tion and by Amann and Leininger (1995, 1996), Krishna and Morgan (1997),
Kura (1999), Moldovanu and Sela (2001) and Gavious, Moldovanu and Sela
(2002) in the context of incomplete information.4
Our results may contribute to explaining why mechanisms such as hier-
archies or other organizational structures have evolved by which the alloc-
ation of prizes is governed by a multi-stage conflict.5 Such structures may
delay the allocation of a given prize, compared to a single stage conflict, but
can considerably reduce the overall resources that are dissipated among the
group of players. Compared to a standard all-pay auction, a tug-of-war that
is not rigged in favor of one of the players also improves allocative efficiency;
the probability with which the prize is awarded to the player who values it
more highly is higher in the tug-of-war than in the standard all-pay auction.
In the next section we outline the structure of the tug-of-war and char-
acterize the unique Markov perfect equilibrium. In section 3 we discuss the
efficiency properties of the tug-of-war and compare it with the all-pay auc-
tion. Section 4 concludes.
2 The analytics of the tug-of-war
A tug-of-war is a multi-stage game with a potentially infinite horizon which
is characterized by the following elements. The set of players is {A, B}. The
set of states of the war is given by a finite ordered grid of m + 1 points
M ≡ {0,1, ...m} in R1. The tug-of-war begins at time t = 1 with players
in the intitial state J(1) = mA, 0 < mA < m, which may either be chosen
by nature, or may be a feature of the institutional design. In each period
4For further applications of the all-pay auction see Arbatskaya (2003), Baik, Kim and
Na (2001), Baye, Kovenock and De Vries (2005), Che and Gale (1998, 2003), Ellingsen
(1991), Kaplan, Luski and Wettstein (2003), Konrad (2004), Moldovanu and Sela (2004),
and Sahuguet and Persico (2005).
5 There are, of course, other explanations for hierarchies more generally, which, however,
focus on different aspects of a hierarchy (see, e.g., the survey in Radner 1992). Radner
(1993) for instance, considers a problem of efficient information aggregation, asking what is
the efficient decision tree. Closer to the issue of allocation of goods in a conflict, Warneryd
(1998) and Müller and Warneryd (2001) consider distributional conflict between rival
groups followed by distributional conflict within the winning group as a type of hierarchical
conflict. Both these approaches focus on the "tree-" or "pyramid"-property of hierarchies
that reduces the number of players when moving to the top, whereas our approach does
not use this property. We consider only two contestants throughout and focus on the
sequential, repeated nature of decision process.