sensing the state of a switch with only one wire

I'm not sure if this is the right section, so if I'm in the wrong place then I'm sorry.

I am currently trying to get into PCB design and I have chosen a very simple project for a start. But I've run into an issue and couldn't really get the needed answers off of Google.

I play Warhammer 40k. There are multiple objectives on the board that can be held by either player.

What I want is simply to make these objectives a bit more intelligent.
Every Objective is supposed to have a switch and an RGB LED. the Switch will have 3 states. "Player1","Player2" or "not held". and will be adjusted manually (Everything else would get really intense really quick). With those I could hook up a Display to my UNO and build a point counter.

My problem:
I want to have that Objective as a separate PCB that sends back the information of which state is active. But I do not want to have 4 wires running(Power,P1,P2,not_held). I want to have only 2 wires(Power and which_Player) so save ports on the Arduino.

My idea how to solve this:
As of now I would just add different Resistors on each switch port and combine those wires into one. I would then connect that to an analogue port and sense the Voltage coming in, kind of like a Potentiometer, but with 3 discrete steps.

My Question:
a)Is that feasible?
b)Is there a neater way that maybe uses digital pins? I need more possible inputs, since a typical Game has 1 to 9 Objectives, depending on the gametype. I would like to build that on my UNO and not have to Buy a Mega just for that.

Thank you in advance.

a) yes it's feasible
b) yes resistor steps between 9 switches can distinguish which button is being pressed using ADC
c) using 2 wires this is your best option

Another possibility but will require more wires is to use port expansion chips like I2C (like MAX7321) or shift registers .