How are power flows between multiple power systems (tie-line flows) determined?
In Australia we have the National Electricity Market, which is run by the Australian Energy Market Operator. Wikipedia describes the operation of the NEM as follows:


  Exchange between electricity producers and electricity consumers is
  facilitated through a spot market where the output from all generators
  is aggregated and instantaneously scheduled to meet demand through a
  centrally-coordinated dispatch process. This process is operated by
  the Australian Energy Market Operator (AEMO) in accordance with the
  provisions of Australian National Electricity Law and Australian
  National Electricity Rules.
  
  Scheduled generators submit offers every five minutes of every day.
  From all offers submitted, AEMO’s systems determine the generators
  required to produce electricity based on the principle of meeting
  prevailing demand in the most cost-efficient way (see also Economic
  dispatch). AEMO then dispatches these generators into production by
  sending automatic generation control (AGC) target signals to each
  generating unit.


The interchange of energy between regions is based on 'economic dispatch'. Every five minutes, each generator submits a bid to the market, i.e. "I will generate 10 MW for $10" or "I will generate 20 MW for $30". The market operator then calculates which combination of generators to run so that the total cost of meeting all customer's loads is minimised. This includes minimisation of transmission line losses and accounts for the maximum capacities of the interconnecting lines.

To answer your original question, the 'amount of power exchanged between areas' is not a controlled quantity. The electricity market is based on meeting the consumer's loads using the cheapest generators, and the power exchange between areas is a consequence of that.

You may wish to read further on 'economic dispatch' as it is a fascinating window into the generation and transmission industries.