Unbundle when:** - Your counterpart is trying to use strength on one issue to extract concessions on an issue where you are strong. - Bundling a security alliance with a trade dispute allows one party to threaten the security arrangement to extract economic concessions. The weaker party on one dimension should insist on separating the games. - Example: Japan insisted the U.S.-Japan military alliance and trade disputes be negotiated separately to prevent the U.S. from leveraging security threats to extract trade concessions. ### Step 7: Brinkmanship and Strikes Strikes and breakdowns happen even when both parties would prefer agreement, because: 1. **Asymmetric information:** Each side must guess the other's cost of waiting. Since a lower cost of waiting is advantageous, each side has incentive to claim its costs are low. Claims without proof are not credible. The only credible proof is actually incurring the cost. 2. **Signaling through pain:** A strike is a costly signal. By actually striking, the union demonstrates that its cost of striking is lower than management believed. The signal is credible precisely because it hurts. 3. **Brinkmanship mechanics:** Rather than an all-or-nothing strike threat (not credible when much time remains), the effective form is gradual escalation — tempers rising, talks souring, increasing probability of breakdown each day. The party that fears breakdown less has the stronger position. Brinkmanship is a weapon for the stronger party. **When strikes occur despite the theory predicting they should not:** Both sides must have a common view of the eventual outcome for agreement to happen immediately. Disagreement about who will concede — caused by private information or genuine strategic ambiguity — causes both sides to hold out, incurring real costs. The strike ends when one side's resolve is tested enough that the other side's belief updates. **Implication for preparation:** Before talks begin, invest in understanding the other side's true cost of delay — their cash position, external pressures, political constraints. The better your model of their impatience, the less likely you are to miscalibrate and accidentally trigger a breakdown. ### Step 8: Virtual Strikes When a real strike or lockout would cause large collateral damage — to customers, third parties, public reputation, or the long-term enterprise — consider proposing a virtual strike arrangement. **Mechanism:** - Workers continue working as normal. - The employer continues producing as normal. - During the virtual strike period, neither side gets paid: workers forfeit wages; employer forfeits all revenue (paid to a third party — government, charity, or customers as free product). - The BATNAs are unchanged: both sides feel the same financial pain as in a real strike. - No third parties are harmed. **Why it works:** The bargaining-theoretic logic of a strike is purely about pain imposition — demonstrating that your cost of not having a deal is lower than the other side believes. A virtual strike replicates this exactly without the collateral harm of service disruption, consumer inconvenience, or reputational damage. **Historical precedent:** WWII-era Jenkins valve plant (Bridgeport, CT); 1960 Miami bus strike (customers rode free); 1999 Meridiana Airlines pilot strike (Italy's first virtual strike — flights operated, Meridiana donated all ticket revenue to charities). In all cases management forfeited gross revenue, not just profits, because profit measurement is too easy to manipulate. **When to propose it:** Propose before the real strike becomes imminent — ideally as a contingency clause in the contract: "If negotiations fail at the next renewal, the default dispute mechanism is a virtual strike." Agreeing in advance avoids the game-theoretic problem of appearing weak by proposing it in the heat of a breakdown. **Limitation:** Public relations benefit of virtual strikes may paradoxically make them harder to implement — some employers prefer the reputational damage of a real strike over the reputational windfall a virtual strike gives workers. ## Worked Example: The Triangle Airfare Negotiation Two companies (Houston and San Francisco) share a New York lawyer. The lawyer flies a triangle route NY-Houston-SF-NY ($2,818) instead of two round trips ($3,818). The savings = $1,000. **Wrong approaches:** - Split the triangle fare 50/50 → Houston pays $1,409. But Houston's standalone round-trip is $1,332. Houston would refuse. - Allocate by leg or mileage → leads to ad hoc results that depend on route geometry, not fairness. **Right approach — measure the pie:** - Houston BATNA: $1,332 (its own round-trip). - SF BATNA: $2,486 (its own round-trip). - Total BATNA sum: $3,818. - Agreement value: $2,818. - Pie = $3,818 - $2,818 = $1,000. - Equal split: each saves $500 above their BATNA. - Houston pays: $1,332 - $500 = **$832** - SF pays: $2,486 - $500 = **$1,986** This is the uniquely fair and stable outcome: each party gets an equal share of the value they jointly created by cooperating. ## Quick Reference | Concept | Formula | |---|---| | Pie | Agreement value - Party A BATNA - Party B BATNA | | Equal split (Party A) | A BATNA + Pie/2 | | Equal split (Party B) | B BATNA + Pie/2 | | Proposer share (Rubinstein) | 1 / (1 + δ) | | Responder share (Rubinstein) | δ / (1 + δ) | | Patient limit (δ → 1) | 50/50 | | Ultimatum limit (δ → 0) | 100/0 | ## Structural Self-Check Before finalizing any negotiation strategy, verify: - [ ] Have I identified each party's BATNA concretely, not aspirationally? - [ ] Have I calculated the pie as the increment above BATNAs, not the total headline figure? - [ ] Have I accounted for asymmetric patience and used the δ/(1+δ) formula if one party is more impatient? - [ ] Have I considered pre-negotiation BATNA improvement moves (raise mine, lower theirs)? - [ ] Have I identified all issues on the table and decided whether bundling benefits me? - [ ] If a strike or breakdown is possible, have I calculated who bears more relative cost? - [ ] If collateral damage is large, have I considered proposing a virtual strike mechanism? - [ ] Is my opening position anchored to the correct number (my BATNA + half the pie), not a naive split of total value? ## References - `references/rubinstein-bargaining-math.md` — Full derivation of the δ/(1+δ) split from backward induction, with worked numerical examples for δ = 0.99, 0.5, and 1/3 - `references/batna-improvement-case-studies.md` — MLB 1980 exhibition season strike, hotel union/management 101-day season, detailed numbers - `references/virtual-strike-mechanics.md` — Meridiana 1999 case, Jenkins valve plant, Miami bus strike, proposal language for contingency clauses - `references/multi-issue-bundling-guide.md` — GATT/WTO bundling logic, Japan-US security/trade separation, health benefits vs. wages example ## License This skill is licensed under [CC-BY-SA-4.0](https://creativecommons.org/licenses/by-sa/4.0/). Source: [BookForge](https://github.com/bookforge-ai/bookforge-skills) — The Art of Strategy by Avinash K. Dixit, Barry J. Nalebuff. ## Related BookForge Skills Install related skills from ClawhHub: - `clawhub install bookforge-backward-reasoning-game-solver` Or install the full book set from GitHub: [bookforge-skills](https://github.com/bookforge-ai/bookforge-skills)

