Powering ESP8266EX with batteries and a voltage divider
There's a good reason why you can't do this.

When you power something like an ESP, the current it consumes will vary over time, as it does different things. For the purposes of current consumption, you could model the device as a resistor  whose resistance varies (greatly) over time. When it's in sleep mode with the radio off, it might be a 10k resistor. When it's active with the radio on full power, maybe a 30ohm resistor. 

A potential divider divides voltage according to the ratio of the resistances. You are talking about putting your ESP in parallel with one of the resistors. Putting two resistors in parallel creates a new resistor with a resistance lower than either of the two.

If you want to calculate the resistance of two parallel resistors, it's R = (R1 x R2) / (R1 + R2). 

What values would you choose for the resistors in the potential divider?  You'd have to go for values much lower than 15ohm in order for the 'resistance' of the ESP not to greatly affect the behavior of the divider - say 5ohm in total. This would mean your divider alone would draw a current of 1A from a 5v supply.

Fortunately, voltage regulators and buck converters are easily and very cheaply available. I recently bought a pack of five 3.3v regulator modules from China, delivered for less than £2.

Alternatively, you can create a reasonably stable supply from a reference voltage with just a single NPN transistor, but I don't know offhand whether it would be good enough for this application.