more on predicting agents

By this definition, you can make it harder for someone to be smarter than you by being more random, even though this will hinder your ability to produce utility and thus make you less intelligent by a more common definition. In the most extreme case, nothing is smarter than a true random number generator, which it seems clear is not intelligent at all.

If you can predict what someone will do, then it seems like you must be at least as intelligent as them, since you can just do what they'd do, but you might underestimate the effectiveness of their strategies and overestimate the effectiveness of your own, and thus use your own, less effective strategy. For example, perhaps Alice favors teamwork and Bob favors independence, and this is common knowledge. Each of them will be able to predict the actions of the opponent, but believe that their own actions would be more advantageous. Only one of them is more intelligent, and you're not likely to figure out which without actually testing them to see which strategy works better.

We would expect that an agent that grows in its understanding would change its utility function--if only because to do so would make it less predictable to adversarial agents that would exploit its simplicity.

Game theory predicts that in some cases, an agent with a fixed utility function will randomize its actions (for example, the Nash equilibrium strategy for rock paper scissors is to randomize equally between all 3). If true randomness is unavailable, an agent may use its computational power to compute expensive pseudorandom numbers that other agents will have difficulty also computing. There is no need for the agent to change its utility function. Changing its utility function would be likely to cause the agent to optimize for different things than the previous utility function would optimize for; therefore, if the agent is acting according to the original utility function, changing the utility function is unlikely to be considered a good action.

In fact, it would be strange for an agent that became more intelligent to have a stable utility function, because the range of possible utility functions available to a more intelligent agent are greater.

Given that changing your utility function is generally a bad thing for a utility maximizer, it does not seem like this will happen. Instead, it seems more likely that the agent's modeling ability will improve and this will change its observed behavior, possibly making it less predictable. You can often change an agent's behavior quite a lot by changing its beliefs.

There is certainly the important issue of deciding what the old utility function, defined relative to the agent's old model of the world, means if the agent's model of the world changes, as explored in this paper, but this does not lead to the agent taking on a fundamentally different utility function, only a faithful representation of the original one.

Note that the second requirement is a doozy. Many dynamical nonlinear systems are in fact formally unpredictable past a certain threshold. In other words, it's quite common for 'a sufficient degree of accuracy' in modeling a system to simply not exist.

In the domain of human-created agents, your system will often be predictable, because the human that created it had a specific goal. But extending this to humans themselves may end up being problematic for the aforementioned reason- in that case, you're likely limited to probabilistic reasoning no matter how great the abilities of your predictor agent.

I miss some discussion of the effects of one agent predicting the other agent predicting itself.

I wonder if there are non-agents who appear hostile because they seem to predict your actions and thwart them.