path: references/batna-improvement-case-studies.md
content: # BATNA Improvement: Case Studies

Source: The Art of Strategy, Ch. 11 (pp. 312–317)

## Principle

Your BATNA and your counterpart's BATNA determine the pie and each party's share of it. Since share = BATNA + Pie/2, anything that raises your BATNA or lowers theirs improves your outcome. Even moves that hurt both parties are worthwhile if they hurt the other party more (asymmetric damage).

## Case Study 1: Hotel Union/Management — 101-Day Season

### Setup
- Hotel season: 101 days. Hotel earns $1,000/day operating.
- Baseline: Union BATNA = $0 (no outside income during negotiations). Management BATNA = $0 (no operation during strike).
- Pie = $1,000 - $0 - $0 = $1,000/day.
- Equal split: each gets $500/day.

### Introducing Outside Income (Union BATNA)
- Union members can earn $300/day in outside activities during negotiations.
- Union BATNA = $300/day. Management BATNA = $0.
- Pie = $1,000 - $300 - $0 = $700/day.
- Union gets: $300 + $350 = $650/day. Management gets: $350/day.

### Introducing Scab Operation (Management BATNA)
- Management can operate with replacement workers at $500/day profit (less efficient, some guest reluctance to cross picket lines).
- If union BATNA = $0 and management BATNA = $500:
- Pie = $1,000 - $0 - $500 = $500/day.
- Management gets: $500 + $250 = $750/day. Union gets: $250/day.

### Combined BATNAs
- Union BATNA = $300/day (outside work). Management BATNA = $500/day (scab operation).
- Pie = $1,000 - $300 - $500 = $200/day.
- Union gets: $300 + $100 = $400/day. Management gets: $500 + $100 = $600/day.

### BATNA Improvement Move: Union Intensifies Picketing
- Union foregoes $100/day of outside income to intensify picketing.
- Picketing reduces management's scab profit by $200/day.
- New BATNAs: Union = $200/day. Management = $300/day.
- New pie = $1,000 - $200 - $300 = $500/day.
- Union gets: $200 + $250 = $450/day. Management gets: $300 + $250 = $550/day.
- Union's net gain: $450 - $400 = +$50/day, despite the $100/day cost. The asymmetry ($200 damage to management vs. $100 cost to union) creates a $50 net gain.

