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Strategic Delegation to Organizations

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Strategic Delegation to Organizations

Abstract

In strategic environments, a principal may increase her payoffs when she delegates decisions to an agent with exogenously or endogenously (e.g. via a contract) diverse preferences. We show that a principal can also increase her payoffs by delegating decisions to an organization of agents-i.e. to a group of rational individuals who interact according to a specified set of rules-even when the agents' preferences are identical to those of the principal. Arguably, this provides novel intuition regarding the contemporary structure of firms in several oligopolistic markets, where decision making is decentralized and the interests of agents and firm owners are, broadly speaking, aligned. JEL classification codes: D71, D72.
Strategic Delegation to Organizations
Petros G. Sekeris
Montpellier Business School
Dimitrios Xefteris
University of Cyprus
July 4, 2021
Abstract
In this paper, we show that a principal can increase her payoffs by delegating
decisions to an organization of agents—a group of rational individuals who interact
according to specified rules—even when the agents’ preferences are identical to those
of the principal. The mechanism driving this result rests on the limited impact of
individual choices on the firm’s policy, when multiple agents interact in shaping it.
In competitive environments, delegating decisions to organizations of agents augments
the set of equilibrium outcomes, allowing for Pareto improvements. Hence, our results
provide a novel rationale for decentralized decision-making in firms.
JEL classification codes: D71, D72.
Keywords: delegation; organizations; decentralization; efficiency.
1 Introduction
The structure of organizations crucially influences their efficiency and profitability. Yet,
although firms often-wise interact strategically, little advances have been made so far in
We are grateful to the editor of this journal, Alessandro Bonatti, and three anonymous referees for
their very constructive comments. We also thank Masaki Aoyagi, Antonio Cabrales, Junichiro Ishida, Frago
Kourandi, Francine Lafontaine, Patrick Legros, In´es Macho-Stadler, Noriaki Matsushima, David P´erez-
Castrillo, Ali Sina Onder, Rapha¨el Soubeyran, Miguel Urdanoz Erviti, and Ansgar Wohlschlegel for valuable
discussions and insights.
Montpellier Business School, 2800 Avenue des Moulins, 34185 Montpellier, France. email:
p.sekeris@montpellier-bs.com. Petros Sekeris is member of the Entrepreneurship and Innovation
Chair, which is part of LabEx Entrepreneurship (University of Montpellier, France) and funded by
the French government (Labex Entreprendre, ANR-10-Labex-11-01)
Department of Economics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus. email:
xefteris.dimitrios@ucy.ac.cy
1
understanding their organization design while accounting for the competitors’ strategic be-
havior (Sengul 2018). This paper attempts to explore the consequences of the strategic
interaction within organizations—or groups of players—when strategic interaction between
organizations is also relevant for outcomes.
To expand our understanding of the question at hand, we develop a two-stage model of
strategic delegation to organizations. In the first stage principals (or the firm’s owners) are
allowed to create “organizations” by delegating decisions to agents (or division managers)
with perfectly aligned, or almost perfectly aligned preferences to the principal, and by defin-
ing the rules of interaction among these agents. All firms’ active players (principals and
delegates) then play a game against other organizations organizations, which may include
unitary actors.
The key feature of delegating decisions to an organization of agents is the following:
in a decentralized decision making structure the overall impact of a single agent on the
firm’s policy is smaller compared to when a single individual decides the firm’s policy alone.
Indeed, certain changes in the firm’s policy that are easy to single-handedly execute under the
centralized structure, require joint deviations of multiple agents when decisions are delegated
to an organization. Therefore, individual incentives for deviations away from a posited profile
can be substantially weaker than under centralized decision making.
Consequently, we show that when decision making is delegated to organizations of agents,
the set of equilibria is always at least as large as the set of equilibria of the game featuring
only unitary actors, i.e. when principals make all the firms’ decisions. We demonstrate
that delegating decisions to organizations is always part of a subgame perfect equilibrium,
including in instances where the game admits a Pareto-superior allocation to the equilibrium
payoffs of the subgame with unitary players. Therefore, creating organizations is incentive
compatible and might generate Pareto-superior equilibria that are absent from the game
with unitary players. Importantly, these positive welfare effects of decentralized decision
making do not hold when a firm operates in a non-strategic framework (monopoly, perfect
competition), but they arise irrespective of whether contracts are observable or not, i.e.
contracts supporting such equilibria are robust to renegotiation attempts.
