Higher order game dynamics

Rida Laraki and Panayotis Mertikopoulos

Journal of Economic Theory, 2013, vol. 148, issue 6, 2666-2695

Abstract: Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the playersʼ strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the playersʼ evolution instead of its velocity (a viewpoint which emerges naturally when it comes to aggregating empirical data of past instances of play). To that end, we derive a wide class of higher order game dynamics, generalizing first order imitative dynamics, and, in particular, the replicator dynamics. We show that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics n orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n⩾2. All in all, higher order payoff-monotonic dynamics lead to the elimination of weakly dominated strategies, followed by the iterated deletion of strictly dominated strategies, thus providing a dynamic justification of the well-known epistemic rationalizability process of Dekel and Fudenberg [7]. Finally, we also establish a higher order analogue of the folk theorem of evolutionary game theory, and we show that convergence to strict equilibria in n-th order dynamics is n orders as fast as in first order.

Keywords: Game dynamics; Higher order dynamical systems; (Weakly) dominated strategies; Learning; Replicator dynamics; Stability of equilibria (search for similar items in EconPapers)
JEL-codes: C61 C62 C72 C73 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:148:y:2013:i:6:p:2666-2695

DOI: 10.1016/j.jet.2013.08.002

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