In ethics, individual responsibility is often defined through Frankfurt's principle of alternative possibilities. This definition is not adequate in a group decision-making setting because it often results in the lack of a responsible party or "responsibility gap". One of the existing approaches to address this problem is to consider group responsibility. Another, recently proposed, approach is "higher-order" responsibility. The paper considers the problem of determining whether higher-order responsibility up to a given degree is sufficient to close the responsibility gap and analyses the computational complexity of this problem.

Traditionally, the goal of mechanism design was to promote socially desirable behaviour of rational agents, to achieve fairness, or to promote efficiency. I would like to suggest a new subfield of mechanism design, Responsible Mechanism Design, focused on achieving individual accountability of agents for their contributions to the outcome of collective decisions.

The paper proposes to treat object awareness as a form of knowledge, breaking the tradition in the existing literature on awareness. It distinguishes the de re and de dicto forms of such knowledge. The work introduces two modalities capturing these forms and formally specifies their meaning using a version of 2D-semantics. The main technical result is a sound and complete logical system describing the interplay between the two proposed modalities and the standard "knowledge of the fact" modality.

A law in a multiagent system is a set of constraints imposed on agents' behaviours to avoid undesirable outcomes. The paper considers two types of laws: useful laws that, if followed, completely eliminate the undesirable outcomes and gap-free laws that guarantee that at least one agent can be held responsible each time an undesirable outcome occurs. In both cases, we study the problem of finding a law that achieves the desired result by imposing the minimum restrictions. We prove that, for both types of laws, the minimisation problem is NP-hard even in the simple case of one-shot concurrent interactions. We also show that the approximation algorithm for the vertex cover problem in hypergraphs could be used to efficiently approximate the minimum laws in both cases.

Common knowledge/belief in rationality is the traditional standard assumption in analysing interaction among agents. This paper proposes a graph-based language for capturing significantly more complicated structures of higher-order beliefs that agents might have about the rationality of the other agents. The two main contributions are a solution concept that captures the reasoning process based on a given belief structure and an efficient algorithm for compressing any belief structure into a unique minimal form.

The responsibility gap is a set of outcomes of a collective decision-making mechanism in which no single agent is individually responsible. In general, when designing a decision-making process, it is desirable to minimise the gap. The paper studies the class of mechanisms for which the gap is empty and proposes a concept of an elected dictatorship. It shows that, in a perfect information setting, the gap is empty if and only if the mechanism is an elected dictatorship. It also proves that in an imperfect information setting, the class of gap-free mechanisms is positioned strictly between two variations of the class of elected dictatorships.

Abstract Traditionally, the formulae in modal logic express properties of possible worlds. Prior introduced “egocentric” logics that capture properties of agents rather than of possible worlds. In such a setting, the article proposes the modality “know how to tell apart” and gives a complete logical system describing the interplay between this modality and the knowledge modality. An important contribution of this work is a new matrix-based technique for proving completeness theorems in an egocentric setting.

In many real-world situations, there is often not enough information to know that a certain strategy will succeed in achieving the goal, but there is a good reason to believe that it will. The paper introduces the term "doxastic" for such strategies. The main technical contribution is a sound and complete logical system that describes the interplay between doxastic strategy and belief modalities.

Abstract The article proposes de dicto and de re versions of ‘knowing-who’ modalities as well as studies the interplay between them and modalities ‘knows’ and ‘for all agents’. It shows that neither of these four modalities is definable through a combination of the three others. In addition, a sound and complete logical system describing the properties of de dicto ‘knows who’, ‘knows’ and ‘for all agents’ modalities is presented.

The article proposes a new approach to reasoning about knowledge and strategies in multiagent systems. It emphasizes data, not agents, as the source of strategic knowledge. The approach brings together Armstrong's functional dependency expression from database theory, a data-informed knowledge modality based on a recent work by Baltag and van Benthem, and a newly proposed data-informed strategy modality. The main technical result is a sound and complete logical system that describes the interplay between these three logical operators.

An operation is called covert if it conceals the identity of the actor; it is called clandestine if the very fact that the operation is conducted is concealed. The paper proposes a formal semantics of clandestine operations and introduces a sound and complete logical system that describes the interplay between the distributed knowledge modality and a modality capturing coalition power to conduct clandestine operations.

The paper studies strategic abilities that rise from restrictions on the information sharing in multi-agent systems. The main technical result is a sound and complete logical system that describes the interplay between the knowledge and the strategic ability modalities.

An agent, or a coalition of agents, is blameable for an outcome if she had a strategy to prevent it. In this paper we introduce a notion of limited blameworthiness, with a constraint on the amount of sacrifice required to prevent the outcome. The main technical contribution is a sound and complete logical system for reasoning about limited blameworthiness in the strategic game setting.

