A taxonomy of learning dynamics in 2 × 2 games

Marco Pangallo, J. Farmer, James Sanders and Tobias Galla

INET Oxford Working Papers from Institute for New Economic Thinking at the Oxford Martin School, University of Oxford

Abstract: Learning would be a convincing method to achieve coordination on an equilibrium. But does learning converge, and to what? We answer this question in generic 2-player, 2-strategy games, using Experience-Weighted Attraction (EWA), which encompasses many extensively studied learning algorithms. We exhaustively characterize the parameter space of EWA learning, for any payoff matrix, and we understand the generic properties that imply convergent or non-convergent behaviour in 2 x 2 games. Irrational choice and lack of incentives imply convergence to a mixed strategy in the centre of the strategy simplex, possibly far from the Nash Equilibrium (NE). In the opposite limit, in which the players quickly modify their strategies, the behaviour depends on the payoff matrix: (i) a strong discrepancy between the pure strategies describes dominance-solvable games, which show convergence to a unique fixed point close to the NE; (ii) a preference towards profiles of strategies along the main diagonal describes coordination games, with multiple stable fixed points corresponding to the NE; (iii) a cycle of best responses defines discoordination games, which commonly yield limit cycles or low-dimensional chaos. While it is well known that mixed strategy equilibria may be unstable, our approach is novel from several perspectives: we fully analyse EWA and provide explicit thresholds that define the onset of instability; we find an emerging taxonomy of the learning dynamics, without focusing on specific classes of games ex-ante; we show that chaos can occur even in the simplest games; we make a precise theoretical prediction that can be tested against data on experimental learning of discoordination games.

Keywords: Behavioural Game Theory; EWA Learning; Convergence; Equilibrium; Chaos. (search for similar items in EconPapers)
JEL-codes: C62 C73 D83 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2017-05
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.inet.ox.ac.uk/files/wp9-taxonomylearning2x2games.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:amz:wpaper:2017-06

Access Statistics for this paper

More papers in INET Oxford Working Papers from Institute for New Economic Thinking at the Oxford Martin School, University of Oxford Contact information at EDIRC.
Bibliographic data for series maintained by INET Oxford admin team ().