arXiv subjects

Joseph Y. Halpern

Publications and source records attributed to Joseph Y. Halpern.

At least 109 records · Page 6Linked to original sources

arXiv2013

Game Theory with Translucent Players

A traditional assumption in game theory is that players are opaque to one another---if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an unrealistic assumption. We develop a framework for reasoning about games where the players may be translucent to one another; in particular, a player may believe that if she were to change strategies, then the other player would also change strategies. Translucent players may achieve significantly more efficient outcomes than opaque ones. Our main result is a characterization of strategies consistent with appropriate analogues of common belief of rationality. Common Counterfactual Belief of Rationality (CCBR) holds if (1) everyone is rational, (2) everyone counterfactually believes that everyone else is rational (i.e., all players i believe that everyone else would still be rational even if $i$ were to switch strategies), (3) everyone counterfactually believes that everyone else is rational, and counterfactually believes that everyone else is rational, and so on. CCBR characterizes the set of strategies surviving iterated removal of minimax dominated strategies, where a strategy s for player i is minimax dominated by s' if the worst-case payoff for i using s' is better than the best possible payoff using s.

cs.GT↗

arXiv2013

Decision Theory with Resource-Bounded Agents

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein, charges an agent for doing costly computation; the second, initiated by Neyman, does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in a decision problem to be Turing machines, and charge players for the ``complexity'' of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases.

cs.GT↗

arXiv2013

A New Approach to Updating Beliefs

We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by Dempster, and avoids many of the well-known problems of that definition. Just as the conditional probability Pr (lB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function Bel (lB) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower envelope (that is, the inf) of a family of conditional probability functions, and provide a closed form expression for it. An alternate way of understanding our definition of conditional belief is provided by considering ideas from an earlier paper [Fagin and Halpern, 1989], where we connect belief functions with inner measures. In particular, we show here how to extend the definition of conditional probability to non measurable sets, in order to get notions of inner and outer conditional probabilities, which can be viewed as best approximations to the true conditional probability, given our lack of information. Our definition of conditional belief turns out to be an exact analogue of our definition of inner conditional probability.

cs.AI↗

arXiv2013

The Relationship between Knowledge, Belief and Certainty

We consider the relation between knowledge and certainty, where a fact is known if it is true at all worlds an agent considers possible and is certain if it holds with probability 1. We identify certainty with probabilistic belief. We show that if we assume one fixed probability assignment, then the logic KD45, which has been identified as perhaps the most appropriate for belief, provides a complete axiomatization for reasoning about certainty. Just as an agent may believe a fact although phi is false, he may be certain that a fact phi, is true although phi is false. However, it is easy to see that an agent can have such false (probabilistic) beliefs only at a set of worlds of probability 0. If we restrict attention to structures where all worlds have positive probability, then S5 provides a complete axiomatization. If we consider a more general setting, where there might be a different probability assignment at each world, then by placing appropriate conditions on the support of the probability function (the set of worlds which have non-zero probability), we can capture many other well-known modal logics, such as T and S4. Finally, we consider which axioms characterize structures satisfying Miller's principle.

cs.AI↗

arXiv2013

Generating New Beliefs From Old

In previous work [BGHK92, BGHK93], we have studied the random-worlds approach -- a particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective (first-order, statistical, and default) information. But allowing a knowledge base to contain only objective information is sometimes limiting. We occasionally wish to include information about degrees of belief in the knowledge base as well, because there are contexts in which old beliefs represent important information that should influence new beliefs. In this paper, we describe three quite general techniques for extending a method that generates degrees of belief from objective information to one that can make use of degrees of belief as well. All of our techniques are bloused on well-known approaches, such as cross-entropy. We discuss general connections between the techniques and in particular show that, although conceptually and technically quite different, all of the techniques give the same answer when applied to the random-worlds method.

cs.AI↗

arXiv2013

Weighted Sets of Probabilities and Minimax Weighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making -- minimizing expected regret -- to obtain minimax weighted expected regret (MWER). We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.

cs.GT↗

arXiv2013

Plausibility Measures: A User's Guide

We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. The lack of structure in a plausibility measure makes it easy for us to add structure on an "as needed" basis, letting us examine what is required to ensure that a plausibility measure has certain properties of interest. This gives us insight into the essential features of the properties in question, while allowing us to prove general results that apply to many approaches to reasoning about uncertainty. Plausibility measures have already proved useful in analyzing default reasoning. In this paper, we examine their "algebraic properties," analogues to the use of + and * in probability theory. An understanding of such properties will be essential if plausibility measures are to be used in practice as a representation tool.

