Neat. Why is it worth calling U “utility,” or even utility-like, though? If I tell you the set of things that I observe that significantly change my behavior, this tells you a lot about me but it doesn’t tell you which function of these observations I’m using to make decisions.
E.g. both teams in a soccer game will respond to the position of the ball (the ball is in U—or some relaxed notion of it, since I think your full notion might be too strong), but want to do different things with it.
I think the position of the ball is in V, since the players are responding to the position of the ball by forcing it towards the goal. It’s difficult to predict the long-term position of the ball based on where it is now. The position of the opponent’s goal would be an example of something in U for both teams. In this case both team’s utility-functions contain a robust pointer to the goal’s position.
Neat. Why is it worth calling U “utility,” or even utility-like, though? If I tell you the set of things that I observe that significantly change my behavior, this tells you a lot about me but it doesn’t tell you which function of these observations I’m using to make decisions.
E.g. both teams in a soccer game will respond to the position of the ball (the ball is in U—or some relaxed notion of it, since I think your full notion might be too strong), but want to do different things with it.
I think the position of the ball is in V, since the players are responding to the position of the ball by forcing it towards the goal. It’s difficult to predict the long-term position of the ball based on where it is now. The position of the opponent’s goal would be an example of something in U for both teams. In this case both team’s utility-functions contain a robust pointer to the goal’s position.