Abstract
A game form is N-solvable for a class of payoff functions. If for every pair of payoff functions of that class, the associated game in strategic form has a Nash equilibrium. A finite game form is N-solvable (for the universal class of preferences) if and only if it is tight—that is if its α-effectivity function and its β-effectivity function are equal. We extend this result to various models of two-player game forms with infinite sets of strategies and/or alternatives. This is done by an appropriate definition of tightness relative to the underlying structure (topology, Boolean algebra, σ-algebra). We apply the current results along with well-known results on the determinacy of games with perfect information to infinitely repeated game forms. We prove that a repeated tight game form is tight on Bore1 sets.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
