  We study how storage, operating as a price maker within a market environment,
may be optimally operated over an extended period of time. The optimality
criterion may be the maximisation of the profit of the storage itself, where
this profit results from the exploitation of the differences in market clearing
prices at different times. Alternatively it may be the minimisation of the cost
of generation, or the maximisation of consumer surplus or social welfare. In
all cases there is calculated for each successive time-step the cost function
measuring the total impact of whatever action is taken by the storage. The
succession of such cost functions provides the information for the storage to
determine how to behave over time, forming the basis of the appropriate
optimisation problem. Further, optimal decision making, even over a very long
or indefinite time period, usually depends on a knowledge of costs over a
relatively short running time horizon -- for storage of electrical energy
typically of the order of a day or so.
  We study particularly competition between multiple stores, where the
objective of each store is to maximise its own income given the activities of
the remainder. We show that, at the Cournot Nash equilibrium, multiple large
stores collectively erode their own abilities to make profits: essentially each
store attempts to increase its own profit over time by overcompeting at the
expense of the remainder. We quantify this for linear price functions
  We give examples throughout based on Great Britain spot-price market data.
