1,686 research outputs found

    Essays in Behavioral Economics and Game Theory

    Get PDF
    This thesis consists of three papers. Chapter 1 conducts experimental research on individual bounded rationality in games, Chapter 2 introduces a novel equilibrium solution concept in behavioral game theory, and Chapter 3 investigates confirmation bias within the framework of game theory. In Chapter 1 (joint with Wei James Chen and Po-Hsuan Lin), we investigate individual strategic reasoning depths by matching human subjects with fully rational computer players in a lab, allowing for the isolation of limited reasoning ability from beliefs about opponent players and social preferences. Our findings reveal that when matched with robots, subjects demonstrate higher stability in their strategic thinking depths across games, in contrast to when matched with humans. In Chapter 2 (joint with Po-Hsuan Lin and Thomas R. Palfrey), we investigate how players’ misunderstanding about the relationship between opponents’ private information and strategies influence their equilibrium behavior in dynamic environments. This theoretical study introduces a framework that extends the analysis of cursed equilibrium from the strategic form to multi-stage games and applies it to various applications in economics and political science. In Chapter 3, I employ a game-theoretic framework to model how decision makers strategically interpret signals, particularly when they face a utility loss from holding beliefs that differ from their partners. The study reveals that the emergence of confirmation bias is positively associated with the strength of prior beliefs about a state, while the impact of signal accuracy remains ambiguous.</p

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Investigations into Proof Structures

    Full text link
    We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is applied in an exemplary manner to a coherent and comprehensive formal reconstruction and analysis of historical proofs of a widely-studied problem due to {\L}ukasiewicz. The underlying approach opens the door towards new systematic ways of generating lemmas in the course of proof search to the effects of reducing the search effort and finding shorter proofs. Among the numerous reported experiments along this line, a proof of {\L}ukasiewicz's problem was automatically discovered that is much shorter than any proof found before by man or machine.Comment: This article is a continuation of arXiv:2104.1364

    Model Checking Strategies from Synthesis Over Finite Traces

    Full text link
    The innovations in reactive synthesis from {\em Linear Temporal Logics over finite traces} (LTLf) will be amplified by the ability to verify the correctness of the strategies generated by LTLf synthesis tools. This motivates our work on {\em LTLf model checking}. LTLf model checking, however, is not straightforward. The strategies generated by LTLf synthesis may be represented using {\em terminating} transducers or {\em non-terminating} transducers where executions are of finite-but-unbounded length or infinite length, respectively. For synthesis, there is no evidence that one type of transducer is better than the other since they both demonstrate the same complexity and similar algorithms. In this work, we show that for model checking, the two types of transducers are fundamentally different. Our central result is that LTLf model checking of non-terminating transducers is \emph{exponentially harder} than that of terminating transducers. We show that the problems are EXPSPACE-complete and PSPACE-complete, respectively. Hence, considering the feasibility of verification, LTLf synthesis tools should synthesize terminating transducers. This is, to the best of our knowledge, the \emph{first} evidence to use one transducer over the other in LTLf synthesis.Comment: Accepted by ATVA 2

    On the Computation of Multi-Scalar Multiplication for Pairing-Based zkSNARKs

    Get PDF
    Multi-scalar multiplication refers to the operation of computing multiple scalar multiplications in an elliptic curve group and then adding them together. It is an essential operation for proof generation and verification in pairing-based trusted setup zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) schemes, which enable privacy-preserving features in many blockchain applications. Pairing-based trusted setup zkSNARKs usually follow a common paradigm. A public string composed of a list of fixed points in an elliptic curve group called common reference string is generated in a trusted setup and accessible to all parties involved. The prover generates a zkSNARK proof by computing multi-scalar multiplications over the points in the common reference string and performing other operations. The verifier verifies the proof by computing multi-scalar multiplications and elliptic curve bilinear pairings. Multi-scalar multiplication in pairing-based trusted setup zkSNARKs has two characteristics. First, all the points are fixed once the common reference string is generated. Second, the number of points n is typically large, with the thesis targeting at n = 2^e (10 ≤ e ≤ 21). Our goal in this thesis is to propose and implement efficient algorithms for computing multi-scalar multiplication in order to enable efficient zkSNARKs. This thesis primarily includes three aspects. First, the background knowledge is introduced and the classical multi-scalar multiplication algorithms are reviewed. Second, two frameworks for computing multi-scalar multiplications over fixed points and five corresponding auxiliary set pairs are proposed. Finally, the theoretical analysis, software implementation, and experimental tests on the representative instantiations of the proposed frameworks are presented

