An Observable Delay Game with Unionised Managerial Firms
| Date | 01 February 2017 |
| Published date | 01 February 2017 |
| DOI | http://doi.org/10.1111/sjpe.12117 |
| Author | Luciano Fanti |
AN OBSERVABLE DELAY GAME WITH
UNIONISED MANAGERIAL FIRMS
Luciano Fanti*
ABSTRACT
The endogenous order of moves is analysed in a unionised Cournot duopoly with
managerial delegation and firm-specific unions, where firms choose whether to
set quantities sequentially or simultaneously. It is shown that, in contrast to the
standard duopoly with profit-maximising firms where both firms prefer to be the
leader and thus simultaneously chosen quantities emerge as an endogenous equi-
librium, a rich set of equilibrium outcomes may occur. In particular, the result
of sequential choices, which reverses the conventional wisdom in regard to Cour-
not duopolies, emerges as the endogenous equilibrium when the union’s wage ori-
entation is sufficiently high.
II
NTRODUCTION
Whether firms play a simultaneous or a sequential move, games should not be
exogenously postulated but should result from the firms’ decisions, because an
alternate order of moves often gives rise to significantly different results –this
is a recent cornerstone result of the literature on industrial organisation. One
of the most popular and important endogenous timing games is the observ-
able delay game, formulated by Hamilton and Slutsky (1990) and extended by
many other authors, such as Anderson and Engers (1994), Amir (1995), Mat-
sumura (1995), Normann (2002).
1
Observable delay games have been intensively developed in many contexts
and not only in the industrial organisation literature. Suitable examples
include works by Lambertini (1999a) in regard to international monetary pol-
icy, Ohkawa et al. (2002) on trade policies under international oligopoly, Jinji
(2004) and Lambertini (1999b) with respect to vertically differentiated duo-
poly, Jafarey and Lahiri (2009) concerning developing-country borrowing
from a monopolist lender.
*University of Pisa
1
For the experimental studies on this game, see Fonseca et al. (2006). Moreover, note that
another strand of this literature focuses, in the case of multiple equilibria, on equilibrium
selection, for instance using the criterion of risk dominance popularised by Harsanyi and Sel-
ten (1988) [e.g. van Damme and Hurkens (2004) and Amir and Stepanova (2006) in price
competition models with differentiated product markets].
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12117, Vol. 64, No. 1, February 2017
©2016 Scottish Economic Society.
50
In the industrial organisation literature, most contributions focus on the
context of mixed markets rather than that of private firms. In such a context,
for instance, under quantity competition and homogeneous products, Pal
(1998) considered only domestic firms, Matsumura (2003) considered only for-
eign firms, and Lu (2006) introduced both domestic and foreign firms into the
analysis, while price competition was assumed by Tomaru and Kiyono (2005),
Tasn0adi (2006), Ogawa and Kato (2006) and Barcena-Ruiz (2007); subse-
quently, Mendez-Naya (2011) showed that in a triopoly a merger between a
public firm and a private firm to form a mixed firm could change the market
structure from Stackelberg to Cournot competition.
Moreover, two striking features characterising modern oligopolies are the
presence of managers and unions. As regards the former, starting from Vick-
ers (1985), Fershtman (1985), Fershtman and Judd (1987) and Sklivas (1987)
(VFJS from here onwards), the oligopoly literature has considered the strate-
gic use of incentive contracts in product markets where decisions are delegated
to managers. In other words, it is assumed in a typical two-stage game that at
the first stage, the owners of each firm simultaneously determine the incentive
structure for their managers; at the second stage, the competing managers
play an oligopoly game, with each firm’s manager knowing his/her incentive
contract and those of competing managers.
In particular, each owner compensates his/her manager with a bonus based
on a weighted sum of objective performance measures, such as profits and
sales (‘sales delegation’), thus instructing the manager to adopt a more aggres-
sive behaviour in the market and thus force the rival firm to reduce output.
On the other hand, it is widely established that unions play a prominent
role in oligopoly contexts, as recently recognised by the growing literature on
unionised oligopolies (e.g. Horn and Wolinsky, 1988; Dowrick, 1989; Naylor,
1999; Lommerud et al., 2005). Also such models typically assume a two-stage
game, where, at stage 1, wages are unilaterally set by monopoly unions or are
bargained between firms and unions,
2
while, at stage 2, each firm (for given
wages) decides its optimal (profit-maximising) output (or price), which also
implies its labour demand.
While most contributions have dealt separately with either ‘managerial’ or
‘unionised’ oligopolies, Szymanski (1994), Fanti and Meccheri (2013) and
Meccheri and Fanti (2014) jointly considered these two features in both quan-
tity and price competition. Szymanski (1994) was the first to extend the man-
agerial delegation model by introducing wage bargaining between firm owners
and firm-specific unions, showing that in such a context, owners set incentives
2
In this paper we concentrate on the monopoly union case. In the literature on unionised
oligopolies, the monopoly union model is widely adopted (e.g. among others, Brekke, 2004;
Haucup and Wey, 2004; Lommerud et al., 2005). Note that, provided that unions are suffi-
ciently strong, the paper’s results can be extended to the case of a union-firm bargaining on
wages, because as noted by Lommerud et al. (2005) ‘As pointed out by, e.g. Dowrick (1989),
this [i.e. monopoly union] can be viewed as a limiting case of the wage-bargaining union,
where the union has all the bargaining strength’ (p. 723). Hence, the results under the present
model also apply, by continuity, to a ‘right-to-manage model’ where wage is bargained by
firm and union as long as the union’s bargaining power is sufficiently high.
AN OBSERVABLE DELAY GAME 51
Scottish Journal of Political Economy
©2016 Scottish Economic Society
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