General dualities between best replies and undominated actions

Sudhir A. Shah
Additional contact information
Sudhir A. Shah: Department of Economics, Delhi School of Economics

No 337, Working papers from Centre for Development Economics, Delhi School of Economics

Abstract: The central results of this paper are dualities between actions in a decision problem that are not strongly (resp., weakly) dominated over a state space and actions that are best (resp., internal-best) replies to a state. These results hold for action and state spaces that are subsets of abstract topological vector spaces, which significantly expands their set of applications in comparison to their predecessors. This is demonstrated in the game theoretic setting by applying the dualities to a player’s decision problem in an abstract many-player game as well as in the s-additive, the absolutely continuous, and the finitely additive mixed extensions of many-player games; the third extension is applicable to discontinuous games. In all these applications, the noncooperative nature of the games is preserved by disallowing correlated decision-making by the players. The results also allow welfare theoretic applications such as the characterisation of various notions of efficient outcomes in terms of the best reply properties of the outcomes. JEL classification: C72, D81 Key words: duality, best reply, internal-best reply, strong domi-nance, weak dominance, Pareto efficiency, Utilitarian efficiency

Pages: 43 pages
Date: 2023-06
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.cdedse.org/pdf/work337.pdf

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cde:cdewps:337

Ordering information: This working paper can be ordered from
http://www.cdedse.org/

The price is free.

Access Statistics for this paper

More papers in Working papers from Centre for Development Economics, Delhi School of Economics Delhi 110 007. Contact information at EDIRC.
Bibliographic data for series maintained by Sanjeev Sharma ().