Human-Computer
Negotiation in ThreePlayer Market Settings
Galit Haim,
Ya'akov Gal, Bo An and Sarit Kraus
Interactive Negotiation
with Three Players
The SPs Goal:
to become the CS’s exclusive provider
The Contract Game
Using the Colored Trails:
An Infrastructure for Agent Design, Implementation and
Evaluation for Open Environments (Gal et al AIJ 2010)
 Main parts:
 negotiation
 movement
 Incomplete information
 Automatically exchange
 Game ends:
 The CS reached one of the SPs
 Did not move for two
consecutive rounds
Negotiation
Odd Rounds 
Accept/Reject????
• To which SP to
propose???
• Which proposal to
propose???
 Even Rounds
Movement
• 150 points bonus:
both the CS and the SPg
• 5 points: for each chip left
• Only the CS can move
• Chip with the same square-color
• Visible movements
• Path to path
• More than one square
The Challenge:
Building an Agent that Can Play One of
the Roles with People
 Sub-Game Perfect Equilibrium
 Machine Learning + Human Behavior
Why not Equilibrium Agents?
No Need for Culture Consideration
 Nash equilibrium: stable strategies; no
agent has an incentive to deviate.
 Results from the social sciences suggest
people do not follow equilibrium strategies:
Aumann
 Equilibrium based agents played against
people failed.
 People do not build agents that follow
equilibrium strategies.
Kahneman
7
Sub-Game-Perfect-Equilibrium
Agent
 Commitment offer:
bind the customer to one of
the SP for the duration of
the game
 Example:
CS proposes 11 grays for
33 red and 7 purple chips
Extensive Empirical Study:
Israel, U.S.A and China
 530 students:
 Israel: 238 students
 U.S.A: 149 students
 China: 143 students
 Baseline: 3 human players
 One agent vs 2 human players
 Lab conditions
 Instructions in the local language:
 Hebrew, English and Chinese
EQ CS Player’s Performance
500
450
400
350
300
250
200
150
100
50
0
420.66
392
351.76
293.77
278.66
230.67
Israel
U.S.A
Human
Agent
China
EQ SPy Player’s Performance
Human are Bounded Rational:
Do not Reach the Goal
1.2
1
1
1
1
0.93
0.83
0.8
0.6
0.6
0.4
0.2
0
Israel
U.S.A
CS:3-human players
China
CS EQ Agent
SPy EQ Agent Improvement
 Assumption
– When a human player attempt to go to the
goal, there is some probability p that he will
fail
 Risk-Averse Agent
– With respect to probability failure
Risk Averse Agent Results
300
254.66
239.7
250
226.76
218.66
200.02
200
195.29
189.5
220
179.23
150
100
50
0
Israel
U.S.A
SPh
SPa
China
SPrap
Conclusions
 Define and analyze a complex three-players
negotiation game successfully
 Equilibrium agents can work well:
 CS EQ agent outperformed the CS human player
 SP EQ agent outperformed the SP human player
(using the probability to fail)
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