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I wonder:
if you had an agent that obviously did have goals (let's say, a player in a game, whose goal is to win, and who plays the optimal strategy) could you deduce those goals from behavior alone?
Let's say you're studying the game of Connect Four, but you have no idea what constitutes "winning" or "losing." You watch enough games that you can map out a game tree. In state X of the world, a player chooses option A over other possible options, and so on. From that game tree, can you deduce that the goal of the game was to get four pieces in a row?
I don't know the answer to this question. But it seems important. If it's possible to identify, given a set of behaviors, what goal they're aimed at, then we can test behaviors (human, animal, algorithmic) for hidden goals. If it's not possible, that's very important as well; because that means that even in a simple game, where we know by construction that the players are "rational" goal-maximizing agents, we can't detect what their goals are from their behavior.
That would mean that behaviors that "seem" goal-less, programs that have no line of code representing a goal, may in fact be behaving in a way that corresponds to maximizing the likelihood of some event; we just can't deduce what that "goal" is. In other words, it's not as simple as saying "That program doesn't have a line of code representing a goal." Its behavior may encode a goal indirectly. Detecting such goals seems like a problem we would really want to solve.
Human games (of the explicit recreational kind) tend to have stopping rules isomorphic with the game's victory conditions. We would typically refer to those victory conditions as the objective of the game, and the goal of the participants. Given a complete decision tree for a game, even a messy stochastic one like Canasta, it seems possible to deduce the conditions necessary for the game to end.
An algorithm that doesn't stop (such as the blue-minimising robot) can't have anything analogous to the victory condition of a game. In that sense, its goals can't be analysed in the same way as those of a Connect Four-playing agent.
So if the blue-minimising robot was to stop after 3 months (the stop condition is measured by a timer), can we say that the robot's goal is to stay "alive" for 3 months? I cannot see a necessry link between deducing goals and stopping conditions.
A "victory condition" is another thing, but from a decision tree, can you deduce who loses (for Connect Four, perhaps it is the one who reaches the first four that loses).
By "victory condition", I mean a condition which, when met, determines the winning, losing and drawing status of all players in the game. A stopping rule is necessary for a victory condition (it's the point at which it is finally appraised), but it doesn't create a victory condition, any more than imposing a fixed stopping time on any activity creates winners and losers in that activity.
Can we know the victory condition from just watching the game?
Just to underscore a broader point: recreational games have various characteristics which don't generalise to all situations modelled game-theoretically. Most importantly, they're designed to be fun for humans to play, to have consistent and explicit rules, to finish in a finite amount of time (RISK notwithstanding), to follow some sort of narrative and to have means of unambiguously identifying winners.
Anecdotally, if you're familiar with recreational games, it's fairly straightforward to identify victory conditions in games just by watching them being played, because their conventions mean those conditions are drawn from a considerably reduced number of possibilities. There are, however, lots of edge- and corner-cases where this probably isn't possible without taking a large sample of observations.
Well, even if we have conditions to end game we still don't know if player's goal is to end the game (poker) or to avoid ending it for as long as possible (Jenga). We can try to deduce it empirically (if it's possible to end game on first turn effortlesly, then goal is to keep going), but I'm not sure if it applies to all games.
If ending the game quickly or slowly is part of the objective, in what way is it not included in the victory conditions?
I mean it could not be visible from a game log (for complex games). We will see the combination of pieces when game ends (ending condition), but it can be not enough.
I don't think we're talking about the same things here.
A decision tree is an optimal path through all possible decision in a game, not just the history of any given game.
"Victory conditions" in the context I'm using are the conditions that need to be met in order for the game to end, not simply the state of play at the point when any given game ends.