Since A Model of Belief and the Capacity to Know, I'm increasingly convinced that to understand how to artifically model human-like behaviour requires a methodical and fundamental understanding of human behaviour (in general), and, more importantly, what causes it. This, of course, is what Psychology pursues.
This might seem implicitly reasonable, but here I want to make it robustly evident.
To begin with, humans make decisions with remarkable flair; they are pretty good at considering the complexity of any particular situation and drawing from a repertoire of reasoning and experience to decide what to do next.
For example, a human can decide what to do even though they do not have a clear picture of all the facts; for example, they make educated guesses, draw from experience, extrapolate and postulate about past tendencies or observations. Can robots do this? This is what what AI researchers inevitably want to know and to provide models to help them (robots) do so.
If robots or artificial entities are capable of knowing how to do this (reason and therefore behave like humans do), then that means fundamentally we have been able to define how humans manufacture behaviours, which, as a consequence, is exactly what Psychology aims to do. There is an explicit connection, therefore, between studying how and why humans behave the way they do (Psychology) and simulating that know-how in artificial entities (Artificial Intelligence) for them to behave that way.
Technically, artificial means such as Bayesian networks, Neural networks, and Reinforcement learning can be used to simulate the kind of reasoning that predicates human behaviour. This is why these are part of the realm of artificial intelligence, and that is why there exists an inevitable connection between AI and Psychology.
Psychology aims to understand why human behaviours occur, while artificial intelligence aims to make those behaviours occur. Artificial intelligence then has a lot of work to do.
Humans also make other complex and interesting decisions, and AI researchers want to emulate those, too. For example, humans appear to think, evaluate, compare, predict and otherwise reason about what they will do next. It is primarily because of these aspects that we likely consider human behaviour to be intelligent. Therefore, this is why endeavours exist in AI to specifically simulate human reasoning or decision-making, for example, the Markov Decision Process.
For example, if humans are fearful, nervous or in a hurry, their individual behaviours would be different. Each person reasons about their individual situation and decides what is a reasonable response or behaviour to perform. Similarly, if a human is sad, tired or otherwise emotional, this might influence how they behave, and therefore understanding or defining that behaviour based on those considerations is what Psychology is concerned with.
Another example. A time-constrained person might put off lower-priority considerations or behaviours to make their goals more timeous. Indeed, a fearful person who is confronted in an alleyway by an armed would-be thief is more likely to hand over his/her wallet than risk injury, particularly if they value their life or need to care for small children. Similarly, a more confident person will do things differently from one who is less sure of himself/herself in any particular situation that requires a response. In this way, Psychology has a lot to offer Artificial Intelligence.
In AI, Bayesian networks can be used to simulate human-like decision-making to a certain degree, as they model an approach to dealing with uncertainty that humans seem to routinely deal with when they make decisions. Decision making is important because it is a precursor to human behaviour, i.e before any behaviour is performed, humans decide (make decisions) what they are going to do, i.e how they are going to respond.
AI, therefore, is interested in simulating that human behaviour creation process systemically, drawing on a (hopefully) very definable and robust set of steps that are repeatable and therefore robustly produce such human-like behaviours, despite the complexities that are inherent in real-life situations, and Psychology can help with that.