Lecture XI: Subgame Perfect Equilibrium
Markus M. M¨obius
April 3, 2004
• Gibbons, chapter 2.1.A,2.1.B,2.2.A
• Osborne, sections 5.4, 5.5
1 Introduction
Last time we discussed extensive form representation and showed that there
are typically lots of Nash equilibria. Many of them look unreasonable because
they are based on out of equilibrium threats. For example, in the entry
game the incumbent can deter entry by threatening to flood the market. In
equilibrium this threat is never carried out. However, it seems unreasonable
because the incumbent would do better accommodating the entrant if entry
in fact occurs. In other words, the entrant can call the incumbent’s bluff by
entering anyway.
Subgame perfection is a refinement of Nash equilibrium. It rules out
non-credible threats.
2 Subgames
Definition 1 A subgame G
0
of an extensive form game G consists of
1. A subset T
0
of the nodes of G consisting of a single node x and all of
its successors which has the property that t ∈ T
0
, t
0
∈ h (t) then t
0
∈ T
0
.
2. Information sets, feasible moves and payoffs at terminal nodes as in G.
1