To better grasp the importance of accounting for the strategic dimension when the struc-
2
ture of organizations is endogenous, consider the following application that we later develop
more extensively. The headquarters of two firms, each featuring two divisions ran by separate
division managers, simultaneously choose whether to take decisions on behalf of the division
managers (centralized organization), or else to let the latter define their own division’s strat-
egy (decentralized organization). A division’s decision impacts the firm through its direct
effect on the profits of its two divisions, while also influencing the profits of the competi-
tor. This will be the case if, for instance, a division’s product positioning or advertising
defines the company’s image (e.g. environmental footprint, CSR orientation, technological
performance) thereby affecting the profitability of the firm’s other product/division, but also
impacting the competing firm’s profits on both markets. Likewise, the geographical location
of a firm’s divisions will generate comparable effects.
Assuming that the incentives of the headquarters and of the division managers are fully
aligned, it is natural that in a decision-theoretic setup where the competing firm’s actions
are fixed the headquarters opt for a centralized organization. Indeed, in this case, any out-
come that could have been achieved with a decentralized organization is also implementable
with a centralized one. However, accounting for strategic interactions radically nuances this
observation. Indeed, each of the division managers of a decentralized firm has a reduced
capacity for deviations compared to a centralized structure, and, hence, they may not find it
profitable to change a policy of the firm from which the headquarters would have deviated.
In other words, profitable changes that the headquarters could single-handedly execute, may
require joint deviations under decentralization.
Strategic delegation to organizations can be thought of in contexts of applied relevance.
Imagine, for instance, low marketing expenses being adopted by competing firms in specific
industries, and any attempt to increase these expenses by a given firm—while profitable if
the other firms stick to the low expenses—provokes a costly race to all firms which decreases
overall profitability. In such instances, the competing firms may find it profitable to jointly
stick to low marketing expenses, where they manage to commit not to deviate from that
decision through the very structure of their organization. For example, if each firm has to
choose between a centralized structure and a decentralized one in which the decision—low
or high marketing costs—is taken by several agents via simple majority voting, then there
3
is always an equilibrium in which all firms delegate and select low marketing expenses.
While this simple example relies on an organizational structure that leads to Pareto-
superior outcomes via “indifference”–that is, deciding low marketing expenses via voting
requires that sufficiently many agents vote for this option, so that no single agent has any
effect on the outcome—as we show, more elaborate organizational structures can lead to
Pareto-superior “strict” Nash equilibria in the agents’ subgame. This is important, as it
suggests that perfect alignment of preferences between principals and agents is not a neces-
sary condition for the emergence of Pareto improvements with decentralized decision making.
In fact, as we show by the means of an application inspired from the coordination-adaptation
literature (e.g. Dessein and Santos 2006, Rantakari 2008), the positive welfare effects of de-
centralized decision making can persist even when the preferences of the principal and the
involved agents are very heterogeneous.
In the next section we review the related literature, before developing our model and the
paper’s main theoretical contributions in Sections 3 and 4. Section 5 shows how delegating
decisions to organizations leads to superior payoffs in a setting of applied interest, and Section
6 concludes.
2 Literature Review
Our main contribution is to the literature on the theory of the firm, and more specifically
on the optimal degree of delegation inside the firm (e.g. Holmstr¨om 1977, Holmstr¨om and
Milgrom 1991). The early literature disregarded the coordination problems that emerge
in complex organizations. Recognizing this limitation, scholars reconsidered the delegation
question by weighing the benefits of having a more decentralized, and thus adapted (to local
conditions), firm against potential costs resulting from reduced coordination capacity (e.g.,
Dessein and Santos 2006, Rantakari 2008, Dessein et al. 2010, Dessein et al. 2019). In
essence, decentralization presents several advantages, since it allows for the better-informed
and apt agent to decide for the firm, but given the (typical) mis-alignment of the agents’ and
the principal’s preferences, centralization can help to overcome coordination issues between
4
the firms’ various departments or divisions.1
The added value of the current analysis is to place firms with such complex organizations
in a strategic environment. Indeed, although scholars have developed elaborate theories re-
lated to the design of incentives and the organization of tasks inside firms (Dessein 2014),
most theoretical advances position the firm in a decision-theoretic setting (e.g. Dessein and
Santos 2006, Rantakari 2008), when reality often involves strategic interaction with com-
peting firms. Alonso et al. (2015) also considered the effect of increased product market
competition on the structure of organizations that juggle between adaptation and coordina-
tion needs, predicting that more competitive settings result in more centralized structures.
In their model, the mechanism operates through higher adaptation needs (which increase
with competition) being best covered by centralized schemes. Instead, our own mechanism
relies exclusively on the strategic dimension of the game. While this idea was introduced
earlier (Corch´on 1991, Polasky 1992, Faul´ı-Oller and Giralt 1995, Baye et al. 1996, and
arcena-Ruiz and Espinosa 1999), we generalize the setup (i.e. not restricting the analy-
sis to Stackelberg settings) and uncover that strategic delegation in organizations produces
Pareto-superior equilibria, therefore contrasting with these earlier works.
