Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs
<Para ID="Par1">An autonomous correlation device in a multistage game is a device that, before every stage, chooses for each player a private signal, possibly in a correlated way, and reveals to each player the signal chosen for him. The chosen signals depend only on previous signals, and not on the actions of the players. An extensive-form correlated <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\varepsilon $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">ε</mi> </math> </EquationSource> </InlineEquation>-equilibrium in a multistage game is an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\varepsilon $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">ε</mi> </math> </EquationSource> </InlineEquation>-equilibrium in an extended game that includes an autonomous correlation device. In this paper we prove that every stochastic game with Borel measurable bounded payoffs has an extensive-form correlated <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\varepsilon $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">ε</mi> </math> </EquationSource> </InlineEquation>-equilibrium, for every <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\varepsilon >0$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">ε</mi> <mo>></mo> <mn>0</mn> </mrow> </math> </EquationSource> </InlineEquation>. Copyright Springer Science+Business Media New York 2015
