Working Paper No. 534

Deterministic Approximation of Stochastic Evolution in Games

Publicerad: June 19, 2000; revised October 2001Antal sidor: 37Nyckelord: Game Theory; Evolution; ApproximationJEL-koder: C70; C72

Deterministic Approximation of Stochastic Evolution in Games Michel Benaim and Jörgen W. Weibull


This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The deterministic approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the stochastic process, for large populations, and its deterministic approximation. In particular, we show that if the deterministic solution through the initial state of the stochastic process at some point in time enters a basin of attraction, then the stochastic process will enter any given neighborhood of that attractor within a finite and deterministic time with a probability that exponentially approaches one as the population size goes to infinity. The process will remain in this neighborhood for a random time that almost surely exceeds an exponential function of the population size. During this time interval, the process spends almost all time at a certain subset of the attractor, its so-called Birkhoff center. We sharpen this result in the special case of ergodic processes.

Två filter:

Varför du har fel om nästan allt, men ändå inte vill ändra dig

Två filter av Andreas Bergh 2017 f hemsidan.jpg

Du har fel om tillståndet i världen, du har fel om vad det beror på och ändå är chansen liten att du ändrar din åsikt. Samhällsdebatten domineras av negativt tänkande förklarar Andreas Bergh, IFN, i denna bok. Han skriver att i takt med att världen blir allt bättre att leva i blir vårt instinktiva negativitetsfilter allt sämre anpassat till verkligheten.

Institutet för Näringslivsforskning, Grevgatan 34 - 2 tr, Box 55665, SE-102 15 Stockholm, Sweden | Tel: +46-(0)8-665 45 00 | info@ifn.se