The stock market continued this week's impressive rally on Thursday morning with modest gains. Investors were once again pleased by the conciliatory tone struck by the Trump administration in its comments about the trade war, which spurred hopes that the long dispute between the U.S. and China might finally enter a stage of constructive dialogue that could lead to longer-term solutions. As of noon EDT, the Dow Jones Industrial Average (DJINDICES:^DJI) was up 116 points to 27,253. The S&P 500 (SNPINDEX:^GSPC) rose 14 points to 3,015, and the Nasdaq Composite (NASDAQINDEX:^IXIC) picked up 47 points to 8,216.

There was also a lot of news coming out of the grocery industry on Thursday morning. Kroger (NYSE:KR) released its latest earnings report and left investors with mixed opinions about where it'll go from here. Meanwhile, Walmart (NYSE:WMT) revealed an innovation that promises to help it compete more effectively against not just Kroger -- the country's largest supermarket chain -- but also the many other players battling for supremacy in the grocery retail arena.

Kroger moves lower

Shares of Kroger  dropped 3% after the grocery store giant reported its second-quarter financial results. Revenue inched higher by 0.5%, driven in large part by a 2.2% rise in same-store sales (excluding the impact of fuel sales). Adjusted net income increased 6% from year-ago levels.

Grocery store aisle with pasta and related items and a shopping cart.

Image source: Getty Images.

Kroger investors had expected it to give a progress report on its restructuring efforts, and the update on its Restock Kroger strategic framework was upbeat. The company has continued to expand the number of stores offering curbside pickup or home delivery, and its new store brands include one dedicated to meat alternatives -- part of its bid to capitalize on that rising consumer trend, as well as to redefine its customer experience. Partnerships with other businesses allowed Kroger to work toward common goals, and employee retention levels remained high even in a tight labor market where workers have plenty of alternatives.

One key aspect of Kroger's transformation involves digital sales, and the company reported a 31% increase in revenue from those sources during the period. Especially as rivals ramp up their e-commerce efforts, Kroger can't afford to get left behind.

Some investors would've preferred to see stronger sales growth. But the dynamics of the grocery industry make it far harder to boost profits, and Kroger's work on that front should leave shareholders feeling confident about the future.

Walmart ships it

Meanwhile, Walmart shares moved slightly higher Thursday morning. The retail behemoth announced a grocery initiative  that could have a big impact on Kroger and other players in the industry.

Walmart said that it would expand its Delivery Unlimited membership option for grocery delivery to 1,400 stores across 200 different markets. The service, for which Walmart will charge $98 per year or $12.95 per month, gives customers the option to get as many deliveries as they want. The retailer will also continue to offer customers who choose not to become members the option of paying one-time fees on a per-delivery basis for the service.

The move comes after Walmart tested the service in four key markets: Houston, Miami, Salt Lake City, and Tampa. Customer response to the program prompted this massive expansion, which will cover more than half of the nation by the end of 2019.

Delivery Unlimited is Walmart's answer to similar services being offered by its department store and e-commerce rivals, and its pricing currently is similar too. Yet some industry watchers believe that if Walmart is to succeed with this strategy, the company will have to bring its delivery services in-house, and take steps to preserve its margins from the high costs involved with shipping.