Finite Approximations of the Sion–Wolfe Game
研究了Sion–Wolfe博弈的有限网格逼近，发现随着网格点增多，逼近值的极限可能落在原博弈下值与上值构成的区间内、边界上甚至之外，提醒学者用有限逼近分析无限博弈时需谨慎。
Sion and Wolfe [Sion M, Wolfe P (1957) On a game without a value. Contributions to the Theory of Games III, Annals of Mathematics Studies (Princeton University Press, Princeton, NJ), 299–306.] presented a two-person zero-sum game on the unit square without a value. In the present paper, we analyze finite-grid approximations of the Sion–Wolfe game. We find that, as the number of grid points tends to infinity and the payoff function approaches that of the infinite game, the limiting value of finite approximations may lie within, on the boundary of, or even outside the interval defined by the lower and upper values of the infinite game. Although these discrepancies can be explained, our findings underscore the need for great care, even in the case of two-person zero-sum games, when using finite approximations for the analysis of infinite games.