Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/316354 
Year of Publication: 
2025
Series/Report no.: 
Working Paper No. 468
Publisher: 
University of Zurich, Department of Economics, Zurich
Abstract: 
This paper identifies a central role of the topological separation axiom T1 in the definition of mixed strategies in noncooperative games with arbitrary pure strategy spaces. Our main result says that a pure strategy space is topologically T1 if and only if (i) all singleton strategy sets are Borel, (ii) all Dirac measures are regular, and (iii) the canonical mapping from pure strategies to Dirac measures is one-to-one. The analysis therefore suggests that the T1 separation axiom is a minimum requirement on the topology of a pure strategy space when randomization is allowed for. Using an example, we show that the T1 assumption is indeed missing from the minimax theorem of Mertens (1986).
Subjects: 
Mixed strategies
Hausdorff spaces
T1 separation axiom
minimax theorem
JEL: 
C72
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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