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Joseph Y. Halpern

Publications and source records attributed to Joseph Y. Halpern.

At least 55 records · Page 3Linked to original sources
arXiv2020

Information Acquisition Under Resource Limitations in a Noisy Environment

We introduce a theoretical model of information acquisition under resource limitations in a noisy environment. An agent must guess the truth value of a given Boolean formula $φ$ after performing a bounded number of noisy tests of the truth values of variables in the formula. We observe that, in general, the problem of finding an optimal testing strategy for $ϕ$ is hard, but we suggest a useful heuristic. The techniques we use also give insight into two apparently unrelated, but well-studied problems: (1) \emph{rational inattention}, that is, when it is rational to ignore pertinent information (the optimal strategy may involve hardly ever testing variables that are clearly relevant to $ϕ$), and (2) what makes a formula hard to learn/remember.

cs.AI↗
arXiv2019

A Conceptually Well-Founded Characterization of Iterated Admissibility Using an "All I Know" Operator

Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (IA), also known as iterated deletion of weakly dominated strategies, where uncertainty is represented using LPSs (lexicographic probability sequences). Their characterization holds in a rich structure called a complete structure, where all types are possible. In earlier work, we gave a characterization of iterated admissibility using an "all I know" operator, that captures the intuition that "all the agent knows" is that agents satisfy the appropriate rationality assumptions. That characterization did not need complete structures and used probability structures, not LPSs. However, that characterization did not deal with Samuelson's conceptual concern regarding IA, namely, that at higher levels, players do not consider possible strategies that were used to justify their choice of strategy at lower levels. In this paper, we give a characterization of IA using the all I know operator that does deal with Samuelson's concern. However, it uses LPSs. We then show how to modify the characterization using notions of "approximate belief" and "approximately all I know" so as to deal with Samuelson's concern while still working with probability structures.

cs.GT↗
arXiv2019

Abstracting Causal Models

We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) called exact transformation that applies to probabilistic causal models, moving to a notion of uniform transformation that applies to deterministic causal models and does not allow differences to be hidden by the "right" choice of distribution, and then to abstraction, where the interventions of interest are determined by the map from low-level states to high-level states, and strong abstraction, which takes more seriously all potential interventions in a model, not just the allowed interventions. We show that procedures for combining micro-variables into macro-variables are instances of our notion of strong abstraction, as are all the examples considered by Rubenstein et al.

cs.AI↗
arXiv2019

Approximate Causal Abstraction

Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal model offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction.

cs.AI↗
arXiv2019

Security in Asynchronous Interactive Systems

Secure function computation has been thoroughly studied and optimized in the past decades. We extend techniques used for secure computation to simulate arbitrary protocols involving a mediator. The key feature of our notion of simulation is that it is bidirectional: not only does the simulation produce only outputs that could happen in the original protocol, but the simulation produces all such outputs. In a synchronous system, it can be shown that this requirement can already be achieved by the standard notion of secure computation. However, in an asynchronous system, new subtleties arise because the scheduler can influence the output. We provide a construction that is secure if $n > 4t$, where $t$ is the number malicious agents, which is provably the best possible. We also show that our construction satisfies additional security properties even if $3t < n \le 4t$.

cs.CR↗
arXiv2019

Blameworthiness in Multi-Agent Settings

We provide a formal definition of blameworthiness in settings where multiple agents can collaborate to avoid a negative outcome. We first provide a method for ascribing blameworthiness to groups relative to an epistemic state (a distribution over causal models that describe how the outcome might arise). We then show how we can go from an ascription of blameworthiness for groups to an ascription of blameworthiness for individuals using a standard notion from cooperative game theory, the Shapley value. We believe that getting a good notion of blameworthiness in a group setting will be critical for designing autonomous agents that behave in a moral manner.

cs.CY↗
arXiv2018

Partial Awareness

We develop a modal logic to capture partial awareness. The logic has three building blocks: objects, properties, and concepts. Properties are unary predicates on objects; concepts are Boolean combinations of properties. We take an agent to be partially aware of a concept if she is aware of the concept without being aware of the properties that define it. The logic allows for quantification over objects and properties, so that the agent can reason about her own unawareness. We then apply the logic to contracts, which we view as syntactic objects that dictate outcomes based on the truth of formulas. We show that when agents are unaware of some relevant properties, referencing concepts that agents are only partially aware of can improve welfare.

cs.LO↗
arXiv2018

Towards Formal Definitions of Blameworthiness, Intention, and Moral Responsibility

We provide formal definitions of degree of blameworthiness and intention relative to an epistemic state (a probability over causal models and a utility function on outcomes). These, together with a definition of actual causality, provide the key ingredients for moral responsibility judgments. We show that these definitions give insight into commonsense intuitions in a variety of puzzling cases from the literature.

