Two sides want one prize; each pays a cost every moment they keep fighting, and whoever quits first loses. The cruel result: in a fair fight both bleed until the total cost spent equals the whole value of the prize — the winner wins nothing net. Bidding wars, strikes, and standoffs all dissipate the thing they’re fought over. Slide the fight forward and watch the prize burn.
In the war of attrition two players compete for a prize V by paying a cost proportional to how long they persist; the last to quit wins, but pays for all the time elapsed. The symmetric equilibrium is MIXED — each quits at a random time drawn so the opponent is indifferent — and its expected payoff is ZERO: the entire prize is dissipated in the fighting (full rent dissipation). Escalation is individually tempting and collectively wasteful; only asymmetry (a credible edge) breaks it. A fail-loud self-check throws unless the equilibrium expected payoff is zero (cost consumes the prize). ◆ real game theory, node-verified.
The symmetric mixed-equilibrium rent-dissipation result (expected payoff 0); a KNOWN asymmetry (deeper pockets, more resolve) yields a pure equilibrium where the stronger wins cheaply — the fair-fight-burns-the-prize core is exact.