Abstract
In this chapter, the problem of solving infinitely repeated games by means of Nash or sub-Nash equilibria is considered. Using the algebraic form of a logical dynamical system, a strategy with finite memory can be expressed as a logical matrix. The Nash equilibria are then computable, providing Nash solutions to the given game. When the Nash equilibrium does not exist, sub-Nash equilibria and ε-tolerance solutions may provide a reasonable solution to the game. Common Nash or sub-Nash equilibria make different memory-length strategies comparable. An optimal or sub-optimal solution can then be obtained. Certain algorithms are proposed. This chapter is based on Cheng et al. (Nash and sub-Nash solutions to infinitely repeated games, 2010; Proc. IEEE CDC’2010, 2010).
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References
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© 2011 Springer-Verlag London Limited
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Cheng, D., Qi, H., Li, Z. (2011). Applications to Game Theory. In: Analysis and Control of Boolean Networks. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-097-7_18
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DOI: https://doi.org/10.1007/978-0-85729-097-7_18
Publisher Name: Springer, London
Print ISBN: 978-0-85729-096-0
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