This paper examined the effects of users' choices and small historical events on the outcomes of competition among technologies under a regime of increasing returns to technology adoption. Extending Arthur's model of competition between two technologies, we modeled cases involving competition among three technologies and situations where technology users have various forms of return functions. Using these models, we presented patterns of how technologies' market shares change over time under various return regimes and derived strategic and policy implications from the results. First, we confirmed that even as the number of competing technologies increases, the distinctive characteristics of decreasing, constant, and increasing return regimes are maintained when the returns to technology adoption increase proportionally with the absolute number of users. In contrast, when the returns to technology adoption do not increase proportionally with the number of users, the characteristics of the increasing returns regime were only partially maintained. Additionally, when the returns to technology adoption increase proportionally with the relative number of users or a technology's market share, depending on the relative magnitudes of the rate of return to technology adoption and innate preferences for technologies, a situation may arise where one technology does not monopolize the market among competing technologies. Second, in markets where learning effects from technology use diminish over time, monopolization by a single technology does not always occur, and in some cases where one technology initially holds a one-half market share, lock-in to that technology may persist. Therefore, this paper demonstrated that for firms to ultimately secure high market shares, it is necessary to attract technology users in the early stages of competition and continuously leverage the learning effects from technology use. To lock in users in the market, firms must be able to exploit first-mover advantages, and the possibility of lock-in was found to depend on the form of the return function and the relative magnitudes of the rate of return to technology adoption and innate preferences for technologies. Finally, the paper concretely demonstrated that under an increasing returns regime, events in the early stages—such as temporary government intervention or firm failures—can have a significant impact on changes in market structure. These results suggest that firms must recognize that small events occurring especially in the early stages of a market under an increasing returns regime can have a critical impact on market outcomes. They also suggest that when government intervention is necessary under an increasing returns regime, timely and carefully targeted intervention of small scale in the early stages can alter the trajectory of market evolution.