# Relaxing Exclusive Control in Boolean Games

arXiv: https://arxiv.org/abs/1707.08736 · HTML: https://mlsanity.com/paper/1707.08736/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2017.

## Built on by (most cited first, 2 of 2)

- [Cyber Physical Games](https://mlsanity.com/paper/2407.05817/) (2024)
- [Model Checking Strategic Abilities in Information-sharing Systems](https://mlsanity.com/paper/2204.08896/) (2022)

## Abstract (arXiv)

In the typical framework for boolean games (BG) each player can change the truth value of some propositional atoms, while attempting to make her goal true. In standard BG goals are propositional formulas, whereas in iterated BG goals are formulas of Linear Temporal Logic. Both notions of BG are characterised by the fact that agents have exclusive control over their set of atoms, meaning that no two agents can control the same atom. In the present contribution we drop the exclusivity assumption and explore structures where an atom can be controlled by multiple agents. We introduce Concurrent Game Structures with Shared Propositional Control (CGS-SPC) and show that they ac- count for several classes of repeated games, including iterated boolean games, influence games, and aggregation games. Our main result shows that, as far as verification is concerned, CGS-SPC can be reduced to concurrent game structures with exclusive control. This result provides a polynomial reduction for the model checking problem of specifications in Alternating-time Temporal Logic on CGS-SPC.