Two-Person Second-Order Games, Part 1: Formulation and Transition Anatomy

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2009-06, Vol.141 (3), p.619-639
Main Authors: Yu, P. L., Larbani, M.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied sciences
Behavior
Calculus of Variations and Optimal Control
Optimization
Engineering
Exact sciences and technology
Game theory
Markov analysis
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Psychological aspects
Psychology
Studies
Theory of Computation
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-008-9487-y