War of attrition with implicit time cost

War of attrition with implicit time cost.

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the strategies of the whole population. We identify and analyse the underlying mechanisms responsible for the implicit time cost. Each player participates in a series of...

The War of Attrition in Continubus Time with Complete Information*

In this paper, we present a general analysis of the War of Attrition in continuous time with complete information. In this game, each of two players must choose a time at which he plans to concede in the event that the other player has not already conceded. The return to conceding decreases with time, but, at any time, a player earns a higher return if the other concedes first. The game was int...

The War of Attrition with Noisy Players

We first consider the Nash equilibria for the two-player normal-form war of attrition, which is equivalent to a second-price all-pay auction. When there is a limit to the maximum effort (for example, a budget constraint), and for low enough prize values, there exists a symmetric mixed-strategy equilibrium under equal prize values. However, the only equilibria when prize values differ involve on...

The Generalized War of Attrition

We model a War of Attrition with N +K firms competing for N prizes. If firms must pay their full costs until the whole game ends, even after dropping out themselves (as in a standard-setting context), each firm’s exit time is independent both of K and of other players’ actions. If, instead, firms pay no costs after dropping out (as in a natural oligopoly), the field is immediately reduced to N ...

The Attrition Dynamics of Multilateral War