On Existence of alpha-Core Solutions for Games with Finite or Infinite Players
This gives two existence results of alpha-core solutions by introducing P-open conditions and strong P-open conditions into games without ordered preferences. The existence of alpha-core solutions is obtained for games with infinite-players. Secondly, it provides a short proof of Kajii's (Journal of Economic Theory 56, 194-205, 1992) existence theorem for alpha-core solutions, further, the Kajii's theorem is equivalent to the Browder fixed point theorem. In addition, the obtained existence results can include many typical results for alpha-core solutions and some recent existence results as special cases.
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