**Lesson:** When evaluating a costly move before or during negotiations, compute (opponent's BATNA damage - your cost) / 2. If positive, the move improves your bargaining position even if it hurts you in absolute terms.

## Case Study 2: MLB 1980 — Exhibition Season Strike Timing

### Structure
- Players negotiated during the exhibition season (March–April), then returned for the regular season.
- Threatened a second strike starting Memorial Day weekend.

### BATNA Asymmetry by Timing

**Exhibition season:**
- Players' cost: no salary during exhibition season (players not paid for exhibition games).
- Owners' cost: owners earned revenue from vacationers and local fans at exhibition games.
- Player cost = 0. Owner cost = positive.
- Asymmetry: owners lose more than players during exhibition season → players hold leverage.

**Memorial Day weekend:**
- Owners' revenue from gate and television rises sharply starting Memorial Day.
- Players' salary is flat throughout the season.
- Striking at Memorial Day maximizes owner loss relative to player cost.

### Outcome
- Owners conceded just before the second threatened strike.
- The first strike (exhibition season) actually occurred — owners called the bluff.
- Key insight: the players chose the timing to maximize relative damage. They did not strike when their own costs were highest; they struck when the owner's costs were highest relative to theirs.

### Lesson for Practice
When choosing the timing of a threat or action, identify the calendar points where the ratio of (cost to opponent) / (cost to yourself) is maximized. Seasonal businesses, quarterly reporting cycles, elections, product launches, and contract renewals all create timing asymmetries.

## General Framework for BATNA Improvement Analysis

Before entering any negotiation, build a two-column table:

| Action | Cost to You | Cost to Opponent | Net Gain to You |
|--------|------------|-----------------|-----------------|
| Develop outside offer | Low (time) | Moderate (competitive pressure) | (Opponent cost - Your cost)/2 |
| Intensify competition for their clients | Low | High | High/2 |
| Public commitment to walk away | Medium (reputational) | High (credibility signal) | Positive |
| Coalition with others against them | Low | High | High/2 |

Select actions where the third column is positive and significant.

## BATNA Improvement vs. BATNA Bluffing

**Improving** your BATNA means actually creating better outside alternatives (competing offers, internal capability, coalition partners). This is durable and credible.

**Claiming** a higher BATNA than you have is not credible — it will be tested. The other side will often call a bluff precisely because they know each side has incentive to exaggerate its outside options. The only credible proof of a low cost of breakdown is to actually incur it (the signaling role of strikes).

Invest in genuine BATNA improvement before negotiations begin. Do not rely on claims that cannot be independently verified.


path: references/multi-issue-bundling-guide.md
content: # Multi-Issue Bundling in Negotiation

Source: The Art of Strategy, Ch. 11 (pp. 320–321)

## Core Insight

When multiple issues are on the table, the decision to bundle them together or negotiate them separately is itself a strategic choice with large consequences. The right choice depends on whether differential valuations create room for mutually beneficial trades.

## When to Bundle

**Bundle multiple issues when the parties value them differently.**

If Party A values Issue X highly and cares less about Issue Y, while Party B values Issue Y highly and cares less about Issue X, then bundling the two issues into one negotiation creates room for a trade where both parties end up better off than they would by negotiating each issue separately.

### Example: Health Benefits vs. Wages

- A company can provide group health coverage for $1,000/worker/year.
- An individual worker would pay $2,000 for the same coverage on the open market.
- The "exchange rate" is 2:1 — a dollar of health benefit is worth $2 of wages to the worker, but costs only $1 for the company to provide.

By bundling health benefits into the wage negotiation:
- The company offers health coverage instead of a $1,500 wage increase.
- The worker is better off (values the coverage at $2,000, which exceeds the $1,500 wage alternative).
- The company is better off (pays $1,000 instead of $1,500).
- Total surplus from the bundle is $500/worker greater than the wage-only negotiation.

**Rule:** When one party can provide something at lower cost than the other party can obtain it on the outside, bundling that item into the negotiation creates joint surplus that can be split.

### Example: GATT and WTO Trade Rounds

Broad, multi-country, multi-sector trade liberalization rounds (GATT/WTO) have consistently achieved more liberalization than narrow sector-by-sector or bilateral negotiations. The reason:

- Each country has different sensitivities and different export strengths.
- In a narrow negotiation, each country must give up something it protects in exchange for access to one specific market.
- In a broad round, Country A can concede on agriculture (where it is weak) in exchange for gains in manufactured goods (where it is strong), while Country B makes the opposite trade.
- The bundling of many issues creates more opportunities for issue-swapping where each party concedes on issues it cares less about.

