Relaxing Exclusive Control in Boolean Games

Belardinelli, Francesco; Grandi, Umberto; Herzig, Andreas; Longin, Dominique; Lorini, Emiliano; Novaro, Arianna; Perrussel, Laurent

doi:10.4204/eptcs.251.4

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…For the strategies, instead of merely revealing the value of propositional variables, we could consider revealing the value of any epistemic proposition, as already considered in for more complex, arbitrary, Kripke models. Instead of having merely partitions (exhaustive and exclusive) of all variables, one could consider overlapping sets of variables (exhaustive but not exclusive, so more than one player may observe the same variables) 7 as for example employed in (Belardinelli, Grandi, Herzig, Longin, Lorini, Novaro, & Perrussel, 2017). Doing the same for Boolean games would create the possibility of conflict, as not more than one player can control the value of a variable.…”

Section: Discussionmentioning

confidence: 99%

Boolean Observation Games

Van Ditmarsch,

Simon

2024

jair

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We introduce Boolean Observation Games, a subclass of multi-player finite strategic games with incomplete information and qualitative objectives. In Boolean observation games, each player is associated with a finite set of propositional variables of which only it can observe the value, and it controls whether and to whom it can reveal that value. It does not control the given, fixed, value of variables. Boolean observation games are a generalization of Boolean games, a well-studied subclass of strategic games but with complete information, and wherein each player controls the value of its variables. In Boolean observation games, player goals describe multi-agent knowledge of variables. As in classical strategic games, players choose their strategies simultaneously and therefore observation games capture aspects of both imperfect and incomplete information. They require reasoning about sets of outcomes given sets of indistinguishable valuations of variables. An outcome relation between such sets determines what the Nash equilibria are. We present various outcome relations, including a qualitative variant of ex-post equilibrium. We identify conditions under which, given an outcome relation, Nash equilibria are guaranteed to exist. We also study the complexity of checking for the existence of Nash equilibria and of verifying if a strategy profile is a Nash equilibrium. We further study the subclass of Boolean observation games with ‘knowing whether’ goal formulas, for which the satisfaction does not depend on the value of variables. We show that each such Boolean observation game corresponds to a Boolean game and vice versa, by a different correspondence, and that both correspondences are precise in terms of existence of Nash equilibria.

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Section: Discussionmentioning

confidence: 99%

Boolean Observation Games

Van Ditmarsch,

Simon

2024

jair

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“…It has since been investigated in relation with the transfer of control [33], the dynamic logic of propositional assignments [28], non-exclusive control [26]. Further, in [5] it is proved that shared control can be simulated by means of exclusive control. However, the present contribution differs from most of the works in this line in two key aspects.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Model Checking Strategic Abilities in Information-sharing Systems

Belardinelli¹,

Boureanu²,

Dima³

et al. 2022

Preprint

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We introduce a subclass of concurrent game structures (CGS) with imperfect information in which agents are endowed with private data-sharing capabilities. Importantly, our CGSs are such that it is still decidable to model-check these CGSs against a relevant fragment of ATL. These systems can be thought as a generalisation of architectures allowing information forks, in the sense that, in the initial states of the system, we allow information forks from agents outside a given set A to agents inside this A. For this reason, together with the fact that the communication in our models underpins a specialised form of broadcast, we call our formalism A-cast systems.To underline, the fragment of ATL for which we show the model-checking problem to be decidable over A-cast is a large and significant one; it expresses coalitions over agents in any subset of the set A. Indeed, as we show, our systems and this ATL fragments can encode security problems that are notoriously hard to express faithfully: terrorist-fraud attacks in identity schemes.

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“…This paper builds on our previous work in which the assumption was that of complete information (Grandi et al, 2017). In complementary work, we studied similar models at a higher perspective, that of concurrent game structures in which the control of Boolean variables is shared among sets of agents, showing that the computational complexity of strategic reasoning is left unchanged-with respect to structures with exclusive propositional control (Belardinelli et al, 2017). Such structures are used to interpret formulas of Alternating-time Temporal Logic (Alur et al, 2002), a logic that can be used to reason about strategic aspects of iterated games.…”

Section: Related Workmentioning

confidence: 99%

Games of influence

Grandi

Lorini

Novaro

et al. 2021

Journal of Logic and Computation

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In this paper, we present two models for reasoning about strategic actions in opinion diffusion. In both models, the agents are endowed with goals expressed compactly in a suitably defined language of linear temporal logic and are connected in an influence network which defines the underlying opinion diffusion process. The agents can act by exerting their influence or retain from it: in one case, we assume an initial state of incomplete information about the agents’ opinions, while in the other, we assume that the agents have complete information. We investigate the interplay between simple network structures (e.g. certain acyclic graphs) and the existence of game-theoretic solution concepts for the unanimity aggregator. We also give bounds for the computational complexity of strategic reasoning in both our models on arbitrary networks.

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Relaxing Exclusive Control in Boolean Games

Cited by 4 publications

References 12 publications

Boolean Observation Games

Boolean Observation Games

Model Checking Strategic Abilities in Information-sharing Systems

Games of influence

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