The traditional representations of games using the extensive form or the strategic (normal) form obscure much of the structure that is present in real-world games. In this paper, we propose a new representation language for general multiplayer games--multi-agent influence diagrams (MAIDs). This representation extends graphical models for probability distributions to a multi-agent decision-making context. MAIDs explicitly encode structure involving the dependence relationships among variables. As a consequence, we can define a notion of strategic relevance of one decision variable to another: D′ is strategically relevant to D if, to optimize the decision rule at D, the decision maker needs to take into consideration the decision rule at D′. We provide a sound and complete graphical criterion for determining strategic relevance. We then show how strategic relevance can be used to detect structure in games, allowing a large game to be broken up into a set of interacting smaller games, which can be solved in sequence. We show that this decomposition can lead to substantial savings in the computational cost of finding Nash equilibria in these games.

/pdf/multi-agent-influence-diagrams-for-representing-and-solving-3oa0zzlhx2.pdf

Multi-agent influence diagrams for representing and solving games

https://www.ics.uci.edu/~dechter/publications/r126.pdf

AND/OR search spaces for graphical models

We introduce the notion ofLImitedMemoryInfluenceDiagram (LIMID) to describe multistage decision problems in which the traditional assumption of no forgetting is relaxed. This can be relevant in situations with multiple decision makers or when decisions must be prescribed under memory constraints, such as in partially observed Markov decision processes (POMDPs). We give an algorithm for improving any given strategy by local computation of single policy updates and investigate conditions for the resulting strategy to be optimal.

/pdf/representing-and-solving-decision-problems-with-limited-54cmh7yhjg.pdf

Representing and Solving Decision Problems with Limited Information

Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential probabilistic dependencies among the costs. Although these dependencies violate the standard dynamic-programming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamic-programming approach based on stochastic dominance. We present a revised path-planning algorithm and prove that it produces optimal paths under time-dependent uncertain costs. We test the algorithm by applying it to a model of stochastic bus networks, and present empirical performance results comparing it to some alternatives. Finally, we consider extensions of these concepts to a more general class of problems of heuristic search under uncertainty.

Path Planning under Time-Dependent Uncertainty

Invited Papers.- Qualitative Decision Rules under Uncertainty.- Applications of Latent Class Analysis in Social Science Research.- Foundations of Uncertainty Concepts.- Transformations from Imprecise to Precise Probabilities.- A Representation Theorem and Applications.- On Modal Probability and Belief.- Bayesian Networks.- A Multi-layered Bayesian Network Model for Structured Document Retrieval.- Using Kappas as Indicators of Strength in Qualitative Probabilistic Networks.- Qualitative Bayesian Networks with Logical Constraints.- Introducing Situational Influences in QPNs.- Classification of Aerial Missions Using Hidden Markov Models.- Algorithms for Uncertainty Inference.- Dynamic Importance Sampling Computation in Bayesian Networks.- Morphing the Hugin and Shenoy-Shafer Architectures.- Learning.- Characterization of Inclusion Neighbourhood in Terms of the Essential Graph: Upper Neighbours.- Approximating Conditional MTE Distributions by Means of Mixed Trees.- Effective Dimensions of Partially Observed Polytrees.- Decision Graphs.- Applying Numerical Trees to Evaluate Asymmetric Decision Problems.- Mixed Influence Diagrams.- Decision Making Based on Sampled Disease Occurrence in Animal Herds.- Decision Network Semantics of Branching Constraint Satisfaction Problems.- Belief Functions.- Web of Trust: Applying Probabilistic Argumentation to Public-Key Cryptography.- A Comparison of Methods for Transforming Belief Function Models to Probability Models.- Fuzzy Matching and Evidential Reasoning.- Modeling Positive and Negative Pieces of Evidence in Uncertainty.- Directed Evidential Networks with Conditional Belief Functions.- Computational-Workload Based Binarization and Partition of Qualitative Markov Trees for Belief Combination.- Risk Assessment in Drinking Water Production Using Belief Functions.- Algebraic Structures Related to the Consensus Operator for Combining of Beliefs.- Fuzzy Sets.- Inclusion Measures in Intuitionistic Fuzzy Set Theory.- A Random Set Model for Fuzzy Labels.- On the Induction of Different Kinds of First-Order Fuzzy Rules.- Reasoning under Vagueness Expressed by Nuanced Statements.- Possibility Theory.- Partial Lattice-Valued Possibilistic Measures and Some Relations Induced by Them.- Coherent Conditional Probability as a Measure of Uncertainty of the Relevant Conditioning Events.- Decision Trees and Qualitative Possibilistic Inference: Application to the Intrusion Detection Problem.- Default Reasoning.- Multi-valued Conditional Events Avoid Lewis' Triviality Result.- Solving Semantic Problems with Odd-Length Cycles in Argumentation.- On the Relation between Reiter's Default Logic and Its (Major) Variants.- Belief Revision and Inconsistency Handling.- Probable Consistency Checking for Sets of Propositional Clauses.- On Iterated Revision in the AGM Framework.- Epistemic Logics for Information Fusion.- Logics.- Propositional Fusion Rules.- Preferential Logics for Reasoning with Graded Uncertainty.- Paraconsistent Reasoning via Quantified Boolean Formulas, II: Circumscribing Inconsistent Theories.- Modal (Logic) Paraconsistency.- A Formal Framework for Handling Conflicting Desires.- A Sequent Calculus for Skeptical Reasoning in Predicate Default Logic (Extended Abstract).- Probabilistic Lexicographic Entailment under Variable-Strength Inheritance with Overriding.- Demo Papers.- ABEL: An Interactive Tool for Probabilistic Argumentative Reasoning.- The Hugin Tool for Learning Bayesian Networks.

Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 7th European Conference, ECSQARU 2003, Aalborg, Denmark, July 2-5, 2003. Proceedings

https://repository.ust.hk/ir/bitstream/1783.1-4/1/tr94-3.pdf

A computational theory of decision networks

As Influence diagrams become a popular representational tool for decision analysis, influence diagram evaluation attracts more and more research interests. In this article, we present a new, two--phase method for influence diagram evaluation. In our method, an influence diagram is first mapped into a decision graph and then the analysis is carried out by evaluating the decision graph. Our method is more efficient than Howard and Matheson''s two--phase method because, among other reasons, the size of the decision graph generated by our method from an influence diagram can be much smaller than that by Howard and Matheson''s method for the same influence diagram. Like those most recent algorithms reported in the literature, our method can also exploit independence relationship among variables of decision problems, and provides a clean interface between influence diagram evaluation and Bayesian net evaluation, thus, various well--established algorithms for Bayesian net evaluation can be used in influence diagram evaluation. In this sense, our method is as efficient as those algorithms. Furthermore, our method has a few unique merits. First, it can take advantage of asymmetric processing in influence diagram evaluation. Second, by using heuristic search techniques, it provides an explicit mechanism for making use of heuristic information that may be available in a domain--specific form. These additional merits make our method more efficient than the current algorithms in general. Finally, by using decision graphs as an intermediate representation, the value of perfect information can be computed in a more efficient way.

A New Method for Influence Diagram Evaluation

While influence diagrams have many advantages as a representation framework for Bayesian decision problems, they have a serious drawback in handling asymmetric decision problems. To be represented in an influence diagram, an asymmetric decision problem must be symmetrized. A considerable amount of unnecessary computation may be involved when a symmetrized influence diagram is evaluated by conventional algorithms. In this paper we present an approach for avoiding such unnecessary computation in influence diagram evaluation.

Solving asymmetric decision problems with influence diagrams

Solving Asymmetric Decision Problems with Influence Diagrams

/pdf/decision-graphs-algorithms-and-applications-to-influence-17tjjfkvf0.pdf

DECISION GRAPHS: Algorithms and Applications to Influence Diagram Evaluation and High-Level Path Planning Under Uncertainty

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