On the analytics of infinite game theory problems
Z. Gambarova and
Working Papers from Department of Economics, City University 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.
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 (search for similar items in EconPapers)
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