I've been working on a design recently that involves an auction. I ripped out some preliminary rules and then sat down to think through a first turn, and realized that the auction wouldn't work at all. After more thought, I think I've come up with a set of requirements for designing effective auctions. I'd welcome any feedback and discussion.
1. Players must value the auctioned items differently.
If the item being auctioned has the same value to all players, there is no point in holding the auction; you might as well just set a fixed price. The auction will be won by the first player who bids the actual value of the item.
Of course it's not as simple as that. Simply having different amounts of cash will cause players to value things differently: a player with $10 will bid $2 much more readily than a player with only $3. But there will be times (for example at the start of the game) when most or all players have similar amounts of cash.
An example: in Power Grid, players bid for power plants that produce different amounts of power when provided with different kinds and amounts of fuel. Because fuel prices and availability vary, and because the need to purchase power plants varies with the current extent of a player's network, each player is likely to have a different opinion of the value of any given power plant.
2. Players should occasionally value the auctioned items similarly.
This makes for tense, high-bid auctions. If the players always differ greatly in their valuations, then the winning bidder will never reach his own pain point: he will always win with his first bid above everybody else's pain point. There's no decision agony in that, and you want some occasional decision agony and some eyes locked across the table.
This principle doesn't really conflict with #1. Bidding between players with similar valuations is tense only if it isn't the norm. You get tense only if you don't know how bad the other guy wants to win the auction.
3. The ultimate value of the auctioned item must be uncertain.
Decisions are agonizing only when you're not sure they're correct. The need to purchase (or forgo) an item now that might be valuable later is another source of tension in the game.
This principle applies to all decisions in games: choice of strategies, for example. You make decisions and just hope they will prove effective. But I think the principle is especially strong in an auction, where the cost can keep rising. It forces you to repeatedly re-evaluate the auctioned item, in a rapid-fire cycle, in light of your opponent's revealed desire for it.
4. Bid increments should be chunky.
If the bidding starts at $10, and each successive bid goes up by one cent... then either the bidding will take all day (and be incredibly dull) or there will be no point to the auction because the difference between the lowest and highest bids will be trivial.
In many games, there is no rule about minimum bid increments and none is needed. This is because the smallest unit of money is chunky enough. Princes of Florence is an example: the minimum unit is 100 Florins (or Guilders or whatever they are), the starting bid is always 200 Florins; typical winning bids range from 200 to 1200 or so. It works just fine. But the game I'm designing may end up with a small money unit in comparison to the typical winning bid, so I may need a minimum-increment rule.
This principle applies only to open auctions, where the players bid in succession and know what their opponents have bid. I think it also doesn't apply when the auction is a single-bid system, where each player gets only one bid. In that case a player will balance his bid somewhere below his pain point and above the other players' pain points (or what he hopes their pain points are), and hope for the best.
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That's what I think I've figured out so far. What do y'all think?
I think some uncertainty is also required, as described in Point 3. And in an open round-robin auction, you can watch your opponents sweat in an attempt to divine their intent. This kind of player interaction is my favorite part about auctions.
But yes, some understanding is needed. Knizia's Ra is driven by exactly that: nothing's hidden except the players' current scores, and the fun is in figuring out how badly your opponents might want the current batch of tiles, and invoking Ra to start an auction at a time when they'll feel forced to bid on a marginal batch.