For the dollar auction, note that according to the wikipedia page for All-pay auction the auction does have a mixed-strategy Nash equilibrium in which the players’ expected payoff is zero and the auctioneer’s expected revenue is $20. So this breaks the pattern of the other examples, which show how Nash equilibrium game theory can be exploited to devious ends when facing rational maximizers.
The dollar auction is an interesting counterpoint to games like the Traveler’s Dilemma in which the game when played by humans reaches outcomes much better than the Nash equilibrium. The Dollar Auction is an example where the outcomes are much worse when played by humans.
It seems humans in the Traveler’s Dilemma and the Dollar Auction fail to reach the Nash equilibrium for an entirely different reason than in, say, the Prisoner’s Dilemma or the Ultimatum Game (in which altruism/fairness are the main factors). In both cases, understanding the game requires iterative thinking, and there’s a sort of “almost-equilibrium” different from the Nash equilibrium when this thinking isn’t fully applied.
For the dollar auction, note that according to the wikipedia page for All-pay auction the auction does have a mixed-strategy Nash equilibrium in which the players’ expected payoff is zero and the auctioneer’s expected revenue is $20. So this breaks the pattern of the other examples, which show how Nash equilibrium game theory can be exploited to devious ends when facing rational maximizers.
The dollar auction is an interesting counterpoint to games like the Traveler’s Dilemma in which the game when played by humans reaches outcomes much better than the Nash equilibrium. The Dollar Auction is an example where the outcomes are much worse when played by humans.
It seems humans in the Traveler’s Dilemma and the Dollar Auction fail to reach the Nash equilibrium for an entirely different reason than in, say, the Prisoner’s Dilemma or the Ultimatum Game (in which altruism/fairness are the main factors). In both cases, understanding the game requires iterative thinking, and there’s a sort of “almost-equilibrium” different from the Nash equilibrium when this thinking isn’t fully applied.