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This chapter introduces a dynamic process called the best response dynamics. This is an evolutionary process that does not require full rationality of the game players.
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This chapter is based on Gilboa and Matsui (1991) and Matsui (1992).
The unperturbed version of this dynamic process has been developed as fictitious play. The mathematical definitions of the unperturbed best response dynamics and the fictitious play are identical even though their setups are very different: the former considers a continuum of players who take myopic best responses against the present strategy distribution, while the latter considers finitely many players who take best responses against the past average of the opponents’ behavior. Earlier contributions concerning fictitious play include Brown (1951), Miyasawa (1961), and Shapley (1962). For more recent development, see, e.g., Monderer and Shapley (1996) and Hofbauer and Sandholm (2002). Fudenberg and Levine (1998) presents a concise introduction to both fictitious play and best response dynamics.
This concept was called “cyclically stable set” in Gilboa and Matsui (1991).
Shapley (1962) gives an example where fictitious play does not converge to a Nash equilibrium.
- Best Response Dynamics
- Springer Singapore
- Chapter 8
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