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Hard and soft preparation sets in Boolean games

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Figure

Figure 1. A three-player game, in which player 1 controls pin the top right corners of the cells indicate the players that have their goals satisfied inthe respective outcome
Figure 2. A three-player game (notational conventions as in Figure 1). Here p ∧ s is aprep formula but none of its satisfying outcomes, pqrs, pqrs¯, pqrs¯, and pq¯rs¯, is a Nashequilibrium
Figure 3. Containment relations between types of formulas.
Figure 4. A three-player game illustrating coalition merging (notational conventions as inFigure 1)
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