Over the past half decade, we have been exploring the use of logic in the specification and analysis of computational economic mechanisms. We believe that this approach has the potential to bring the same benefits to the design and analysis of computational economic mechanisms that the use of temporal logics and model checking have brought to the specification and analysis of reactive systems. In this paper, we give a survey of our work. We first discuss the use of cooperation logics such as Alternating-time Temporal Logic (ATL) for the specification and verification of mechanisms such as social choice procedures. We motivate the approach, and then discuss the work we have done on extensions to ATL to support incomplete information, preferences, and quantification over coalitions. We then discuss is the use of ATL-like cooperation logics in the development of social laws.

Summary. It cannot always be assumed that agents will behave as they are supposed to behave. Agents may fail to comply with system norms deliberately, in open agent systems or other competitive settings, or unintentionally, in unreliable environments because of factors beyond their control. In addition to analysing system properties that hold if specifications/norms are followed correctly, it is also necessary to predict, test, and verify the properties that hold if system norms are violated, and to test the effectiveness of introducing proposed control, enforcement, and recovery mechanisms. C+ ++ is an extended form of the action language C+ of Giunchiglia, Lee, Lifschitz, McCain, and Turner, designed for representing norms of behaviour and institutional aspects of (human or computer) societies. We present the permission component of C+ ++ and then illustrate on a simple example how it can be used in conjunction with standard model checkers for the temporal logic CTL to verify system properties in the case where agents may fail to comply with system norms. 1

Abstract. In this paper, we combine deontic logic with Alternatingtime Temporal Logic (ATL) into a framework that makes it possible to model and reason about obligations and abilities of agents. The way both frameworks are combined is technically straightforward: we add deontic accessibility relations to ATL models (concurrent game structures), and deontic operators to the language of ATL (an additional operator UP is proposed for “unconditionally permitted ” properties, similar to the “all I know ” operator from epistemic logic). Our presentation is rather informal: we focus on examples of how obligations (interpreted as requirements) can be confronted with ways of satisfying them by actors of the game. Though some formal results are presented, the paper should not be regarded as a definite statement on how logics of obligation and strategic ability must be combined; instead, it is intended for stimulating discussion about such kinds of reasoning, and the models that can underpin it.

In this paper, we investigate the link between logics of games and “mentalistic” logics of rational agency, in which agents are characterized in terms of attitudes such as belief, desire and intention. In particular, we investigate the possibility of extending the logics of games with the notion of agents ’ intentions (in the sense of Cohen and Levesque’s BDI theory). We propose a new operator (straσ) that can be used to formalize reasoning about outcomes of strategies in game-like scenarios. We briefly discuss the relationship between intentions and goals in this new framework, and show how capture dynamic logic-like constructs can be captured. Finally, we demonstrate how game-theoretical concepts like Nash equilibrium can be expressed to reason about rational intentions and their consequences.

Power indices such as the Banzhaf index were originally developed within voting theory in an attempt to rigorously characterise the influence that a voter is able to wield in a particular voting game. In this paper, we show how such power indices can be applied to understanding the relative importance of agents when we attempt to devise a coordination mechanism using the paradigm of social laws, or normative systems. Understanding how pivotal an agent is with respect to the success of a particular social law is of benefit when designing such social laws: we might typically aim to ensure that power is distributed evenly amongst the agents in a system, to avoid bottlenecks or single points of failure. After formally defining the framework and illustrating the role of power indices in it, we investigate the complexity of computing these indices, showing that the characteristic complexity result is #P-completeness. We then investigate cases where computing indices is computationally easy.

In this paper we look at the problem of composing services that export their behavior in terms of a transition system, characterizing the choices of actions given to a client at each point in time. The composition consists of synthesizing an orchestrator that coordinates the available services so as to mimic the desired target service asked by the client. Specifically, in this paper we study the “conformant form ” of the problem, where available services are partially controllable and partially observable, and hence, the orchestrator has to make its decisions exploiting the observations made so far only. We give a sound and complete procedure to synthesize the orchestrator in such case, and characterize the computational complexity of the problem. The procedure is based on working with belief (or knowledge) states, a standard technique to tackle conformant planning. Moreover we show that, although in general unavoidable, the powerset construction at the base of the belief state approach can be delegated to the symbolic manipulations of the game-structure model checking tool (TLV), which can be used to efficiently implement the orchestrator synthesis procedure.

Although normative systems, or social laws, have proved to be a highly influential approach to coordination in multi-agent systems, the issue of compliance to such normative systems remains problematic. In all real systems, it is possible that some members of an agent population will not comply with the rules of a normative system, even if it is in their interests to do so. It is therefore important to consider the extent to which a normative system is robust, i.e., the extent to which it remains effective even if some agents do not comply with it. We formalise and investigate three different notions of robustness and related decision problems. We begin by considering sets of agents whose compliance is necessary and/or sufficient to guarantee the effectiveness of a normative system; we then consider quantitative approaches to robustness, where we try to identify the proportion of an agent population that must comply in order to ensure success, and finally, we consider a more general approach, where we characterise the compliance conditions required for success as a logical formula.

Social norms enable coordination in multiagent systems by constraining agent behaviour in order to achieve a social objective. Automating the design of social norms has been shown to be NP-complete, requiring a complete state enumeration. A planning-based solution has been proposed previously to improve performance. This approach leads to verbose, problem-specific norms due to the propositional representation of the domain. We present a first-order extension of this work that benefits from state and operator abstractions to synthesise more expressive, generally applicable norms. We propose optimisations that can be used to reduce the search performed during synthesis, and formally prove the correctness of these optimisations. Finally, we empirically illustrate the benefits of these optimisations in an example domain.

The Game Description Language (GDL) is a special purpose declarative language for defining games. GDL is used in the AAAI General Game Playing Competition, which tests the ability of computer programs to play games in general, rather than just the ability to play a specific game. Participants in the competition are provided with a previously unknown game specified in GDL, and are required to dynamically and autonomously determine how best to play this game. Recently, there has been much interest in the use of strategic cooperation logics for reasoning about game-like scenarios—the Alternating-time Temporal Logic (ATL) of Alur, Henzinger, and Kupferman is perhaps the best known example. Such logics are specifically intended to support reasoning about game-theoretic properties of multi-agent systems. In short, the aim of this article is to make a concrete link between ATL and GDL, with the ultimate goal of using ATL to reason about GDL-specified games. We make the following contributions. First, we demonstrate that GDL can be understood as a specification language for ATL models, and prove that the problem of interpreting ATL formulae over propositional GDL descriptions is EXPTIME-complete. Second, we use ATL to characterize a class of ‘fair playability’ conditions, which might or might not hold of various games.

In this paper we combine existing work in the area of social laws with a framework for reasoning about knowledge in multi-agent systems. The unifying framework in which this is done is based on Alternating-time Temporal Logic (ATL), to which semantics we add epistemic accessibility relations (to deal with the knowledge), actions (in order to naturally talk about allowed and forbidden actions) and updates (to model the e#ect of the implementation of the constraint in a social law). Apart from a constraint, a social law has an objective: in our formalism, such objectives may refer to the knowledge that agents possess or do not possess. The result is a framework in which we can, for example, express that a desirable property (objective) of a social law is that one agent has the ability to bring about a certain type of knowledge in another agent, or that if one agent knows something, then it should behave in a certain way. We illustrate our approach with a case study, and we use model checking to demonstrate that properties of social laws with respect to this case study.