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A Negotiator's Backup Plan: Optimal Concessions with a Reservation Value

Tamara C. P. Florijn, Pinar Yolum, Tim Baarslag

TL;DR

The paper addresses optimal bidding under private reservation values in bilateral negotiations and introduces the Marginal Improvement Algorithm for Reservation Values (MIA-RVelous), a greedy method that inserts the reservation value and iteratively adds bids with maximal marginal improvement to maximize $EU_{rv}(\pi)$, achieving $O(n^2D)$ time. It proves the optimality of the resulting bid sequence and demonstrates how the reservation value can drive the selection of riskier, higher-utility bids. The discussion outlines extensions to probabilistic reservation values and to concurrent, multi-thread negotiations, underscoring practical impacts for backup-plan aware negotiation strategies.

Abstract

Automated negotiation is a well-known mechanism for autonomous agents to reach agreements. To realize beneficial agreements quickly, it is key to employ a good bidding strategy. When a negotiating agent has a good back-up plan, i.e., a high reservation value, failing to reach an agreement is not necessarily disadvantageous. Thus, the agent can adopt a risk-seeking strategy, aiming for outcomes with a higher utilities. Accordingly, this paper develops an optimal bidding strategy called MIA-RVelous for bilateral negotiations with private reservation values. The proposed greedy algorithm finds the optimal bid sequence given the agent's beliefs about the opponent in $O(n^2D)$ time, with $D$ the maximum number of rounds and $n$ the number of outcomes. The results obtained here can pave the way to realizing effective concurrent negotiations, given that concurrent negotiations can serve as a (probabilistic) backup plan.

A Negotiator's Backup Plan: Optimal Concessions with a Reservation Value

TL;DR

The paper addresses optimal bidding under private reservation values in bilateral negotiations and introduces the Marginal Improvement Algorithm for Reservation Values (MIA-RVelous), a greedy method that inserts the reservation value and iteratively adds bids with maximal marginal improvement to maximize , achieving time. It proves the optimality of the resulting bid sequence and demonstrates how the reservation value can drive the selection of riskier, higher-utility bids. The discussion outlines extensions to probabilistic reservation values and to concurrent, multi-thread negotiations, underscoring practical impacts for backup-plan aware negotiation strategies.

Abstract

Automated negotiation is a well-known mechanism for autonomous agents to reach agreements. To realize beneficial agreements quickly, it is key to employ a good bidding strategy. When a negotiating agent has a good back-up plan, i.e., a high reservation value, failing to reach an agreement is not necessarily disadvantageous. Thus, the agent can adopt a risk-seeking strategy, aiming for outcomes with a higher utilities. Accordingly, this paper develops an optimal bidding strategy called MIA-RVelous for bilateral negotiations with private reservation values. The proposed greedy algorithm finds the optimal bid sequence given the agent's beliefs about the opponent in time, with the maximum number of rounds and the number of outcomes. The results obtained here can pave the way to realizing effective concurrent negotiations, given that concurrent negotiations can serve as a (probabilistic) backup plan.
Paper Structure (4 sections, 1 theorem, 2 equations, 2 tables, 1 algorithm)

This paper contains 4 sections, 1 theorem, 2 equations, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Concession Behavior
  4. Discussion

Key Result

theorem 1

MIA-RVelous selects the optimal sequence of bids $\pi^* = \mathop{\mathrm{argmax}}\limits\limits_{\pi \in \Omega^{D}} EU_\textbf{rv}(\pi)$ given deadline $D$.

Theorems & Definitions (3)

  • Example 1
  • theorem 1
  • Example 2