Multi-period games

Assuming demand is stationary and independently distributed across periods Di = D we further obtain that G y ) = Gi y ) since the single-period game is the same in each period. By restricting consideration to the stationary inventory policy yi — yj t = 1,2,..., we can find the solution to the multi-period game as a sequence of the solutions to a single-period game Gi yi) which is... 

To find an equilibrium of a Stackelberg game which often called the Stackelberg equilibrium we need to solve a dynamic multi-period problem via backwards induction. We will focus on a two-period problem for analytical convenience. First, find the solution X2 x ) for the second player as a response to any decision made by the first player ... 

This is a combination of linear and multi-path structures. Diverging paths areni done very often, because this approach requires the creation of up to twice the assets—money that could be used for other aspects of the game. Still, some games do have paths that split for a period of time. 

When designers use a multi-path structure, the nrast common approach is for the game s path to fork for just a short period, and then for the paths to rejoin into a single route through the game. 

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