Dutch vs all-pay auctions: the payment rule changes the game

A falling price trades surplus against availability

In a Dutch auction, a posted price descends until a bidder accepts it. Waiting can improve the price paid if the item remains available, but another bidder can end the sale first. A private value tells you what the item is worth to you; it does not reveal how long rivals will wait or determine a universally optimal stopping price.

Play the Dutch auction game. Your value is eighty, the clock begins at one hundred and each tick falls by five. Scripted rival thresholds are revealed after play. The highest is fifty, so fifty-five is the cheapest winning tick under the declared ordering rule. This result belongs to this discrete bot scenario. Stanford’s algorithmic game-theory notes provide broader teaching material on auction and mechanism design; the game does not claim to solve strategic bidding under an unspecified distribution of rivals.

In an all-pay contest, losing still costs something

An all-pay auction charges every bidder their bid while only the winner receives the prize, subject to the tie rule. Net payoff therefore subtracts the bid even after a loss. This can resemble contests with irrecoverable effort, but any real application needs a careful argument about how effort, winning probabilities and prize values are represented.

The all-pay auction game uses a prize worth twelve and a rival who bids uniformly from one through ten. Highest bid wins and equal bids split the prize. A bid above twelve cannot generate a positive net payoff even if it wins outright. That observation does not solve the game against strategic opponents; it is a direct consequence of the specified prize and cost. Keep the payment rule visible before comparing this activity with a winner-pays auction.

Worked example: calculate an all-pay bid’s average payoff

Take a bid of four against the board’s declared uniform rival. Enumerating the ten equally likely rival bids is more informative than judging the strategy by one lucky outcome. All amounts below are invented game units, not monetary advice.

1. Against rival bids one, two or three, your four-unit bid wins twelve and nets eight each time. There are three winning cases, contributing twenty-four units to the ten-case payoff sum.
2. Against a rival bid of four, the prize is split and your net is six minus four, or two. Against bids five through ten, you lose and still pay four, contributing minus twenty-four across those six cases.
3. Add the ten case payoffs and divide by ten: the expected net is 0.2. Compare that exact bot average with the realised result, then change the bid to see why one win cannot establish a profitable general strategy.

A contract menu reveals information through self-selection

Screening begins with private information on one side of an interaction. A menu can make different types prefer different choices, but only if their utility comparisons actually support that separation. Calling one tier premium does not force a high-value customer to select it. The cheaper option and the option to walk away remain part of the calculation.

Try screening contracts. Customers value a quality unit at four or eight. At prices four and twelve, the stated tie rule supports different quality choices. Raise the second price to fourteen and the high-value customer can prefer the cheaper tier instead. The Nobel Prize overview of asymmetric-information research provides context for screening and related mechanisms. This two-customer exercise isolates self-selection rather than representing a complete competitive market or an optimal pricing solution.

Read these rules before importing a strategy

A strategy learned in one mechanism can become costly when transferred to another with a different payment or information rule. Before generalising from a successful round, describe the mechanism in enough detail that another reader could replay the same choices. If a crucial detail is unknown, label it as uncertainty rather than filling it with an unstated convenient assumption.

• Identify whether only the winner pays, all participants pay or some effort cost is sunk before allocation.
• Specify how the clock moves, who can act at a tick and how equal actions or bids are resolved.
• Separate your private value from beliefs about rival values and strategies.
• Compare net payoff with gross prize value, including the cost of losing.
• Distinguish a fixed scripted bot comparison from an equilibrium claim about strategic participants.

Use the games to ask better mechanism questions

Suppose a team is designing an internal idea contest. A large prize may encourage effort, but participants can spend time that remains costly even if they lose. The relevant question is not merely whether the winning idea is valuable; it also includes total effort, participation and what information evaluators observe. A small all-pay model can surface that question without estimating the actual costs.

Likewise, a service menu can reveal preferences only under the choices and constraints customers actually face. An expensive tier might fail to separate users because the lower tier is already sufficient, because switching is costly, or because quality is misunderstood. The simulations offer a starting language for these questions. Treat their transparent arithmetic as a way to inspect incentives, then gather evidence about the people and constraints before turning a game result into a real policy.