What is the role of the player in games? To what extent do we allow them to feel that *their* decisions or actions are important, and that *they* have succeeded because they did things *their* way?

Thats really the whole Linear Versus Non-Linear battle.

Do we go open-ended gameplay, or strict one-solution puzzle?

(I find the strict one-solution puzzles are great when the solution is pretty intuitive, or has an internal open-ended strategy format.

Their role is to play, have fun in the gameworld, and escape the real world for some time. In RPG''s there is a little more investment in a role. I don''t think you have to worry about this choice of theirs so much as your choices as a designer guided by the rules you write. The rules are going define the context in which the player plays the game anyway. The width of the context is the latitude we provide them to have a verisimilitudinous experience "as if" they are doing things their way.

They are still going to get to the end of the level or not no matter which choices they make. They will still want to win, or get to the end of the game, which by definition is linear. Non-linear entertainment is having a hard time proving that it even exists, because even a game has an objective to get to, proving there is an end, and starting the game wherever it starts is the beginning, the "non-linearity" you speak of is really just not a straight line but a bunch of alternative lines that will eventually lead back to the forward progress of the gameplay.

All those alternative end up back at the core line of action sooner or later, so no open endedness exists, just big tangents to explore that lead back to the main line of action.

There does not have to be an either or situation extant, because one of the choices under scrutinization appears to just be a variant of linear choice. What matter is you design for the lattitude that the player feels they have choice and decision at the scale where they feel like they are in control of the game, but indeed, only the designer really is. You as the designer are just defining the box they get to run around in, and their escapist psychology will fill in the fantasy they are off in their own little world doing what they want to do.

Adventuredesign
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You know, Socrates never told us that ''know thyself'' sometimes came by way of ''scare thyself''.