cs.AI↗

arXiv2013

A Qualitative Markov Assumption and its Implications for Belief Change

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. Roughly, revision treats a surprising observation as a sign that previous beliefs were wrong, while update treats a surprising observation as an indication that the world has changed. In general, we would expect that an agent making an observation may both want to revise some earlier beliefs and assume that some change has occurred in the world. We define a novel approach to belief change that allows us to do this, by applying ideas from probability theory in a qualitative setting. The key idea is to use a qualitative Markov assumption, which says that state transitions are independent. We show that a recent approach to modeling qualitative uncertainty using plausibility measures allows us to make such a qualitative Markov assumption in a relatively straightforward way, and show how the Markov assumption can be used to provide an attractive belief-change model.

cs.AI↗

arXiv2013

Defining Explanation in Probabilistic Systems

As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing explanations. We examine two representative approaches to explanation in the literature - one due to Gärdenfors and one due to Pearl - and show that both suffer from significant problems. We propose an approach to defining a notion of "better explanation" that combines some of the features of both together with more recent work by Pearl and others on causality.

cs.AI↗

arXiv2013

Probability Update: Conditioning vs. Cross-Entropy

Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization, to handle updates that involve uncertain information. In this paper we re-examine such a case: van Fraassen's Judy Benjamin problem, which in essence asks how one might update given the value of a conditional probability. We argue that -- contrary to the suggestions in the literature -- it is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as cross-entropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update.

cs.AI↗

arXiv2013

Causes and Explanations: A Structural-Model Approach --- Part 1: Causes

We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother definitions and resolves major difficulties in the traditionalaccount. In a companion paper, we show how the definition of causality can beused to give an elegant definition of (causal) explanation.

cs.AI↗

arXiv2012

Viewpoint: Journals for Certification, Conferences for Rapid Dissemination

The publication culture in Computer Science is different from that of all other disciplines. Whereas other disciplines focus on journal publication, the standard practice in CS has been to publish in a conference and then (sometimes) publish a journal version of the conference paper. We discuss the role of journal publication in CS. Indeed, it is through publication in selective, leading conferences that the quality of CS research is typically assessed.

cs.DL↗

arXiv2012

Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making-minimizing expected regret-to obtain minimax weighted expected regret (MWER).We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.

cs.GT↗

arXiv2012

Optimizing Scrip Systems: Crashes, Altruists, Hoarders, Sybils and Collusion

Scrip, or artificial currency, is a useful tool for designing systems that are robust to selfish behavior by users. However, it also introduces problems for a system designer, such as how the amount of money in the system should be set. In this paper, the effect of varying the total amount of money in a scrip system on efficiency (i.e., social welfare---the total utility of all the agents in the system) is analyzed, and it is shown that by maintaining the appropriate ratio between the total amount of money and the number of agents, efficiency is maximized. This ratio can be found by increasing the money supply to just below the point that the system would experience a "monetary crash," where money is sufficiently devalued that no agent is willing to perform a service. The implications of the presence of altruists, hoarders, sybils, and collusion on the performance of the system are examined. Approaches are discussed to identify the strategies and types of agents.

cs.GT↗

arXiv2012

Modeling Adversaries in a Logic for Security Protocol Analysis

Logics for security protocol analysis require the formalization of an adversary model that specifies the capabilities of adversaries. A common model is the Dolev-Yao model, which considers only adversaries that can compose and replay messages, and decipher them with known keys. The Dolev-Yao model is a useful abstraction, but it suffers from some drawbacks: it cannot handle the adversary knowing protocol-specific information, and it cannot handle probabilistic notions, such as the adversary attempting to guess the keys. We show how we can analyze security protocols under different adversary models by using a logic with a notion of algorithmic knowledge. Roughly speaking, adversaries are assumed to use algorithms to compute their knowledge; adversary capabilities are captured by suitable restrictions on the algorithms used. We show how we can model the standard Dolev-Yao adversary in this setting, and how we can capture more general capabilities including protocol-specific knowledge and guesses.

cs.CR↗

arXiv2012

Ambiguous Language and Differences in Beliefs

Standard models of multi-agent modal logic do not capture the fact that information is often ambiguous, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents' beliefs regarding whether or not there is ambiguity. We consider the impact of ambiguity on a seminal result in economics: Aumann's result saying that agents with a common prior cannot agree to disagree. This result is known not to hold if agents do not have a common prior; we show that it also does not hold in the presence of ambiguity. We then consider the tradeoff between assuming a common interpretation (i.e., no ambiguity) and a common prior (i.e., shared initial beliefs).

cs.AI↗

arXiv2011

Conditional Plausibility Measures and Bayesian Networks

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures. It is shown that algebraic conditional plausibility measures can be represented using Bayesian networks.

cs.AI↗

arXiv2011

Actual causation and the art of modeling

We look more carefully at the modeling of causality using structural equations. It is clear that the structural equations can have a major impact on the conclusions we draw about causality. In particular, the choice of variables and their values can also have a significant impact on causality. These choices are, to some extent, subjective. We consider what counts as an appropriate choice. More generally, we consider what makes a model an appropriate model, especially if we want to take defaults into account, as was argued is necessary in recent work.

cs.AI↗