In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker's preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.
Bibliographical noteFunding Information:
I am grateful to two anonymous referees and the participants in the Yonsei–Kyoto–Osaka Economic Theory Workshop for helpful comments. I acknowledge the hospitality of the Institute of Economic Research at Kyoto University, where part of this research was conducted. This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2016S1A5A2A02925750).
© 2019 Walter de Gruyter GmbH, Berlin/Boston.
All Science Journal Classification (ASJC) codes
- Economics, Econometrics and Finance(all)