A Folk theorem for stochastic games with finite horizon

<Para ID="Par1">This paper provides assumptions for a limit Folk theorem in stochastic games with finite horizon. In addition to the asymptotic assumptions à la Dutta (J Econ Theory 66:1–32, <CitationRef CitationID="CR5">1995</CitationRef>) I present an additional assumption under which the Folk theorem holds in stochastic games when the horizon is long but finite. This assumption says that the limit set of SPE payoffs contains a state invariant payoff vector <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$w$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>w</mi> </math> </EquationSource> </InlineEquation> and, for each player <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>i</mi> </math> </EquationSource> </InlineEquation>, another payoff vector that gives less than <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$w$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>w</mi> </math> </EquationSource> </InlineEquation> to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>i</mi> </math> </EquationSource> </InlineEquation>. I present two alternative assumptions, one on a finite truncation of the stochastic game and the other on stage games and on the transition function, that imply this assumption. Copyright Springer-Verlag Berlin Heidelberg 2015