The paper studies preferences of agents about other agents in a social network. It proposes a logical system that captures the properties of such preferences, called "likes". The system can express nested constructions "agent likes humbled people", "agent likes those who like humbled people", etc. The main technical results are a model checking algorithm and a sound, complete, and decidable axiomatization of the proposed system.

The paper proposes a data-centred approach to reasoning about the interplay between trust and beliefs. At its core, is the modality "under the assumption that one dataset is trustworthy, another dataset informs a belief in a statement". The main technical result is a sound and complete logical system capturing the properties of this modality.

If an agent, or a coalition of agents, has a strategy, knows that she has a strategy, and knows what the strategy is, then she has a know-how strategy. Several modal logics of coalition power for know-how strategies have been studied before. The contribution of the article is three-fold. First, it proposes a new class of know-how strategies that depend on the intelligence information about the opponents' actions. Second, it shows that the coalition power modality for the proposed new class of strategies cannot be expressed through the standard know-how modality. Third, it gives a sound and complete logical system that describes the interplay between the coalition power modality with intelligence and the distributed knowledge modality in games with imperfect information.

The article proposes a new approach to reasoning about knowledge and strategies in multiagent systems. It emphasizes data, not agents, as the source of strategic knowledge. The approach brings together Armstrong's functional dependency from database theory, a data-informed knowledge modality based on a recent work by Baltag and van Benthem, and a newly proposed data-informed strategy modality. The main technical result is a sound and complete logical system that describes the interplay between these three logical operators.

Abstract Discounting future costs and rewards is a common practice in accounting, game theory and machine learning. In spite of this, existing logics for reasoning about strategies with cost and resource constraints do not account for discounting. The article proposes a sound and complete logical system for reasoning about budget-constrained strategic abilities that incorporates discounting into its semantics.

The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.

The ability of an agent to comprehend a sentence is tightly connected to the agent's prior experiences and background knowledge. The paper suggests to interpret comprehension as a modality and proposes a complete bimodal logical system that describes an interplay between comprehension and knowledge modalities.

An agent, or a coalition of agents, faces an ethical dilemma between several statements if she is forced to make a conscious choice between which of these statements will be true. This paper proposes to capture ethical dilemmas as a modality in strategic game settings with and without limit on sacrifice and for perfect and imperfect information games. The authors show that the dilemma modality cannot be defined through the earlier proposed blameworthiness modality. The main technical result is a sound and complete axiomatization of the properties of this modality with sacrifice in games with perfect information.

Discounting future costs and rewards is a common practice in accounting, game theory, and machine learning. In spite of this, existing logics for reasoning about strategies with cost and resource constraints do not account for discounting. The paper proposes a sound and complete logical system for reasoning about budget-constrained strategic abilities that incorporates discounting into its semantics.

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.

If an agent, or a coalition of agents, has a strategy, knows that she has a strategy, and knows what the strategy is, then she has a know-how strategy. Several modal logics of coalition power for know-how strategies have been studied before. The contribution of the article is three-fold. First, it proposes a new class of know-how strategies that depend on the intelligence information about the opponents’ actions. Second, it shows that the coalition power modality for the proposed new class of strategies cannot be expressed through the standard know-how modality. Third, it gives a sound and complete logical system that describes the interplay between the coalition power modality with intelligence and the distributed knowledge modality in games with imperfect information.

Abstract The article compares two different approaches of incorporating probability into coalition logics. One is based on the semantics of games with stochastic transitions and the other on games with the stochastic failures. The work gives an example of a non-trivial property of coalition power for the first approach and a complete axiomatization for the second approach. It turns out that the logical properties of the coalition power modality under the second approach depend on whether the modal language allows the empty coalition. The main technical results for the games with stochastic failures are a strong completeness theorem for the logical system without the empty coalition and an incompleteness theorem which shows that there is no strongly complete logical system in the language with the empty coalition.

The article proposes a trimodal logical system that can express the strategic ability of coalitions to learn from their experience. The main technical result is the completeness of the proposed system.

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.

Logical systems containing knowledge and know-how modalities have been investigated in several recent works. Independently, epistemic modal logics in which every knowledge modality is labeled with a degree of uncertainty have been proposed. This article combines these two research lines by introducing a bimodal logic containing knowledge and know-how modalities, both labeled with a degree of uncertainty. The main technical results are soundness, completeness, and incompleteness of the proposed logical system with respect to two classes of semantics.

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.

