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Indirect Dynamic Negotiation in the Nash Demand Game

Tatiana V. Guy, Jitka Homolová, Aleksej Gaj

TL;DR

A decision model is proposed that helps agents to successfully bargain by performing indirect negotiation and learning the opponent’s model, and indicates that the established negotiation results in maximising success rate of the game and brings more individual profit to the players.

Abstract

The paper addresses a problem of sequential bilateral bargaining with incomplete information. We proposed a decision model that helps agents to successfully bargain by performing indirect negotiation and learning the opponent's model. Methodologically the paper casts heuristically-motivated bargaining of a self-interested independent player into a framework of Bayesian learning and Markov decision processes. The special form of the reward implicitly motivates the players to negotiate indirectly, via closed-loop interaction. We illustrate the approach by applying our model to the Nash demand game, which is an abstract model of bargaining. The results indicate that the established negotiation: i) leads to coordinating players' actions; ii) results in maximising success rate of the game and iii) brings more individual profit to the players.

Indirect Dynamic Negotiation in the Nash Demand Game

TL;DR

A decision model is proposed that helps agents to successfully bargain by performing indirect negotiation and learning the opponent’s model, and indicates that the established negotiation results in maximising success rate of the game and brings more individual profit to the players.

Abstract

The paper addresses a problem of sequential bilateral bargaining with incomplete information. We proposed a decision model that helps agents to successfully bargain by performing indirect negotiation and learning the opponent's model. Methodologically the paper casts heuristically-motivated bargaining of a self-interested independent player into a framework of Bayesian learning and Markov decision processes. The special form of the reward implicitly motivates the players to negotiate indirectly, via closed-loop interaction. We illustrate the approach by applying our model to the Nash demand game, which is an abstract model of bargaining. The results indicate that the established negotiation: i) leads to coordinating players' actions; ii) results in maximising success rate of the game and iii) brings more individual profit to the players.
Paper Structure (20 sections, 12 equations, 20 figures, 5 tables)

This paper contains 20 sections, 12 equations, 20 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. General Conventions
  4. Markov Decision Process
  5. Optimal Decision Policy
  6. Learning Transition Model
  7. Methodology
  8. MDP Formalisation of Nash Demand Game
  9. Heuristic Model of Opponent
  10. ${\mathcal{B}}$ had Low Demand in the Previous Round
  11. ${\mathcal{B}}$ had High Demand in the Previous Round
  12. Prior Models Used in Learning
  13. Simulated Experiments
  14. Test 1: $\mathcal{A}$ is a non-learning MDP player, $\mathcal{B}$ behaves heuristically
  15. Test 2: $\mathcal{A}$ optimises and learns, $\mathcal{B}$ behaves heuristically
  16. ...and 5 more sections

Figures (20)

  • Figure 1: Test 1 - $\mathcal{A}$'s cumulative profit on weight $\omega^{\mathcal{A}}$
  • Figure 2: Test 1 - $\mathcal{B}$'s cumulative profit on weight $\omega^{\mathcal{A}}$
  • Figure 3: Test 1 - Total Profit of Players.
  • Figure 4: Test 1 - Success Rate of the Games.
  • Figure 5: Test 2 - $\mathcal{A}$'s cumulative profit on weight $\omega^{\mathcal{A}}$.
  • ...and 15 more figures

Theorems & Definitions (2)

  • Definition 1: MDP
  • Definition 2: Bargaining as an MDP task