**Rule:** Larger bundles create more opportunities for mutually beneficial trades among parties with heterogeneous valuations. Advocate for broad agendas in multi-party negotiations where you have uneven strengths.

## When to Unbundle

**Unbundle issues when your counterpart is trying to use leverage in one game to extract concessions in another.**

If Party B is strong on Issue X and uses the threat of deterioration on Issue X to force concessions on Issue Y (where Party A is strong), Party A should insist on separating the negotiations.

### Example: U.S.-Japan Security and Trade

- The United States had leverage in military/security arrangements with Japan.
- The U.S. could theoretically threaten to withdraw military protection unless Japan made trade concessions.
- But the U.S. has no real interest in withdrawing — it is purely a threat.
- Japan insisted these issues be negotiated separately to prevent the U.S. from using security threats as leverage in trade negotiations.

**Rule:** If your counterpart has strong positions on issues where you are vulnerable, separating those issues from the issues where you are strong prevents cross-contamination of leverage. Insist on single-issue negotiations when the bundled agenda would give the other side unfair leverage.

### When You Are the Weaker Party on Some Issues

- If you are weaker on Issue X but stronger on Issue Y, and your counterpart wants to bundle, consider the following:
  - Bundling will allow your counterpart to use their strength on X to dominate the entire package.
  - You may do better by isolating Issue Y (where you have strength) and negotiating it separately.
  - Push for separate tracks or sequential negotiations that start with issues where you have leverage.

## The Linkage Decision Matrix

| Situation | Bundle or Unbundle? | Reason |
|-----------|--------------------|----|
| You value issues differently from counterpart | Bundle | Enables mutually beneficial trades |
| Your counterpart is strong on one issue, you on another, and strength doesn't transfer | Bundle | Allows issue-swapping |
| Counterpart wants to use strength on Issue X to dominate Issue Y where you are strong | Unbundle | Prevents leverage transfer |
| You are uniformly weak across issues | Unbundle | Limits the scope of damage; isolate each battleground |
| Multi-party negotiation with heterogeneous valuations | Bundle | More parties = more trade opportunities |
| Two-party negotiation with one-sided leverage | Depends | Bundle if it creates joint surplus; unbundle if it transfers leverage to your disadvantage |

## Linkage as a Threat Mechanism

Bundling can also be used as a coercive threat rather than a cooperative opportunity. A party may offer to link two issues to create a new threat: "Unless you concede on X, we will withdraw cooperation on Y (where you need us)."

This is a strategic use of bundling as leverage, not a search for mutual gain. The target party's defense is to insist on separating the games — formally or publicly — so that the threat has no legal, contractual, or reputational basis.

In international relations, this manifests as "issue linkage" diplomacy. Countries with more issue areas to link (larger powers) generally benefit more from this strategy than smaller countries, which is why smaller countries often advocate for rules-based, single-issue negotiations in multilateral forums like the WTO.


path: references/rubinstein-bargaining-math.md
content: # Rubinstein Bargaining: Mathematical Derivation

Source: The Art of Strategy, Ch. 11 Appendix (pp. 326–330)

## Setup

Two parties alternate making proposals for how to divide a pie of size 1. The pie is described as (X, 1-X) where X is the proposer's share. As soon as one side accepts the other's proposal, the game ends. Delay is costly: a dollar received next period is worth δ times a dollar received today.

δ (delta) is the patience parameter:
- δ close to 1: parties are patient, delay is cheap
- δ close to 0: parties are very impatient, delay destroys most of the value
- δ = 0: ultimatum game (entire pie disappears if offer is not accepted immediately)

## Finding the Equilibrium

Let L = the minimum share you will ever accept (your "lowest acceptable").

**Step 1:** If you turn down today's offer and wait to make a counteroffer tomorrow, the other side knows you will never accept less than L. So the most they can ever hope for is 1 - L. But that is what they get in one period. What they get today is δ(1 - L).

Since the best you can offer them tomorrow is δ(1 - L), they will accept it. That means by rejecting today and countering tomorrow, you can secure 1 - δ(1 - L).

