City Research Online

On the analytics of infinite game theory problems

Gambarova, Z. & Glycopantis, D. (2021). On the analytics of infinite game theory problems (21/02). London, UK: Department of Economics, City, University of London.


We consider zero-sum and a non zero-sum games of two players with generalized, not necessarily linear, utility functions and infinite, compact pure strategy spaces. Emphasis is given to comparisons with results obtained in mathematical theorems. The games chosen make specific points in relation to the conditions of the theorems. The idea of δ functions is exploited to construct mixed strategies. We interpret their significance in joining pure strategies and show the application in confirming NE. Uniqueness of NE is looked at. An issue is also how far an analogy can be drawn from the case of the finite matrix games. The usually discussed game theory problems are easy to analyze but they do not cover the whole range of possibilities.

Publication Type: Monograph (Discussion Paper)
Additional Information: Copyright 2021, the authors.
Publisher Keywords: Nash Equilibrium (NE), Infinite games, Compact set of strategies, Reaction functions, Dirac δ function, Mixed strategies, Quasi-concave utility function, Nash-von Neumman-Debreu-Fan-Glisberg theorems, multiple Nash equilibria, minimax theorem, saddle point, games with perfect recall, behavioural strategies
Subjects: H Social Sciences > HB Economic Theory
Departments: School of Policy & Global Affairs > Economics
School of Policy & Global Affairs > Economics > Discussion Paper Series
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