Massachusetts Republicans finally have a candidate to challenge Gov. Michael S. Dukakis (D). He is George S. Kariotis, a former Democrat who was secretary of economic affairs in the administration of then-Democratic governor Edward J. King. In 1983 Kariotis switched parties and has been a key Republican fund-raiser.

The party's search committee selected Kariotis, head of a high-technology company, Tuesday evening after a three-week hunt. The two Republicans running for the gubernatorial nomination were forced to drop out of the race after controversies developed about them and their campaigns, but their names will remain on the Sept. 16 primary ballot. Kariotis will have to run as a write-in candidate. Robb's Novel Ideas

Former Virginia governor Charles S. Robb (D) offered novel ideas on how to increase productivity and encourage corporations to plan for long-term growth. "Workers aren't the only ones in need of more modern systems of incentives," Robb said this week in a speech in San Francisco.

Robb proposed that "to get business executives to look beyond short-term profits, management pensions could be tied to how a company performs after an individual retires."

He also proposed a system in which workers would receive some percentage of their pay in bonuses, depending on the fortunes of their company. "By giving companies the flexibility to, in effect, lower payroll costs by trimming or forgoing bonuses during bad times, layoffs could be avoided and workers could gain in job security what they lose in compensation."

The speech was part of a California tour by Robb, chairman of the Democratic Leadership Council. Money Trouble

Bernard Sanders, socialist candidate for governor in Vermont, laid off his entire paid staff of three this week, because he has no money to pay them. But his campaign manager said, "He's better off than some people who worry about money all the time."

Sanders has raised only $19,000. Gov. Madeleine Kunin (D) and Lt. Gov. Peter Smith (R), the other candidates, have each raised about $130,000. Despite his nearly depleted campaign coffers, the Burlington mayor plans to stay in the race, a spokesman said.

Recent polls show that Sanders could pull enough of Kunin's vote to deny her the 50 percent needed to win outright on Election Day, throwing the election to the legislature. The Singing Candidate

Rep. Edwin V.W. Zschau (R-Calif.), who is challenging Sen. Alan Cranston (D), treated Washington Post editors and reporters yesterday to a rendition of the campaign song he wrote. When last seen, the candidate was riding down the Post elevator, still singing the multi-verse ditty: "Z-S-C-H-A-U, I can spell it; so can you!" And then there was, "California will be dancin' . . . When I beat Alan Cranston!".