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Introduction to Automated Negotiation

Dave de Jonge

TL;DR

This work presents an accessible, formal tract of automated negotiation beginning with core concepts (offer spaces, alternating offers, utilities, and rationality) and extending to strategy design (time-based, adaptive, and imitative) and opponent modeling (Bayesian, scalable Bayesian, frequency analysis, Gaussian processes). It situates negotiation as a game-theoretic problem, connecting deterministic and non-deterministic turn-taking games, including imperfect information and subgame-perfect considerations, while highlighting practical frameworks like NegMas and the NegoSimulator. The text contributes practical BOA-based agent architecture guidance, reproposing techniques, and a detailed treatment of learning opponents’ utilities and strategies, together with a critical view on equilibrium concepts and their applicability to real-world automated negotiation. Together, these elements provide a structured route from foundational definitions to advanced negotiation dynamics, offering both theoretical insights and actionable methods for algorithmic negotiation design and evaluation.

Abstract

This book is an introductory textbook targeted towards computer science students who are completely new to the topic of automated negotiation. It does not require any prerequisite knowledge, except for elementary mathematics and basic programming skills. This book comes with an simple toy-world negotiation framework implemented in Python that can be used by the readers to implement their own negotiation algorithms and perform experiments with them. This framework is small and simple enough that any reader who does not like to work in Python should be able to re-implement it very quickly in any other programming language of their choice.

Introduction to Automated Negotiation

TL;DR

This work presents an accessible, formal tract of automated negotiation beginning with core concepts (offer spaces, alternating offers, utilities, and rationality) and extending to strategy design (time-based, adaptive, and imitative) and opponent modeling (Bayesian, scalable Bayesian, frequency analysis, Gaussian processes). It situates negotiation as a game-theoretic problem, connecting deterministic and non-deterministic turn-taking games, including imperfect information and subgame-perfect considerations, while highlighting practical frameworks like NegMas and the NegoSimulator. The text contributes practical BOA-based agent architecture guidance, reproposing techniques, and a detailed treatment of learning opponents’ utilities and strategies, together with a critical view on equilibrium concepts and their applicability to real-world automated negotiation. Together, these elements provide a structured route from foundational definitions to advanced negotiation dynamics, offering both theoretical insights and actionable methods for algorithmic negotiation design and evaluation.

Abstract

This book is an introductory textbook targeted towards computer science students who are completely new to the topic of automated negotiation. It does not require any prerequisite knowledge, except for elementary mathematics and basic programming skills. This book comes with an simple toy-world negotiation framework implemented in Python that can be used by the readers to implement their own negotiation algorithms and perform experiments with them. This framework is small and simple enough that any reader who does not like to work in Python should be able to re-implement it very quickly in any other programming language of their choice.

Paper Structure

This paper contains 85 sections, 4 theorems, 157 equations, 17 figures, 3 tables, 9 algorithms.

Table of Contents

  1. Introduction
  2. Characteristics of Negotiation
  3. History of Automated Negotiation
  4. Basic Negotiations
  5. Informal Description
  6. Formal Model
  7. The Offer Space
  8. The Alternating Offers Protocol
  9. Some Remarks
  10. Utility Functions
  11. Von Neumann-Morgenstern Utilities
  12. Self-interested Agents
  13. Linear Utility Functions
  14. Reservation Values
  15. Discount Factors
  16. ...and 70 more sections

Key Result

Theorem 1

Every finite 2-player normal-form game has at least one mixed Nash equilibrium.

Figures (17)

  • Figure 1: The alternating offers protocol as a finite-state machine.
  • Figure 2: Utility space diagram. Every dot is the utility vector of one offer $\omega$ in the offer space $\Omega$. The red lines represent the reservation values of the two respective agents.
  • Figure 3: Utility space diagram of a split-the-pie domain. Note that all utility vectors lie on the line $y=1-x$.
  • Figure 4: The individually rational offers are those for which their utility vector lies above the horizontal line representing $rv_2$ and to the right of the vertical line representing $rv_1$. Here these utility vectors are all drawn with a circle around them.
  • Figure 5: Example of domination. The offer $\omega$ lies to the top-right of $\omega'$ and we therefore say that $\omega$ dominates $\omega'$.
  • ...and 12 more figures

Theorems & Definitions (47)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Definition 10
  • ...and 37 more