SAN FRANCISCO — A decade ago, a developer from the South Korean game maker Nexon threw a few lines of code together to create an image of a flower to present to his girlfriend, buying himself more video game time as she sat impatiently by his side at an Internet cafe.

And, so the industry legend goes, the “virtual good” was born. In the years since, digitally created items for games and social media — from beers on Facebook to weapons in role-playing worlds — have grown into a $15 billion globe-spanning business. They helped generate the likes of Zynga and underpin a fast-expanding online gaming industry.

Now, companies like Nexon that pioneered the model across Asia are muscling onto Zynga’s turf, hoping to cash in on fast-growing U.S. spending by bringing their distinct Asian brand of fast-paced “freemium” games — free with optional in-game purchases.

With PC sales stagnating even in China, the industry’s heavyweights are increasingly doubling down on mobile services and targeting the Western market as more smartphones and tablets land in users’ hands. Pushed also by slowing growth in casual games on Facebook, they have stepped up their investments this year.

“The emphasis of the Asian publishers is to successfully set foot in Western markets, and that gives you a blueprint of what’s to come,” said Joost van Dreunen, managing director of the digital goods intelligence firm SuperData Research. “The free-to-play games for mobile are where we identify huge growth.”

Asian gaming bigwigs began exploring the Western market a few years ago with high-engagement, addictive and often hard-core Web-browser titles. But this year has brought a spike in activity that threatens to undermine Zynga’s own efforts to diversify into mobile gaming and wean itself off Facebook.

The Japanese social gaming powerhouse DeNA aims to enlarge its social and mobile gaming network Mobage in America. It is releasing games based on the Marvel superhero and Transformers franchises. Gree, another Japanese company, has bought two San Francisco-based mobile game developers since May and is spending heavily to lure American users.

Nexon, which went public in December, also wants to be a prominent American player and is gearing up for a big introduction of Epic of the Three Kingdoms in 3D.

The new competition comes at a bad time for Zynga, the $2 billion company behind FarmVille. Zynga gets more than 90 percent of its revenue selling virtual goods that are offered for small amounts, often less than $1, as enhancements in games that are free to download and play.

The company helped convert large numbers of nongamers into players through colorful, less time-consuming casual games like CityVille, but is now struggling to make money from mobile games, stanch executive losses and resuscitate a stock that has dropped steeply since the beginning of the year.

“Zynga and other American game companies are already feeling some pain from the marketing and advertising side from Gree in particular, but also DeNA, in terms of the significant amount that they are spending on acquiring users in the U.S.,” said Colin Sebastian, an analyst at the asset management firm Robert W. Baird.

Asia’s gaming titans hope the United States will be the source of the industry’s next phase of expansion, perhaps at Zynga’s expense, in a reversal of how Western companies typically rely on emerging markets to bolster growth.

With the proliferation of mobile devices, the worldwide market for virtual goods will surpass $20 billion by 2015, according to SuperData Research. U.S. gamers spend much less than Asians, but their expenditure is growing faster.

Revenue from U.S. virtual goods is expected to grow 36 percent to $3 billion this year and to double to about $6 billion in two years, versus shrinking sales of traditional video game products, according to Bonnie Ho, lead research analyst at Inside Network. The Asian market is more than $10 billion.

Lower Internet speeds in the United States pose a challenge for free games that stream on browsers or on mobile devices. For instance, the average Internet speed of 16 megabytes per second in South Korea is more conducive to the online gaming business than the U.S average rate of about seven megabytes per second.

But with expanding infrastructure — Google introduced a one-gigabyte-per-second service in Kansas City, Missouri, in July — that barrier is gradually dissipating.

The trick is to give U.S. gamers reasons to spend via more immersive games. Analysts say the casual crowd is less likely to spend for that extra edge and stay absorbed than the intensely competitive action-gamers that Nexon and others draw.

In the United States, conversion rates for transforming a casual player into one who will splurge on virtual goods have doubled to about 3.1 percent since last year, according to Mr. van Dreunen.

To keep up sales of virtual items, Zynga may need to introduce more immersive titles — strategy games, even action-shooters — and capture robust growth in the mobile segment.

“When you deal with a noncore, nondedicated, nonloyal segment, it’s almost like you have to treat them like they are 10-year-olds with attention deficit disorder,” said Jesse Divnich, an analyst at the video game research firm Eedar.

That means constantly designing new games, introducing fresh elements into existing ones, and otherwise giving players a reason to keep coming back and hopefully spring for items.

Zynga said last month it would buy the digital game studio A Bit Lucky to offer “midcore” games — titles that sit between slickly produced, addictive video games and basic casual games like Zynga’s popular Words with Friends.

“In Asia and beyond, this model is here to stay, and it’s definitely not a fad,” Allison Luong of the video game analysis firm Pearl Research said of the free-to-play model.