All-pay war

Asymmetric all‐pay auctions with spillovers

“…Our paper is also connected more broadly to the literature of spillovers in other auction and auction‐like frameworks. Hodler and Yektaş (2012), for example, use a linear first‐price auction with spillovers to model war. The authors refer to this as an all‐pay contest, but only the winner actually pays because of the way funds are handled.…”

All-pay auctions as models for military annexation

“…Military conflicts provide perhaps the ultimate form of competition, and here we employ all pay auctions as a model of military territorial expansions. Building on the work of Hodler and Yektaş [22] in which an all-pay auction is used to model total military conquest, we expand this framework to study the case of partial military conquest in which the victor takes only a fraction of the loser's resources, i.e. the victor expands their territory at the expense of the loser.…”

“…Emulating [22], we characterize the two countries (labelled by i = 1, 2) by their aggressive (e.g. military) power λi ∈ R + , production level βi ∈ R + , and expected resource level R i ∈ R + .…”

“…Suppose that b i is the resource allocation, such that b i λ i is allocated to aggressive actions and (r i − b i )β i is allocated to production and define the equilibrium strategies f i (r i ) = b i such that f i (r i ) : [0, 1] → [0, r i ]. It will be useful to note the follow lemma from [22]: Lemma 1 (HY [22]). For a function f i (r i ) ∈ [0, r i ], in any monotone equilibrium then f 1 (0) = f 2 (0) = 0.…”

All-Pay Auctions with Different Forfeits

“…Notably, conflicts among animals [1] can be represented by the war of attrition. On the other hand all-pay auctions have be used to model the arms race [2] and war outcomes [3], also rent-seeking scenarios such as lobbying [4] or competition with sunk investments [5].…”