Knowledge and Blameworthiness

Proceedings of the AAAI Conference on Artificial Intelligence, 2019

There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical system that describes properties of blameworthiness in one-shot games.

Artificial Intelligence

Blameworthiness of an agent or a coalition of agents can be defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should be a minimal one that had a strategy to prevent the outcome. In this article we argue that in the settings with imperfect information, not only should the coalition have had a strategy, but it also should be the minimal one that knew that it had a strategy and what the strategy was. The main technical result of the article is a sound and complete bimodal logic that describes the interplay between knowledge and blameworthiness in strategic games with imperfect information.

2020

The paper investigates the second-order blameworthiness or duty to warn modality "one coalition knew how another coalition could have prevented an outcome". The main technical result is a sound and complete logical system that describes the interplay between the distributed knowledge and the duty to warn modalities.

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

The paper studies two forms of responsibility, seeing to it and being blamable, in the setting of strategic games with imperfect information. The paper shows that being blamable is definable through seeing to it, but not the other way around. In addition, it proposes a bimodal logical system that describes the interplay between the seeing to it modality and the individual knowledge modality.

Proceedings of the AAAI Conference on Artificial Intelligence, 2020

Security games are an example of a successful real-world application of game theory. The paper defines blameworthiness of the defender and the attacker in security games using the principle of alternative possibilities and provides a sound and complete logical system for reasoning about blameworthiness in such games. Two of the axioms of this system capture the asymmetry of information in security games.

2008

Results in social choice theory such as the Arrow and Gibbard-Satterthwaite theorems constrain the existence of rational collective decision making procedures in groups of agents. The Gibbard-Satterthwaite theorem says that no voting procedure is strategy-proof. That is, there will always be situations in which it is in a voter's interest to misrepresent its true preferences i.e., vote strategically. We present some properties of strategic voting and then examine-via a bimodal logic utilizing epistemic and strategizing modalities-the knowledge-theoretic properties of voting situations and note that unless the voter knows that it should vote strategically, and how, i.e., knows what the other voters' preferences are and that it should vote a certain preference P , the voter will not strategize. Our results suggest that opinion polls in election situations effectively serve as the first n − 1 stages in an n stage election.

Games and Economic Behavior, 1996

Mathematical Social Sciences, 1991

This paper attempts to explain the Nash equilibrium concept from the viewpoint of its one-shot play interpretation. We consider a final decision to be made by each player before the game is actually played. We formalize this game situation in terms of an infinitary first-order predicate logic. Then we give an axiom for final decisions-in the two-person case, the central requirement for this axiom is: for players i and j, if x is a possible final decision for player i, then (1) player i knows that x is his final decision; (2) there is a final decision y for player j; and (3) for any final decision y for j, x is a best response to y and player i knows that y is j's final decision. The entire axiom takes the form of the common knowledge of the above requirement by its very nature. We assume that the complete logical abilities of the players are common knowledge. Then we prove that for solvable games in Nash's sense, x is a final decision for player i iff it is common knowledge that x is a Nash strategy. A similar result will be obtained for unsolvable games.

International Game Theory Review, 2013

We propose a theory of the interaction between knowledge and games. Epistemic game theory is of course a well-developed subject but there is also a need for a theory of how some agents can affect the outcome of a game by affecting the knowledge which other agents have and thereby affecting their actions. We concentrate on games of incomplete or imperfect information, and study how conservative, moderate, or aggressive players might play such games. We provide models for the behavior of a knowledge manipulator who seeks to manipulate the knowledge states of active players in order to affect their moves and to maximize her own payoff even while she herself remains inactive, except for influencing the states of knowledge of the other players.

Studia Logica 86, 3, 2007, 353-373. Special issue on formal epistemology, edited by B. Fitelson