    Trocq: Proof Transfer for Free, With or Without Univalence

    Full text link
    Libraries of formalized mathematics use a possibly broad range of different representations for a same mathematical concept. Yet light to major manual input from users remains most often required for obtaining the corresponding variants of theorems, when such obvious replacements are typically left implicit on paper. This article presents Trocq, a new proof transfer framework for dependent type theory. Trocq is based on a novel formulation of type equivalence, used to generalize the univalent parametricity translation. This framework takes care of avoiding dependency on the axiom of univalence when possible, and may be used with more relations than just equivalences. We have implemented a corresponding plugin for the Coq proof assistant, in the CoqElpi meta-language. We use this plugin on a gallery of representative examples of proof transfer issues in interactive theorem proving, and illustrate how Trocq covers the spectrum of several existing tools, used in program verification as well as in formalized mathematics in the broad sense

    The Distributed Complexity of Locally Checkable Labeling Problems Beyond Paths and Trees

    Full text link
    We consider locally checkable labeling LCL problems in the LOCAL model of distributed computing. Since 2016, there has been a substantial body of work examining the possible complexities of LCL problems. For example, it has been established that there are no LCL problems exhibiting deterministic complexities falling between ω(logn)\omega(\log^* n) and o(logn)o(\log n). This line of inquiry has yielded a wealth of algorithmic techniques and insights that are useful for algorithm designers. While the complexity landscape of LCL problems on general graphs, trees, and paths is now well understood, graph classes beyond these three cases remain largely unexplored. Indeed, recent research trends have shifted towards a fine-grained study of special instances within the domains of paths and trees. In this paper, we generalize the line of research on characterizing the complexity landscape of LCL problems to a much broader range of graph classes. We propose a conjecture that characterizes the complexity landscape of LCL problems for an arbitrary class of graphs that is closed under minors, and we prove a part of the conjecture. Some highlights of our findings are as follows. 1. We establish a simple characterization of the minor-closed graph classes sharing the same deterministic complexity landscape as paths, where O(1)O(1), Θ(logn)\Theta(\log^* n), and Θ(n)\Theta(n) are the only possible complexity classes. 2. It is natural to conjecture that any minor-closed graph class shares the same complexity landscape as trees if and only if the graph class has bounded treewidth and unbounded pathwidth. We prove the "only if" part of the conjecture. 3. In addition to the well-known complexity landscapes for paths, trees, and general graphs, there are infinitely many different complexity landscapes among minor-closed graph classes

    Cognitive Hierarchies in Multi-Stage Games of Incomplete Information: Theory and Experiment

    Full text link
    Sequential equilibrium is the conventional approach for analyzing multi-stage games of incomplete information. It relies on mutual consistency of beliefs. To relax mutual consistency, I theoretically and experimentally explore the dynamic cognitive hierarchy (DCH) solution. One property of DCH is that the solution can vary between two different games sharing the same reduced normal form, i.e., violation of invariance under strategic equivalence. I test this prediction in a laboratory experiment using two strategically equivalent versions of the dirty-faces game. The game parameters are calibrated to maximize the expected difference in behavior between the two versions, as predicted by DCH. The experimental results indicate significant differences in behavior between the two versions, and more importantly, the observed differences align with DCH. This suggests that implementing a dynamic game experiment in reduced normal form (using the "strategy method") could lead to distortions in behavior.Comment: 48 pages for the main text, 52 pages for the appendi

    The Geometric Median and Applications to Robust Mean Estimation

    Full text link
    This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper bound for the distance between the mean and the median for general absolutely continuous distributions in R^d, and examples of specific classes of distributions for which these bounds do not depend on the ambient dimension dd; (b) exponential deviation inequalities for the distance between the sample and the population versions of the geometric median, which again depend only on the trace-type quantities and not on the ambient dimension. As a corollary, we deduce improved bounds for the (geometric) median of means estimator that hold for large classes of heavy-tailed distributions. Finally, we address the error of numerical approximation, which is an important practical aspect of any statistical estimation procedure. We demonstrate that the objective function minimized by the geometric median satisfies a "local quadratic growth" condition that allows one to translate suboptimality bounds for the objective function to the corresponding bounds for the numerical approximation to the median itself. As a corollary, we propose a simple stopping rule (applicable to any optimization method) which yields explicit error guarantees. We conclude with the numerical experiments including the application to estimation of mean values of log-returns for S&P 500 data.Comment: 28 pages, 2 figure
    corecore