The dozen companies seeking to operate motorized scooter rental businesses in San Francisco promise a well-behaved, cooperative atmosphere — a sharp contrast to the unregulated chaos of scooters being ridden and dumped on sidewalks that occurred over the past couple of months.

In permit applications to the Municipal Transportation Agency obtained by The Chronicle Friday, the firms vowed to snatch scooters illegally dumped on sidewalks, provide significant discounts to low-income riders, offer etiquette tips and free helmets, remove scooters from the streets each night, and pick up two-wheelers that have fallen.

The 12 companies are competing for up to five permits the MTA may issue to businesses renting electric-powered stand-up scooters within the city limits. A pilot program will allow up to 1,250 scooters total during the first six months and as many as 2,500 in the next six.

City officials created the permit requirement, and ensuing contest, after three companies — Bird, Lime and Spin — surreptitiously and suddenly deposited hundreds of the stand-up scooters on the streets and sidewalks of San Francisco.

The two-wheeled transportation devices became a hit with commuters eager for a cheap, quick and fun way to get between BART and work, take a quick trip for lunch or head to a meeting without driving or taking the bus.

Critics reacted just as quickly, flooding City Hall with complaints about scooters tossed on sidewalks, blocking doorways and bus stops. Some complained about people riding scooters on sidewalks, weaving between pedestrians and occasionally colliding with them. Others noted that none of the riders seemed to be wearing helmets, as required by state law.

Applications required the companies to reveal their strategies on such issues as protecting pedestrians from scooters, preventing scooters from being abandoned on sidewalks, ensuring access to low-income residents and those without cell phones, and protecting the privacy of data harvested from users’ trips or phones.

As part of the permitting process, the three original companies were ordered to remove their scooters from the streets by June 4 and cautioned that their prior behavior could be taken into account in deciding who gets permits.

MTA spokesman Paul Rose said the agency’s sustainable streets division is reviewing the applications and would have no comment on their contents until it decides late this month which companies, if any, receive permits to participate in a one-year pilot program.

“We are currently evaluating each application and plan to get back to the companies by the end of June,” he said. “Our goal is to issue permits to companies that fulfill all the requirements but there isn’t a guarantee that any one will be selected.”

Applicants in the running include electric-bike rental firm Jump, recently bought by Uber, and Uber’s San Francisco rival Lyft. All three firms that introduced scooters to San Francisco submitted applications.

Other applicants include Skip, also known as Waybots, which operates rental e-scooters in Washington; popular scooter maker Razor; Ofo, a Chinese company that rents millions of dockless shared bikes; sit-down moped rental firm Scoot; Hopr, a dockless bike sharing business; Ridecell, a firm that offers software to manage rental fleets and autonomous vehicles; and Uscooters, a maker of folding scooters.

All stressed that they plan to be good citizens, but had some variations in how they’d achieve that goal. Most cited previous experience in various types of rentals.

Scoot, which worked with San Francisco on a license for its rental mopeds, said it can use existing garages and legal on-street parking spaces for what it calls “mini-scoots.” Its e-scooters will have swappable batteries.

Skip, which noted that it is the only applicant with a current permit to rent scooters in a U.S. city, said it would employ an in-app camera for passersby to document bad behavior and send out employees to flag users and educate them about legalities, as well as to find improperly parked scooters.

Lyft said it would draw upon its massive data repository and algorithms to appropriately balance scooter distribution and ensure good links to public transit. A “tilt” sensor will inform it when scooters were left sprawled on the sidewalks. Lime mentioned a similar sensor.

Bird, Lime and Spin all pointed to their existing bikes and scooter rentals in other cities, sidestepping the issue of how they handled their San Francisco debut.

San Francisco asked the companies to discuss how they might arrange for their scooters to be locked in the future — removing the chance that they’d block sidewalks. The companies’ solutions ranged form scooter racks to lockable docking stations to bungee cords.

Several companies offered to donate money as a community benefit. Bird and Lyft both said they’d remit $1 per scooter per day to the city to help with bike lanes and other safe riding infrastructure. Assuming each got one-fifth of the scooter allocation, or 250 each, that would come to $7,500 a month, doubling after six months if their allotment rose. Skip offered a richer donation: $1 million, split between “calmed shared streets” and training for mechanics.

Most of the companies said they’d offer incentives such as free rides to riders for “good behavior” such as submitting photos to show they’d properly parked scooters, and would provide in-app notices about rules of the road. Several said they’d offer free helmets by mail or for pickup. Only Scoot discussed including helmets with its rental scooters.

All the companies proposed fairly similar programs to provide free or heavily subsidized rides to people from low-income neighborhoods, as well as ways for people without smartphones or bank accounts to rent the scooters.

Chronicle staff writers Lauren Hernandez, Natasha Mascarenhas and Erin Stone contributed to this report.

Carolyn Said and Michael Cabanatuan are San Francisco Chronicle staff writers. Email: csaid@sfchronicle.com, mcabanatuan@sfchronicle.com Twitter: @CSaid, @ctuan