Supplementary Materials for Bounded Memory Folk Theorem

Claims A.1 to A.15 establish results needed to show that the strategy given in (28) is welldefined and subgame perfect. The first two claims establish some properties of the paths π̂, . . . , π̂. Claim A.1 For all i ∈ {0, . . . , n} and d, d′ ∈ N with d = d′: −B(1− δ) + δ(n+5)(T+1)Vd(π̂(d)) > B(1− δ) + δVd(π̂), (A.1) −B(1− δ) + δVd(π̂) > (1− δ)B + δVd(π̂), (A.2) −(1− δ)B + δVd(π̂) > (1− δ)B + δVd(π̂). (A.3) Proof. First, by (25) and the definitions of {xj}j=0, {yj}j=0, {π̂}j=0, ξ, ζ, and ζ ′, we have