FORMALIZATION OF MULTI-LEVEL GAMES

Kjell Hausken and Ross Cressman
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Ross Cressman: Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada

International Game Theory Review (IGTR), 2004, vol. 06, issue 02, 195-221

Abstract: The article presents multilevel game theory, as a generalization of conventional single-level game theory as it has developed since von Neumann and Morgenstern (1944). We define a multilevel game structure, multilevel games, payoffs and distribution rules, upward feasible strategies and the solution concept multilevel Nash equilibrium (MNE) in such games. A MNE must be, for each player, a best reply against itself with respect to alternative strategies that may have other players deviate as well, in contrast to the NE for conventional games where simultaneous deviations by more than one player are not considered. Although every pure or mixed MNE must give the same outcome as a NE of the extensive form representation, a NE is not necessarily a MNE. It is shown that a MNE need not exist in pure or mixed strategies and, if it does, it may not be unique. In the former case, the multilevel structure is considered unmaintainable.

Keywords: Multilevel game theory; methodological individualism; empowerment from below; multilevel Nash equilibrium; JEL Classification Number C79 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219198904000150

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