Using Tarski's Fixpoint Lemma for order preserving maps of a complete lattice into itself, a new, lattice theoretic proof is given for the existence of persistent strategies for combinatorial games as well as for games with a topological tolerance and games on lattices. Further, the existence of winning strategies is obtained for games on superalgebraic lattices, which includes the case of ordinary combinatorial games. Finally, a basic representation theorem is presented for those lattices.
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Communicated by D. Duffus
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Banaschewski, B., Pultr, A. Tarski's Fixpoint Lemma and combinatorial games. Order 7, 375–386 (1990). https://doi.org/10.1007/BF00383202
AMS subject classifications (1980)
- combinatorial games
- Tarski's Fixpoint Lemma
- persistent strategies
- winning strategies
- superalgebraic lattices