Paper Info
Title
Support Set Invariancy For Interval Bimatrix Games
Abstract
Traditionally, game theory problems were considered for exact data, and the decisions were based on known payoffs. However, this assumption is rarely true in practice. Uncertainty in measurements and imprecise information must be taken into account. The interval-based approach for handling such uncertainties assumes that one has lower and upper bounds on payoffs. In this paper, interval bimatrix games are studied. Especially, we focus on three kinds of support set invariancy. Support of a mixed strategy consists of that pure strategies having positive probabilities. Given an interval-valued bimatrix game and supports for both players, the question states as follows: Does every bimatrix game instance have an equilibrium with the prescribed support? The other two kinds of invariancies are slight modifications: Has every bimatrix game instance an equilibrium being a subset/superset of the prescribed support? It is computationally difficult to answer these questions: the first case costs solving a large number of linear programs or mixed integer programs. For the remaining two cases a sufficient condition and a necessary condition are proposed, respectively.
Year
DOI
Venue
2019
10.1142/S0218488519500107
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
Keywords
Field
DocType
Bimatrix game, support set invariancy, interval matrix, interval analysis
Discrete mathematics,Algebra,Mathematics
Journal
Volume
Issue
ISSN
27
2
0218-4885
Citations 
PageRank 
References 
0
0.34
9
Authors
1
Name
Order
Citations
PageRank
Milan Hladík126836.33