cs.AI↗
arXiv2018

Implementing Mediators with Asynchronous Cheap Talk

A mediator can help non-cooperative agents obtain an equilibrium that may otherwise not be possible. We study the ability of players to obtain the same equilibrium without a mediator, using only cheap talk, that is, nonbinding pre-play communication. Previous work has considered this problem in a synchronous setting. Here we consider the effect of asynchrony on the problem, and provide upper bounds for implementing mediators. Considering asynchronous environments introduces new subtleties, including exactly what solution concept is most appropriate and determining what move is played if the cheap talk goes on forever. Different results are obtained depending on whether the move after such "infinite play" is under the control of the players or part of the description of the game.

cs.DC↗
arXiv2017

Is state-dependent valuation more adaptive than simpler rules?

McNamara, Trimmer, and Houston (2012) claim to provide an explanation of certain systematic deviations from rational behavior using a mechanism that could arise through natural selection. We provide an arguably much simpler mechanism in terms of computational limitations, that performs better in the environment described by McNamara, Trimmer, and Houston (2012). To argue convincingly that animals' use of state-dependent valuation is adaptive and is likely to be selected for by natural selection, one must argue that, in some sense, it is a better approach than the simple strategies that we propose.

q-bio.PE↗
arXiv2017

Games With Tolerant Players

A notion of pi-tolerant equilibrium is defined that takes into account that players have some tolerance regarding payoffs in a game. This solution concept generalizes Nash and refines epsilon-Nash equilibrium in a natural way. We show that pi-tolerant equilibrium can explain cooperation in social dilemmas such as Prisoner's Dilemma and the Public Good game. We then examine the structure of particularly cooperative pi-tolerant equilibria, where players are as cooperative as they can be, subject to their tolerances, in Prisoner's Dilemma. To the extent that cooperation is due to tolerance, these results provide guidance to a mechanism designer who has some control over the payoffs in a game, and suggest ways in which cooperation can be increased.

cs.GT↗
arXiv2017

An Epistemic Foundation for Authentication Logics (Extended Abstract)

While there have been many attempts, going back to BAN logic, to base reasoning about security protocols on epistemic notions, they have not been all that successful. Arguably, this has been due to the particular logics chosen. We present a simple logic based on the well-understood modal operators of knowledge, time, and probability, and show that it is able to handle issues that have often been swept under the rug by other approaches, while being flexible enough to capture all the higher- level security notions that appear in BAN logic. Moreover, while still assuming that the knowledge operator allows for unbounded computation, it can handle the fact that a computationally bounded agent cannot decrypt messages in a natural way, by distinguishing strings and message terms. We demonstrate that our logic can capture BAN logic notions by providing a translation of the BAN operators into our logic, capturing belief by a form of probabilistic knowledge.

cs.CR↗
arXiv2017

A Knowledge-Based Analysis of the Blockchain Protocol

At the heart of the Bitcoin is a blockchain protocol, a protocol for achieving consensus on a public ledger that records bitcoin transactions. To the extent that a blockchain protocol is used for applications such as contract signing and making certain transactions (such as house sales) public, we need to understand what guarantees the protocol gives us in terms of agents' knowledge. Here, we provide a complete characterization of agent's knowledge when running a blockchain protocol using a variant of common knowledge that takes into account the fact that agents can enter and leave the system, it is not known which agents are in fact following the protocol (some agents may want to deviate if they can gain by doing so), and the fact that the guarantees provided by blockchain protocols are probabilistic. We then consider some scenarios involving contracts and show that this level of knowledge suffices for some scenarios, but not others.

cs.CR↗
arXiv2017

From Type Spaces to Probability Frames and Back, via Language

We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this "language parameter" is made explicit, it reveals a close relationship between universal type spaces and canonical models: namely, that they are essentially the same construct. As the nature of a canonical model depends heavily on the background logic used to generate it, this work suggests a new view into a corresponding landscape of universal type spaces.

cs.LO↗
arXiv2016

Bayesian Games with Intentions

We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games, and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.

cs.GT↗
arXiv2016

Translucent Players: Explaining Cooperative Behavior in Social Dilemmas

In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is particularly puzzling. Here we propose a novel approach to explain cooperation, assuming what Halpern and Pass call translucent players. Typically, players are assumed to be opaque, in the sense that a deviation by one player in a normal-form game does not affect the strategies used by other players. But a player may believe that if he switches from one strategy to another, the fact that he chooses to switch may be visible to the other players. For example, if he chooses to defect in Prisoner's Dilemma, the other player may sense his guilt. We show that by assuming translucent players, we can recover many of the regularities observed in human behavior in well-studied games such as Prisoner's Dilemma, Traveler's Dilemma, Bertrand Competition, and the Public Goods game.

cs.GT↗