Negotiation Simulation | Alternating-Offers Bargaining

Negotiation Setup

Agent A patience δ_A 0.90

Agent B patience δ_B 0.85

Concession aggressiveness 50%

Current State

Round 0 — no offer yet

A gets 50%B gets 50%

Round

Pie remaining

100.0%

SPE prediction (A share)

—

Status

Bargaining

How it works

This models Rubinstein's alternating-offers bargaining game: two agents split a pie of size 1 by taking turns proposing a division. Every round that passes without agreement shrinks the pie each agent values it at, because each side discounts future payoffs by a patience factor δ ∈ (0,1):

Agent i's payoff from x, received t rounds from now:  δᵢ^t · x
Offer alternates: A proposes on even rounds, B on odd rounds
Responder accepts if the offer beats their own continuation value,
else counter-offers next round (pie effectively shrinks by δ per pass)

For the infinite-horizon game with fixed discount factors, Rubinstein proved a unique subgame-perfect equilibrium (SPE) — the split both sides should rationally converge to immediately, in closed form:

A's equilibrium share = (1 − δ_B) / (1 − δ_A · δ_B)
B's equilibrium share = δ_B · (1 − δ_A) / (1 − δ_A · δ_B)

A more patient agent (higher δ, willing to wait) captures a larger share — patience is bargaining power. The concession aggressiveness slider controls how quickly each simulated agent's actual offers move toward its own reservation floor versus holding firm near the SPE prediction, and each round the responder accepts once the standing offer is worth at least as much as what they'd get by countering next round and waiting one more discount step.

Next Round — advance one alternating offer/counter-offer exchange.
Auto-Play — runs rounds automatically until a deal is struck or the pie decays below a negligible threshold (impasse).
Reset — clears the negotiation back to round 0 with a fresh pie of 1.0.

Real-world relevance: this exact structure — discounted alternating offers converging to a patience-weighted split — underlies models of labor/wage negotiation, diplomatic settlements, and business contract bargaining.

Agent A Agent B

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.

Negotiation Simulation: Alternating-Offers Bargaining