The article generalizes the standard threshold models of diffusion in social networks by introducing the notion of recalcitrant agents, i.e. agents that are fully resistant to the diffusion process. The focus of the article is on capturing a ternary influence relation between groups of agents: agents in one group can indirectly influence agents in another group in spite of the agents in the third group being recalcitrant. The main technical result is a sound and complete axiomatization of this relation.

The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by a weaker principle. The main technical results are soundness and completeness theorems for the logical systems describing properties of navigability with and without perfect recall.

The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness theorems for the proposed logical system.

The article studies navigability of an autonomous agent in a maze where some rooms may be indistinguishable. In a previous work the authors have shown that the properties of navigability in such a setting depend on whether an agent has perfect recall. Navigability by strategies with perfect recall is a transitive relation and navigability by memoryless strategies is not. Independently, Li and Wang proposed a notion of navigability with intermediate constraints for linear navigation strategies. Linear strategies are different from both perfect recall and memoryless strategies. This article shows that a certain form of transitivity, expressible in the language with intermediate constraints, holds for memoryless strategies. The main technical result is a sound and complete logical system describing the properties of memoryless strategies in the language with intermediate constraints.

The paper introduces a notion of a budget-constrained multiagent transition system that associates two financial parameters with each transition: a pre-transition minimal budget requirement and a post-transition profit. The paper also proposes a new modal language for reasoning about such a system. The language uses a modality labeled by agent as well as by budget and profit constraints. The main technical result is a sound and complete logical system that describes all universal properties of this modality. Among these properties is a form of Transitivity axiom that captures the interplay between the budget and profit constraints.

The article introduces a modal logic for reasoning about combined effect of economic policies imposed on a group of rational agents. Modalities in this language are labelled by policies applied to the players in a strategic game. The resulting logical system allows to reason about properties that are true in all Nash equilibria of the game modified by a specific policy. The main technical result is the completeness theorem for the proposed logical system.

The article investigates epistemic properties of information flow under communication protocols with a given topological structure of the communication network. The main result is a sound and complete logical system that describes all such properties. The system consists of a variation of the multi-agent epistemic logic S5 extended by a new network-specific Gateway axiom.

Although first proposed in the database theory as properties of functional dependencies between attributes, Armstrong’s axioms capture general principles of information flow by describing properties of dependencies between sets of pieces of information. This article generalizes Armstrong’s axioms to a setting in which there is a cost associated with information. The proposed logical system captures general principles of dependencies between pieces of information constrained by a given budget.

The notion of interchangeability was introduced by Nash in one of his original papers on equilibria in strategic games. It has been recently shown that propositional theory of this relation is the same as propositional theories of the non-deducibility relation in the information flow theory, the independence relation in probability theory, and the non-interference relation in concurrency theory. Propositional theories of conditional non-deducibility and conditional independence have been studied before. This article introduces a notion of conditional interchangeability and gives complete axiomatization of this relation with conditioning by a single player.

The notion of interchangeability has been introduced by John Nash in one of his original papers on equilibria. This article studies properties of Nash equilibria interchangeability in cellular games that model behaviour of infinite chain of homogeneous economic agents. The article shows that there are games in the which strategy of any given player is interchangeable with strategies of players in an arbitrary large neighbourhood of the given player, but is not interchangeable with the strategy of a remote player outside of the neighbourhood. The main technical result is a sound and complete logical system describing universal properties of interchangeability common to all cellular games.

The interchangeability property of Nash equilibria in two-player zero-sum games is well known. This article studies possible generalizations of this property to multi-player zero-sum games.Aform of interchangeability property for strict Nash equilibria in such games is established. It is also shown, by proving a completeness theorem, that strict Nash equilibria do not satisfy any other non-trivial properties.

The article introduces a new formal system, the calculus of cooperation, for reasoning about coalitions of players in a certain class of games. The calculus is an extension of the propositional intuitionistic logic that adds a coalition parameter to intuitionistic implication. The system is shown to be sound and complete with respect to a game semantics. One intended application of the calculus of cooperation is the verification of privacy properties in multiparty computation protocols. The article argues that such properties can be established by providing a set of strategies for a non-zero-sum, perfect information game based on the protocol. It concludes with several examples of such verifications formalized in the calculus of cooperation.

The paper introduces and studies the ternary relation "secret a reveals at least as much information about secret c as secret b." In spite of its seeming simplicity, this relation has many non-trivial properties. The main result is a complete infinite axiomatization of the propositional theory of this relation.

The paper proposes Logic of Secrets in Collaboration Networks, a formal logical system for reasoning about a set of secrets established over a fixed configuration of communication channels. The system's key feature, a multi-channel relation called independence, is a generalization of a two-channel relation known in the literature as nondeducibility. The main result is the completeness of the proposed system with respect to a semantics of secrets.