Pricing of vanillas is basically interpolation of existing (or past) quotes.
It is easier to interpolate in implied volatility space , than in price space.
Reasons are we need to interpolate in multidimensional space (maturity, strike,forward, etc) and satisfy non-arbitrage conditions.
Using Black-scholes formula is convenient mapping which would also ...
If you want to compare quotes across markets or over time it can be useful to use fixed points: eg the 110%/90% points to compute skew or the +/-25 delta points for risk-reversal. You can't rely on quotes existing at exactly those points so you would want to interpolate.
This book sounds like exactly what you want: Gaming the Market: Applying Game Theory to Create Winning Trading Strategies by Ronald Shelton. It is written from a traders' point of view rather than a quant's.
I also found this old paper very helpful: A Game Theory Analysis of Options: Contributions to the Theory of Financial Intermediation in Continuous ...