We can use the arrow method to check for the existence of Nash equilibria. If the game were at Heads, Heads Player 2 would want to swith to Tails (green arrow), but at Heads Tails Player 1 would switch to Tails and so on...

   Every cell has an arrow pointing away so there are no Nash equilibria in this game. It turns out that, in fact, there is a kind of Nash equilibrium for this game, but only if we allow our players to use what are called mixed strategies.

   So far all the strategies we've considered have been pure strategies. Always charging the high price, or always using feature set 2 are examples of pure strategies. By contrast mixed strategies mean playing more than one pure strategy with some probability placed on each strategy.

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