131 research outputs found

    Reasoning in Bayesian Opinion Exchange Networks Is PSPACE-Hard

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    We study the Bayesian model of opinion exchange of fully rational agents arranged on a network. In this model, the agents receive private signals that are indicative of an unkown state of the world. Then, they repeatedly announce the state of the world they consider most likely to their neighbors, at the same time updating their beliefs based on their neighbors' announcements. This model is extensively studied in economics since the work of Aumann (1976) and Geanakoplos and Polemarchakis (1982). It is known that the agents eventually agree with high probability on any network. It is often argued that the computations needed by agents in this model are difficult, but prior to our results there was no rigorous work showing this hardness. We show that it is PSPACE-hard for the agents to compute their actions in this model. Furthermore, we show that it is equally difficult even to approximate an agent's posterior: It is PSPACE-hard to distinguish between the posterior being almost entirely concentrated on one state of the world or another

    Why Philosophers Should Care About Computational Complexity

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    One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and beyond," MIT Press, 2012. Some minor clarifications and corrections; new references adde

    Bayesian Decision Making in Groups is Hard

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    Hardness of Making Rational Group Decisions </jats:p

    Learning And Decision Making In Groups

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    Many important real-world decision-making problems involve group interactions among individuals with purely informational interactions. Such situations arise for example in jury deliberations, expert committees, medical diagnoses, etc. We model the purely informational interactions of group members, where they receive private information and act based on that information while also observing other people\u27s beliefs or actions. In the first part of the thesis, we address the computations that a rational (Bayesian) decision-maker should undertake to realize her optimal actions, maximizing her expected utility given all available information at every decision epoch. We use an approach called iterated eliminations of infeasible signals (IEIS) to model the thinking process as well as the calculations of a Bayesian agent in a group decision scenario. Accordingly, as the Bayesian agent attempts to infer the true state of the world from her sequence of observations, she recursively refines her belief about the signals that other players could have observed and beliefs that they would have hold given the assumption that other players are also rational. We show that IEIS algorithm runs in exponential time; however, when the group structure is a partially ordered set the Bayesian calculations simplify and polynomial-time computation of the Bayesian recommendations is possible. We also analyze the computational complexity of the Bayesian belief formation in groups and show that it is NP-hard. We investigate the factors underlying this computational complexity and show how belief calculations simplify in special network structures or cases with strong inherent symmetries. We finally give insights about the statistical efficiency (optimality) of the beliefs and its relations to computational efficiency. In the second part, we propose the no-recall model of inference for heuristic decision-making that is rooted in the Bayes rule but avoids the complexities of rational inference in group interactions. Accordingly to this model, the group members behave rationally at the initiation of their interactions with each other; however, in the ensuing decision epochs, they rely on heuristics that replicate their experiences from the first stage and can be justified as optimal responses to simplified versions of their complex environments. We study the implications of the information structure, together with the properties of the probability distributions, which determine the structure of the so-called ``Bayesian heuristics\u27\u27 that the agents follow in this model. We also analyze the group decision outcomes in two classes of linear action updates and log-linear belief updates and show that many inefficiencies arise in group decisions as a result of repeated interactions between individuals, leading to overconfident beliefs as well as choice-shifts toward extreme actions. Nevertheless, balanced regular structures demonstrate a measure of efficiency in terms of aggregating the initial information of individuals. Finally, we extend this model to a case where agents are exposed to a stream of private data in addition to observing each other\u27s actions and analyze properties of learning and convergence under the no-recall framework

    Model Checking Trust-based Multi-Agent Systems

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    Trust has been the focus of many research projects, both theoretical and practical, in the recent years, particularly in domains where open multi-agent technologies are applied (e.g., Internet-based markets, Information retrieval, etc.). The importance of trust in such domains arises mainly because it provides a social control that regulates the relationships and interactions among agents. Despite the growing number of various multi-agent applications, they still encounter many challenges in their formal modeling and the verification of agentsā€™ behaviors. Many formalisms and approaches that facilitate the specifications of trust in Multi-Agent Systems (MASs) can be found in the literature. However, most of these approaches focus on the cognitive side of trust where the trusting entity is normally capable of exhibiting properties about beliefs, desires, and intentions. Hence, the trust is considered as a belief of an agent (the truster) involving ability and willingness of the trustee to perform some actions for the truster. Nevertheless, in open MASs, entities can join and leave the interactions at any time. This means MASs will actually provide no guarantee about the behavior of their agents, which makes the capability of reasoning about trust and checking the existence of untrusted computations highly desired. This thesis aims to address the problem of modeling and verifying at design time trust in MASs by (1) considering a cognitive-independent view of trust where trust ingredients are seen from a non-epistemic angle, (2) introducing a logical language named Trust Computation Tree Logic (TCTL), which extends CTL with preconditional, conditional, and graded trust operators along with a set of reasoning postulates in order to explore its capabilities, (3) proposing a new accessibility relation which is needed to define the semantics of the trust modal operators. This accessibility relation is defined so that it captures the intuition of trust while being easily computable, (4) investigating the most intuitive and efficient algorithm for computing the trust set by developing, implementing, and experimenting different model checking techniques in order to compare between them in terms of memory consumption, efficiency, and scalability with regard to the number of considered agents, (5) evaluating the performance of the model checking techniques by analyzing the time and space complexity. The approach has been applied to different application domains to evaluate its computational performance and scalability. The obtained results reveal the effectiveness of the proposed approach, making it a promising methodology in practice
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