Minimax selection theorems
Consider a two-person zero-sum game G modelled as follows: \(G=(S,{\mathcal S},X,Y,C,r)\), where (S,\({\mathcal S})\) is a measurable state space, X and Y are action spaces for two players, \(C=\{(s,x,y):\) \(s\in S\), (s,x)\(\in A\) and (s,y)\(\in B\}\), where \(A\subset S\times X\), \(B\subset S\times Y\), and \(r: C\to R\) is the payoff function. The paper gives three different sets of sufficient assumptions on the primitive data of G for the measurability of the (lower) value, which is a function of the state variable, as well as for the existence, for either or both players, of measurable optimal or \(\epsilon\)-optimal strategies.
measurable optimal or \(\epsilon \) -optimal strategies
scientific article; zbMATH DE number 3948029
scientific article