Joko matematikoen hurbilketa: kasu diskretua

Abstract

Joko-teoriaren helburua eragile arrazioanalen portaera estrategikoak aztertzea da. Eragile kopurua oso handia bada, batez besteko eremuko jokoak joko lehiakor finituen hurbilketa onak dira eta, hori dela eta, biziki ikertuak izan dira azken urteotan. Hala ere, literaturan, artikulu gutxitan onartzen da jokalarien akzio-espazioa diskretua dela. Eredu horiek dira, hain zuzen ere, gure ikerketan aztertzen ditugunak. Jokalariak simetrikoak direla onartuko dugu, baita jokalarien kostu-funtzioa eta dinamikak jarraituak direla ere. Artikulu honetan erakutsiko dugu badela beti oreka bat batez besteko eremuko joko horietan.; Game-theory is the set of mathematical tools to study the rational behavior of interacting agents or players. When the number of players is large, mean-field games have been proposed as an approximation of non-cooperative finite games. Con-trarily to most of the literature in this area, we analyse mean-field games when the number of possible actions that players can take is discrete. We consider that players are symmetric and that the cost function and the dynamics of the players are continu-ous. In this article we show that a solution of these type of mean-field games always exists.