Authors:
Paul Varkey
and
Piotr Gmytrasiewicz
Affiliation:
University of Illinois at Chicago, United States
Keyword(s):
Bilateral bargaining, Decision theory, Interactive epistemology, Higher order beliefs, Belief sampling.
Related
Ontology
Subjects/Areas/Topics:
Agents
;
Artificial Intelligence
;
Artificial Intelligence and Decision Support Systems
;
Autonomous Systems
;
Distributed and Mobile Software Systems
;
Economic Agent Models
;
Enterprise Information Systems
;
Formal Methods
;
Informatics in Control, Automation and Robotics
;
Intelligent Control Systems and Optimization
;
Knowledge Engineering and Ontology Development
;
Knowledge-Based Systems
;
Multi-Agent Systems
;
Planning and Scheduling
;
Simulation and Modeling
;
Software Engineering
;
Symbolic Systems
;
Uncertainty in AI
Abstract:
In this paper we study the sequential strategic interactive setting of bilateral, two-stage, seller-offers bargaining under uncertainty. We model the epistemology of the problem in a finite interactive decision-theoretic framework and solve it for three types of agents of successively increasing (epistemological) sophistication (i.e. capacity to represent and reason with higher orders of beliefs). We relax typical common knowledge assumptions, which, if made, would be sufficient to imply the existence of a, possibly unique, game-theoretic equilibrium solution. We observe and characterize a systematic monotonic relationship between an agent's beliefs and optimal behavior under a particular moment-based ordering of its beliefs. Based on this characterization, we present the \emph{spread-accumulate} technique of sampling an agent's higher order belief by generating ``evenly dispersed" beliefs for which we (pre)compute offline solutions. Higher order prior belief identification is then a
pproximated to arbitrary precision by identifying a (previously solved) belief ``closest" to the true belief. These methods immediately suggest a mechanism for achieving a balance between efficiency and the quality of the approximation -- either by generating a large number of offline solutions or by allowing the agent to search online for a ``closer" belief in the vicinity of best current solution.
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