Is there a name for this kind of game?

I read about a certain kind of situation a few years back but I don’t know whether it has a formal name.

One player adopted a strategy that is expected to give him an advantage. It could be a new weapon, or a shopper’s discount, or a product warranty, or whatever. For a short time, he enjoys the advantage even though it requires an investment cost. However, the competition very quickly adopts the same strategy. Now everyone is investing but nobody is realizing the benefits they expected. The cost and inconvenience becomes burdensome.

Now each player continues to invest resources but nobody gets an advantage. They all wish they could drop out, but whoever drops out first cedes an advantage to the remaining players. Each player is trapped with a permanent resource drain but equilibrium prevents them from seeking a different strategy.

Is there a name for this type of situation?

An arms race, which is a form of prisoners dilemma.

Never mind.

The Dollar Auction is a fun example. I offer a dollar bil lto the highest bidder. Say “50 cents” and get the dollar for half-price … if no one outbids you.

Note to anyone who doesn’t follow septimus’ link: The catch in a Dollar Auction is that even though only the top bidder gets the prize, both of the top two bidders must pay the price.

I’ve heard it described as a “race to the bottom”. Everyone tries to undercut each other and nobody wins.

Some of us might remember “Green Shield Stamps” (or some local equivalent). The idea was that when you purchased from a participating retailer, you collected actual stamps which you stuck in a book. Eventually, you would have enough stamps to trade for something from their catalogue.

They were quite successful and more and more retailers, especially filling stations, subscribed. Then, to gain an advantage, some places offered double and even treble stamps.

I am sure that you can spot the problem: Once everyone offers stamps, no one has any advantage so retailers looked for alternatives like reducing prices. Green Shield Stamps eventually closed down and morphed into a catalogue shop, selling discounted goods direct to the public.

I think you’re referring to S&H Green Stamps. The Wikipedia article lists some of their competitors.

Some of these stamps have philatelic value now … not much, but some …