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In this paper, we address dynamic network selection problems of mobile usersin an Intelligent Reflecting Surface (IRS)-enabled wireless network. Inparticular, the users dynamically select different Service Providers (SPs) andnetwork services over time. The network services are composed of IRS resourcesand transmit power resources. To formulate the SP and network serviceselection, we adopt an evolutionary game in which the users are able to adapttheir network selections depending on the utilities that they achieve. Forthis, the replicator dynamics is used to model the service selection adaptationof the users. To allow the users to take their past service experiences intoaccount their decisions, we further adopt an enhanced version of theevolutionary game, namely fractional evolutionary game, to study the SP andnetwork service selection. The fractional evolutionary game incorporates thememory effect that captures the users' memory on their decisions. Wetheoretically prove that both the game approaches have a unique equilibrium.Finally, we provide numerical results to demonstrate the effectiveness of ourproposed game approaches. In particular, we have reveal some important finding,for instance, with the memory effect, the users can achieve the utility higherthan that without the memory effect

Dynamic Network Service Selection in Intelligent Reflecting Surface-Enabled Wireless Systems: Game Theory Approaches