Subgame perfect equilibrium

Mb Ms) The maximum share the buyer (the supplier) could receive in a subgame perfect equilibrium for any subgame initiated with the buyer s (the supplier s) offer. 

Figure 3.2. A tree defining the largest share the buyer could obtain in a subgame perfect equilibrium...

Since the roles of the supplier and buyer are completely symmetrical in the game, we can write the expressions for Mg and rris by simply changing the indices, and we end up with four linear equations with four unknowns. The following proposition summarizes the subgame perfect equilibrium description. 

Proposition 1 The following system of equations defines the subgame perfect equilibrium for the bilateral bargaining between the supplier and the buyer. 

We may solve the linear equations in Proposition 1 and find the exact expressions for Mb, mb, Ms and m. We can now specify the subgame perfect equilibrium strategies of the players as follows. 

Proposition 2 The unique subgame perfect equilibrium strategy for the players is as follows if the buyer (supplier) initiates the offer, she should ask... 

Our equilibrium for G is therefore defined as a symmetric (subgame-perfect Bayesian) Nash equilibrium and the BU equilibrium for G2 is a Nash equilibrium in the secondary market. By solving the problem with backward-induction, we can prove the following theorem that characterizes the equilibrium for G ... 

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