Abstract
This paper introduces a new solution concept for games with incomplete preferences. The concept is based on rationalizability and it is more general than the existing ones based on Nash equilibrium. In rationalizable strategies, we assume that the players choose nondominated strategies given their beliefs of what strategies the other players may choose. Our solution concept can also be used, e.g., in ordinal games where the standard notion of rationalizability cannot be applied. We show that the sets of rationalizable strategies are the maximal mutually nondominated sets. We also show that no new rationalizable strategies appear when the preferences are refined, i.e., when the information gets more precise. Moreover, noncooperative multicriteria games are suitable applications of incomplete preferences. We apply our framework to such games, where the outcomes are evaluated according to several criteria and the payoffs are vector valued. We use the sets of feasible weights to represent the relative importance of the criteria. We demonstrate the applicability of the new solution concept with an ordinal game and a bicriteria Cournot game.
Highlights
This paper examines games with incomplete preferences (Bade 2005)
We propose a notion of rationalizable strategies, where the players have nonprobabilistic beliefs and they choose nondominated strategies given their beliefs
Since the multicriteria games are a special case of games with incomplete preferences, rationalizable strategies and the rationality concept elaborated in this paper can be applied to the multicriteria games as well
Summary
This paper examines games with incomplete preferences (Bade 2005). A player has incomplete preferences when he is unable to compare or is indecisive between some of the outcomes. This paper extends the solution concept of rationalizability to the games with incomplete preferences. The maximization of expected utility may not be possible under incomplete preferences or nonprobabilistic beliefs This may, e.g., happen in ordinal games (Durieu et al 2008) where the players only have a preference order but no numeric values are assigned to the outcomes. Our framework enables analyzing the impact of additional preference information about the relative importance of the criteria to the solutions of the multicriteria games To our knowledge, this is the first paper to consider rationalizable strategies in the multicriteria games while representing incomplete preference information as sets of feasible weights. Games with incomplete preferences as well as the rationality concept are defined, and the rationalizable strategies are defined in Sect.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
