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Mendes, V. & Mendes, D. A. (2021). Learning to Play Nash Equilibrium in Chaotic Dynamics. CCS2021-SATELLITE ON ECONOPHYSICS 2021.

V. M. Mendes and D. E. Mendes,  "Learning to Play Nash Equilibrium in Chaotic Dynamics", in CCS2021-SATELLITE ON ECONOPHYSICS 2021, Lyon, 2021

@misc{mendes2021_1732202114699,
	author = "Mendes, V. and Mendes, D. A.",
	title = "Learning to Play Nash Equilibrium in Chaotic Dynamics",
	year = "2021",
	url = "https://econophysics.ihu.gr/ec2021/"
}

TY  - CPAPER
TI  - Learning to Play Nash Equilibrium in Chaotic Dynamics
T2  - CCS2021-SATELLITE ON ECONOPHYSICS 2021
AU  - Mendes, V.
AU  - Mendes, D. A.
PY  - 2021
CY  - Lyon
UR  - https://econophysics.ihu.gr/ec2021/
AB  - In a bounded rational game where players cannot be as super-rational as in Kalai and Leher
(1993), are there simple adaptive heuristics or rules that can be used to secure convergence to
Nash equilibria? Robinson (1951) showed that for certain types of games, such rules exist.
Nevertheless, the types of games to which they apply are pretty restrictive. Following Hart and
Mas-Colell (2003) terminology, are there games with uncoupled deterministic dynamics in
discrete time that converge to Nash equilibrium or not? Young (2009) argues that if an adaptive
learning rule follows three conditions -- (i) it is uncoupled, (ii) each player's choice of action
depends solely on the frequency distribution of past play, and (iii) each player's choice of action,
conditional on the state, is deterministic -- no such rule leads the players' behavior to converge
to the Nash equilibrium. This paper shows that there are simple adaptive rules that secure
convergence, in fact, fast convergence, in a fully deterministic and uncoupled game. We use
the Cournot model with nonlinear costs and incomplete information for this purpose and
illustrate that this convergence can be achieved without any coordination of the players'
actions.
ER  -