Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 141, Issue 3, Pages 619-639Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-008-9487-y
Keywords
Habitual domains; Normal form games; Second-order games; Win-win mind profiles; Markov chains
Funding
- National Science Council, Taiwan [NSC96-2416-H009-013]
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It is well known that human psychology determines his/her action and behavior. This fact has not been fully incorporated in game theory. This paper intends to incorporate human psychology in formulating games as people play them. In Part 1 of the paper, we formulate a two-person game by the habitual domain theory and the Markov chain theory. Using the habitual domains theory, we present a new model describing the evolution of the states of mind of players over time, the two-person second-order game. We introduce the concept of the focal mind profile as well as the solution concept of the win-win mind profile. In addition, we provide also a method to predict the average number of steps needed for a game to reach a focal or win-win mind profile. Then, in Part 2 of the paper, under some reasonable assumptions, we derive the possibility theorem stating that it is always possible to reach a win-win mind profile when suitable conditions are satisfied.
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