**Step 2:** You should therefore never accept less than 1 - δ(1 - L) today.

Setting L = 1 - δ(1 - L) and solving:

```
L = 1 - δ(1 - L)
L = 1 - δ + δL
L - δL = 1 - δ
L(1 - δ) = 1 - δ
```

Wait — that gives L = 1 regardless of δ, which is wrong. The correct setup is:

The minimum you accept must satisfy: L ≥ δ(1 - δ(1 - L))

Working through the algebra as shown in the text:

```
L ≥ δ(1 - L) [the other side accepts δ(1-L) tomorrow]

Setting L = δ(1 - δ(1 - L)):
L = δ - δ²(1 - L)
L = δ - δ² + δ²L
L - δ²L = δ - δ²
L(1 - δ²) = δ(1 - δ)
L = δ(1 - δ) / (1 - δ²)
L = δ(1 - δ) / [(1 - δ)(1 + δ)]
L = δ / (1 + δ)
```

So L = δ/(1 + δ). This is the least you will ever accept when you are the responder (i.e., the person receiving an offer).

By symmetry, this is also the most you will ever offer the other side (since they will use the same logic). Therefore:

**Proposer's share = 1 - L = 1 - δ/(1 + δ) = 1/(1 + δ)**

**Responder's share = δ/(1 + δ)**

## Numerical Examples

### δ = 0.99 (weekly offers, 1% weekly discount — very patient)

```
Proposer gets: 1 / (1 + 0.99) = 1 / 1.99 ≈ 0.503
Responder gets: 0.99 / 1.99 ≈ 0.497
Split: approximately 50.3 / 49.7
```

Interpretation: With very short intervals between offers, the proposer's first-mover advantage nearly vanishes. The split is almost exactly 50/50.

### δ = 0.5 (each delay loses half the pie — moderately impatient)

```
Proposer gets: 1 / (1 + 0.5) = 1 / 1.5 = 2/3
Responder gets: 0.5 / 1.5 = 1/3
Split: 67 / 33
```

Interpretation: The proposer claims the half that would disappear if the responder said no (since δ = 1/2, half is lost per round), plus half of the remainder. Each round, the proposer collects twice as much as the responder.

### δ = 1/3 (impatient — two-thirds of value lost each delay)

```
Proposer gets: 1 / (1 + 1/3) = 1 / (4/3) = 3/4
Responder gets: (1/3) / (4/3) = 1/4
Split: 75 / 25
```

### δ → 1 (limit case: perfectly patient)

```
Proposer gets: 1/(1+1) = 1/2
Responder gets: 1/(1+1) = 1/2
Split: 50/50
```

### δ → 0 (limit case: ultimatum game)

```
Proposer gets: 1/(1+0) = 1
Responder gets: 0/(1+0) = 0
Split: 100/0
```

This matches the ultimatum game result from Chapter 2: if the pie disappears entirely if the responder says no, the proposer can demand everything.

## Applying to Real BATNAs

The Rubinstein formula applies to the pie (surplus above BATNAs), not to total value. The full split is:

```
Party A (proposer) receives: A_BATNA + Pie × [1/(1+δ)]
Party B (responder) receives: B_BATNA + Pie × [δ/(1+δ)]
```

If both parties have the same δ and alternate making offers, use δ = 1 as the practical approximation (50/50 pie split) unless there is a clear impatience asymmetry.

## Differing Impatience

If the two parties have different discount factors δ_A and δ_B, and the time between offers shrinks to zero, the pie is split in the ratio of their waiting costs. If one party is twice as impatient as the other, it gets one-third of the pie (half as much as the more patient party).

Practical implication: institutional structures that force impatience (electoral cycles, quarterly reporting, public media pressure) systematically reduce bargaining power. The U.S. government's impatience in international negotiations is repeatedly exploited by more patient counterparts.


path: references/virtual-strike-mechanics.md
content: # Virtual Strike Mechanics

Source: The Art of Strategy, Ch. 11 (pp. 321–323)

## The Problem with Real Strikes

A traditional strike (or lockout) imposes costs on:
1. Workers (lost wages)
2. Management (lost profits)
3. Customers (lost service)
4. Third parties (supply chain disruption, economic spillover)

The dock-worker lockout of 2002: the dispute involved ~$20 million in productivity enhancements. The lockout disrupted the U.S. economy by more than $10 billion. Collateral damage was 500 times the size of the dispute.

**The strike's logic is purely signaling:** each party needs to prove its cost of not having a deal is lower than the other believes. The collateral damage to third parties is pure waste — it serves no bargaining purpose.

## The Virtual Strike Mechanism

**Mechanism:**
- Workers continue working as normal (no service disruption).
- Employer continues producing as normal (no lost output for customers).
- All revenue during the virtual strike period is forfeited by the employer to a third party: government, charity, or customers (as free product/service).
- Workers receive no wages during the virtual strike period.

