I'm writing a theoretical (control theory) paper. I'm not a native English speaker and I need guidance about the following. Often, the subject of my sentences is "an agent", or "decision-maker", who is a completely gender neutral entity. A convention in the field seems to be using "she/her" to refer to this entity, to compensate that in the past it would always be "he/his". I was wondering if this remains currently true (emphasis in currently, I'm aware of this question but it's ten years old and this is a rapidly evolving subject), with the increasing usage of "they/their" as gender neutral pronouns. Should I move to this? Should I conjugate the verbs in singular or plural if I use it? It feels weird to me to use the verb in plural given that "the agent" is clearly a singular entity, but I'm aware that "they" followed by a singular verb conjugation is grammatically incorrect. Help is very appreciated.
If you are discussing a single agent, there is little downside to going with they as pronoun. Regardless of whether you are using they as singular or plural pronoun, it goes with verbs in the plural case (exactly the same as you -- we say you are, not you art when addressing one person).
However, only in rare situations sticking to she/her could be contrued as problematic. So if that's what you are used it, I don't think you need to feel obliged to change.
In the adjacent field of game theory you often have situations with two decision makers. Here it can be very useful to make one of them male and one of them female to make pronoun use unambigious.
APA and others support singular 'they' for cases where gender is "unknown or irrelevant to the context of the usage".
Arguments that this usage is broadly incorrect seem to be outdated in terms of modern style guides (though there are of course exceptions), and short-sighted regarding the history of the use of 'they' as a singular pronoun.
In some artificial contexts it can be useful for readability to use an "Alice and Bob"-style gender assignment, where the scenario is more clear by specifically choosing characters that use different pronouns, but if you have a single genderless entity it seems most correct to use "they". There are also likely ways you can eliminate personal pronouns entirely from the writing when the entity you are describing is not truly animate, and I'd recommend that approach if you are writing under a particular style guide that does oppose the singular 'they' usage.
If you look at some other languages, like Spanish and Russian (these happen to be ones I speak, other than English), the default gender is male. The same was true in English for centuries until somewhat recently when political correctness took hold and people started writing either "she" (as if that's any better) or "they".
The problem with "they" is that it can introduce a confusion in some contexts; yes, we can have a complex rule where you either use "they" in the right context, or something like "he or she" in other contexts. However, that complicates the language for no good reason.
Personally, I think there is no problem with just using "he" all the time. It's singular, so the other grammar rules are unaffected; it's consistent with other languages where a similar dilemma exists; and it's not meant to degrade women in any way.
However, I would be happy to use a special new pronoun for this, like "ze" or whatever. Yes I know some of those pronouns have been claimed by individuals to express their unique identities - we can just pick one that's not in use already and is easy to pronounce, and stick with it.
The proper pronoun in English for an entity that is neither male nor female is "it."
https://en.wikipedia.org/wiki/It_(pronoun) It is considered to be neuter or impersonal / non-personal in gender.
Example: The thing drifted up. It got higher. The group made a decision. Its decision was to stop.
Pronouns for persons are currently a hot topic. While newly invented pronouns are all the rage (e.g., xe), and while the politically-correct insist on using the plural "they" instead of a singular form. "It" is a better form and technically correct for something with no gender.
This is actually one of the harder-to-argue-with uses of singular "they". In Math, if you have a statement along the lines of "For all x, P(x) is true", x is known as a "dummy variable" or "bound variable", and it wouldn't make sense to assign a gender, as x varies across a set with different genders. If we use "they" to refer to x, we are in some sense using "they" in a "singular" sense, but in another sense it's plural, as it's encompassing the entire set that x ranges over. For instance, "An agent has utility function" can be considered alternative phrasing for "All of the agents have a utility function". The latter wording can be clunky and ambiguous (for instance, is there a constant utility function that all of them have, or do they each have their own), while the former raises issues if we use plural pronouns. If you do use "they", the verb should be conjugated in the plural.
Singular "they" (ie "they" used to refer to a single entity) is "gaining traction", is growing in adoption and acceptance.
But, because this is a change from usual(*) practice, you will meet with both acceptance and rejection. Some people (e.g. some reviewers or editors, some readers) will object. Some people are even vocal about it. :-) So perhaps you will face some criticism, but stick with your choice.
Why not go with 'it/its'? Is it because your agents are people?
As a way to ameliorate the impact of pronouns, you can try rewriting sentences to avoid pronouns where possible (e.g. joining sentences, using "get+verb", using passive voice, introducing names ("agent A"), etc.).
(*)Usual means "from a few years ago" or "from a few decades ago", depending on context and rate of generational change. :-)