the opponent drops out with probability , raising gives the player an expected payoff of On the other hand, dropping out yields zero, so indifference requires that the opponent drops out with 5% probability each period. Notice that this probability is independent of how high the bids currently are; this follows from the fact that past bids are a sunk cost. The maximum bid follows a binomial distribution with mean 0.5 (recall the bidders make zero profits each, on average). See also All-pay auction Bidding fee auction Escalation of commitment Tragedy of the commons War of attrition (game) Notes References Non-cooperative games Paradoxes in economics Social science experiments Types of auction