Paolo Turrini

Strategic games and truly playable effectivity functions

A well-known result in the logical analysis of cooperative games states that the so-called playable effectivity functions exactly correspond to strategic games. More precisely, this result states that for every playable effectivity function E there exists a strategic game that assigns to coalitions of players exactly the same power as E, and every strategic game generates a playable effectivity function. While the latter direction of the correspondence is correct, we show that the former does not hold for a number of infinite state games. We point out where the original proof of correspondence goes wrong, and we present examples of playable effectivity functions for which no equivalent strategic game exists. Then, we characterize the class of truly playable effectivity functions, that do correspond to strategic games. Moreover, we discuss a construction that transforms any playable effectivity function into a truly playable one while preserving the power of most (but not all) coalitions. We also show that Coalition Logic (CL), a formalism used to reason about effectivity functions, is not expressive enough to distinguish between playable and truly playable effectivity functions, and we extend it to a logic that can make that distinction while still enjoying the good meta-logical properties of CL, such as finite axiomatization and decidability via finite model property.

Coping with shame and sense of guilt: a Dynamic Logic Account

Aim of this work is to provide a formal characterization of those emotions that deal with normative reasoning, such as shame and sense of guilt, to understand their relation with rational action and to ground their formalization on a cognitive science perspective. In order to do this we need to identify the factors that constitute the preconditions and trigger the reactions of shame and sense of guilt in cognitive agents, that is when agents feel ashamed or guilty and what agents do when they feel so. We will also investigate how agents can induce and silence these feelings in themselves, i.e. the analysis of defensive strategies they can employ. We will argue that agents do have control over their emotions and we will analyze some operations they can carry out on them.

A Deontic Logic for Socially Optimal Norms

The paper discusses the interaction properties between preference and choice of coalitions in a strategic interaction. A language is presented to talk about the conflict between coalitionally optimal and socially optimal choices. Norms are seen as social constructions that enable to enforce socially desirable outcomes.

Dependence in games and dependence games

In the multi-agent systems community, dependence theory and game theory are often presented as two alternative perspectives on the analysis of agent interaction. The paper presents a formal analysis of a notion of dependence between players, given in terms of standard game-theoretic notions of rationality such as dominant strategy and best response. This brings the notion of dependence within the realm of game theory providing it with the sort of mathematical foundations which still lacks. Concretely, the paper presents two results: first, it shows how the proposed notion of dependence allows for an elegant characterization of a property of reciprocity for outcomes in strategic games; and second, it shows how the notion can be used to define new classes of coalitional games, where coalitions can force outcomes only in the presence of reciprocal dependencies.

Rational Agents That Blush

A student, supported by his classmates, throws a piece of chalk at the teacher who is writing on the blackboard. The teacher rapidly turns back and promptly catches him in the act. The student blushes and suddenly realizes how bad it was what he did.

Norms in Game Theory

This chapter summarizes two main views on norms and games as emerging in literature on game theory, social science, philosophy and artificial intelligence. The first view originates in the field of mechanism design or implementation theory and characterizes norms as mechanisms enforcing desirable social properties in classes of games. According to the second view, originating from work in the social sciences and evolutionary game theory, norms are studied via the notion of equilibrium and are viewed as emergent social contracts or conventions.

Normative Reasoning and Consequence

In this chapter, we first provide a general introduction to the research area methodology and relevance, then we discuss normative reasoning for multiagent systems, and finally we discuss current research challenges. We cover the main issues in modern deontic logic, which is much broader than the traditional modal logic framework of deontic logic, with an emphasis to our in- tended audience. To emphasize this broadness, we typically refer to deontic logic and normative systems rather than deontic logic only.

Forbidding undesirable agreements: a dependence-based approach to the regulation of multi-agent systems

The purpose of this contribution is to set up a language to evaluate the results of concerted action among interdependent agents against predetermined properties that we can recognise as desirable from a deontic point of view. Unlike the standard view of logics to reason about coalitionally rational action, the capacity of a set of agents to take a rational decision will be restricted to what we will call agreements, that can be seen as solution concepts to a dependence structure present in a certain game. The language will identify in concise terms those agreements that act accordingly or disaccordinglywith the desirable properties arbitrarily set up in the beginning, and will reveal, by logical reasoning, a variety of structural properties of this type of collective action.

An update operator for strategic ability

Coalition Logic does not explicitly talk about the effects of a coalitional move on the strategic ability of the remaining players, while in Game Theory reasoning patterns involving this concept often occur. To fill this gap, we study an update operator for strategic ability update in coalition structures. Its formal connections with the update operators known from Dynamic Epistemic Logic will be discussed.

Agreements as norms

Deontic logic has extensively been used to reason about what a player (or coalition) should do when confronted with several choices at its disposal while being aware of its opponents possibilities. So far this line of research, inspired by Hortys utilitarian account of obligations, has been focused on interpreting coalitional oughts as rational choices, going on to characterizing game-theoretical solution concepts, such as Nash equilibria. With the present contribution we would like to extend the scope of this account to include contractual aspects of coalitional choices, arguing that deontic logic can be used as a comprehensive reasoning tool for the normative aspects of game theory.