TY - JOUR
T1 - An application of a discrete fixed point theorem to a game in expansive form
AU - Kawasaki, Hidefumi
AU - Kira, Akifumi
AU - Kira, Shinpei
N1 - Funding Information:
The authors would like to thank the referees for valuable comments. This work is supported by Grants-in-Aid for General Scientific Research from the Japan Society for the Promotion of Science No. 23540142.
PY - 2013/6
Y1 - 2013/6
N2 - In this paper, we first present a discrete fixed point theorem for contraction mappings from the product set of integer intervals into itself, which is an extension of Robert's discrete fixed point theorem. Next, we derive an existence theorem of a pure-strategy Nash equilibrium for a noncooperative n-person game from our fixed point theorem. Finally, we show that Kuhn's theorem for a game in expansive form can be explained by our existence theorem.
AB - In this paper, we first present a discrete fixed point theorem for contraction mappings from the product set of integer intervals into itself, which is an extension of Robert's discrete fixed point theorem. Next, we derive an existence theorem of a pure-strategy Nash equilibrium for a noncooperative n-person game from our fixed point theorem. Finally, we show that Kuhn's theorem for a game in expansive form can be explained by our existence theorem.
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U2 - 10.1142/S0217595913400137
DO - 10.1142/S0217595913400137
M3 - Article
AN - SCOPUS:84879680932
SN - 0217-5959
VL - 30
JO - Asia-Pacific Journal of Operational Research
JF - Asia-Pacific Journal of Operational Research
IS - 3
M1 - 1340013
ER -