**Result:**
- Workers feel the same financial pain as in a real strike (no pay).
- Employer feels the same financial pain as in a real strike (no revenue — in practice, gross revenue is used rather than profit because profit is too easy to manipulate).
- Customers are unharmed.
- The BATNAs are unchanged relative to a real strike.
- The bargaining incentives are unchanged.

## Historical Precedents

### Jenkins Company Valve Plant — Bridgeport, CT (World War II)
- The U.S. Navy used a virtual strike to settle a labor dispute.
- Workers continued working; management forfeited profits.
- First documented industrial use of the mechanism.

### Miami Bus Strike (1960)
- Bus drivers staged a virtual strike.
- Buses ran on their normal schedule.
- Passengers rode for free — the revenue that would normally go to the transit authority was effectively given to riders.
- "Customers got a free ride, literally."

### Meridiana Airlines — Italy (1999)
- Italy's first virtual strike in aviation.
- Pilots and flight attendants worked their normal flights, unpaid.
- Meridiana donated all ticket revenue from virtually-struck flights to charities.
- Flights were not disrupted. No stranded passengers.
- The virtual strike worked as predicted — the threat was credible and management settled.

### Italy Transport Union (2000)
- 300 pilots participated in a virtual strike.
- The union forfeited 100 million lire (strike payments to charity).
- The union chose a medical device for a children's hospital as the recipient.
- Public relations benefit: instead of destroying consumer goodwill (as in NHL 2004-5), the virtual strike generated a positive story.

### NHL Lockout (2004–5)
- Management imposed a lockout rather than accepting virtual strike terms.
- The entire season was cancelled. No Stanley Cup awarded.
- Arena attendance took years to recover.
- This is the counterfactual: real disruption permanently destroys consumer demand and enterprise value. Virtual strikes avoid this.

## Implementation Design

### Revenue vs. Profit Forfeiture

In all four documented cases, management agreed to forfeit gross revenue, not profit. The reason: profit is a residual after costs, and management can shift costs or accounting choices to minimize reported profit during the dispute period. Gross revenue is harder to manipulate.

Workers forfeit wages. Employer forfeits gross revenue. The escrowed funds go to the third party.

### Third-Party Recipient Options
- **Government (tax authority):** Neutral, accepted by both parties, legally clean.
- **Charity:** Creates positive public relations; may be preferred by labor as a signal of strength.
- **Customers (free product/service):** Most consumer-visible option; aligns customer interests with quick resolution.

### Timing of Agreement

The right time to agree to a virtual strike mechanism is **before the real strike becomes imminent** — ideally as a contingency clause in the labor contract:

> "If contract negotiations fail to reach agreement by [date], both parties agree to enter a virtual strike arrangement beginning [date+n], under which [revenue escrow terms], until agreement is reached."

Agreeing in advance avoids the game-theoretic problem where proposing a virtual strike during a real dispute signals weakness or loss of resolve.

## Limitations and Complications

1. **Public relations benefit may backfire:** If a virtual strike generates positive PR for workers (charity donations, customer goodwill), management may prefer the reputational damage of a real strike — it is a known threat rather than an unknown one.

2. **Customer inconvenience as a strategic weapon:** Some real strikes are deliberately designed to inconvenience customers so they pressure management to settle. A virtual strike removes this pressure. Workers who rely on customer pressure as part of their strategy may not want to go virtual.

3. **Revenue measurement disputes:** Even gross revenue can be contested in industries with complex pricing, barter, intercompany transactions, or subscription models. The escrow mechanism must specify exactly what counts.

4. **Worker motivation during virtual strike:** Workers who work for nothing during a virtual strike must believe settlement is imminent and that the sacrifice is worth it. If the dispute drags on, worker participation may erode.

## Decision Rule: When to Propose a Virtual Strike

Propose a virtual strike mechanism when:
- The collateral damage to customers or third parties is large relative to the size of the dispute.
- The enterprise's long-term customer relationships or brand value are at risk from disruption.
- Both parties genuinely want to settle but need a credible signaling mechanism.
- You are the party whose BATNAs are better protected under a virtual arrangement than a real one.

Do not propose a virtual strike when:
- Customer pressure is a key part of your negotiating strategy.
- Management will use the virtual strike's PR benefit to undercut your leverage.
- The dispute is so bitter that neither party wants to cooperate even on the mechanism.


Security scan verdicts — ClawScan: clean | static analysis: clean | VirusTotal: clean | SkillSpector: clean (LOW)