0587911 - ÚI 2025 RIV DE eng J - Journal Article
Černý, M. - Bok, J. - Hartman, David - Hladík, M.
Positivity and convexity in incomplete cooperative games.
Annals of Operations Research. Roč. 338, č. 1 (2024). ISSN 0254-5330. E-ISSN 1572-9338
Institutional support: RVO:67985807
Keywords : Cooperative games * Incomplete games * Upper game * Lower game * Positive games * Convex games * Totally monotonic games
Impact factor: 4.4, year: 2023 ; AIS: 0.861, rok: 2023
Method of publishing: Open access
Result website:
https://doi.org/10.1007/s10479-024-06082-6DOI: https://doi.org/10.1007/s10479-024-06082-6

Incomplete cooperative games generalize the classical model of cooperative games by omitting the values of some of the coalitions. This allows for incorporating uncertainty into the model and studying the underlying games and possible payoff distributions based only on the partial information. In this paper, we conduct a systematic investigation of incomplete games, focusing on two important classes: positive and convex games. Regarding positivity, we generalize previous results from a special class of minimal incomplete games to a general setting. We characterize the non-extendability to a positive game by the existence of a certificate and provide a description of the set of positive extensions using its extreme games. These results also enable the construction of explicit formulas for several classes of incomplete games with special structures. The second part deals with convexity. We begin with the case of non-negative, minimal incomplete games. We establish the connection between incomplete games and the problem of completing partial functions and, consequently, provide a characterization of extendability and a full description of the set of symmetric convex extensions. This set serves as an approximation of the set of convex extensions.
Permanent Link: https://hdl.handle.net/11104/0354981