Our paper also relates to and partially builds on the strategic delegation literature that
considers principal-agent relationships inside firms that compete strategically (e.g. Vickers
1985, Fershtman and Judd 1987, Sklivas 1987). By delegating decisions to agents, a principal
or owner can pre-commit to an action the principal would rationally refrain from implement-
ing. In the context of quantity competition, while it is individually rational for principals
to incentivize their managers to be aggressive, this eventually gives rise to Pareto-inferior
outcomes for all firms’ principals. In a seminal contribution, Fershtman et al. (1991) estab-
lish a “folk theorem” in strategic delegation games whereby firms may nevertheless achieve
Pareto-superior outcomes by appropriately designing contracts. Notice that a key compo-
nent of the strategic delegation literature is the commitment power of contracts, whether
observed or not (Katz 1991, Caillaud et al. 1995, Fershtman and Kalai 1997, Kockesen and
1Alonso et al. (2008) develop a setup where coordination may be better achieved in a decentralized firm
because of the distorted incentives to communicate the true information over local needs under centralization.
This result is further confirmed by Rantakari (2013), who also shows that increased environment volatility
(i.e. volatility in adaptation needs) is conducive to more decentralization.
5
Ok 2004), for otherwise the principal would not be able to communicate his commitment to
non-individually rational strategies to the competitor(s). Our contribution stands in sharp
contrast to this strand of the literature since the commitment in our setup is instead rooted
in the firms’ organizational design which has been recognized as “more visible and harder to
reverse” (Sengul 2018) than contracts.
Last, we contribute to the literature on teams that studies the incentives to assign tasks
to teams of individuals to benefit from the members’ differential abilities, the superior ra-
tionality of a group over individuals, or even from idiosyncratic group members’ behavioral
biases (e.g. Becker and Murphy 1992, Chen 1999, Brandts and Cooper 2006, Charness and
Sutter 2012, Alonso et al. 2015). Our study complements these findings by uncovering the
strategic consequences the creation of teams bears on the interactions with other decision-
makers. von Stengel and Koller (1997) and Charness and Jackson (2007) also study teams
operating in strategic settings, and we expand their contributions by proposing a generic
and encompassing model that allows for strategic interaction among teams. Last, Kim et
al. (forthcoming) identify conditions under which the equilibrium under team-play will con-
verge with the number of team members (non-monotonically though) to the game’s Nash
equilibrium, even though agents may not be fully rational; a theory that is experimentally
explored in specific setups in Kim and Palfrey (2021). Our own contribution establishes how
Pareto-superior payoffs to the Nash equilibrium may be attained by allowing team-leaders
to design the rules of within-team interaction.
3 The model
3.1 Formal description
Consider a two-player normal form game involving player Awith strategy set SAand player
Bwith strategy set SB. The payoffs of the two players at every strategy profile (sA, sB)
SA×SBare given by UA(sA, sB) and UB(sA, sB) respectively. We will refer to this game by
the term “original”.
To study delegation to organizations we define the “delegation” game: a two-stage, six-
6
player extensive form game such that in the first stage of the game delegation decisions are
made and in the second stage of the game players engage in a simultaneous interaction that
determines their payoffs.
The set of players is {A, A, a, B, B, b}. The players named by calligraphic capital letters
will be the “principals” and players named by corresponding non-calligraphic letters will
be their “agents”. In the first stage of the game, the principals simultaneously choose
their delegation strategies: player J ∈ {A,B} selects ωJJ⊆ QJ={(F;S, S0)|F:
S×S0SJ}. A delegation strategy, or an organization of agents, ωJ= (FJ;SJ
J, SJ
j)
is such that (SJ
J, SJ
j) are the strategy sets of J’s agents, Jand j, in the second-stage of
the game; and FJis a surjective function such that FJ: (SJ
J, SJ
j)SJ. By assuming
that FJis a surjection we impose that the principals cannot limit the set of possible firm
decisions through their delegation strategies. This allows us to focus on the pure effects of
decentralized decision making in strategic contexts, and not be distracted by other forms of
principal intervention (e.g. prohibiting certain firm decisions, and/or incentivizing others).
In the second stage of the game, the delegation strategies of the principals become
public knowledge and the agents’ subgame begins: the other four players simultaneously
choose a strategy from their corresponding strategy sets, SA
A, SA
a, SB
B,and SB
b.The payoffs
of player i∈ {A, A, a}at every strategy profile (sA
A, sA
a, sB
B, sB
b)SA
A×SA
a×SB
B×SB
bof each
second-stage subgame, are given by UA(FA(sA
A, sA
a), F B(sB
B, sB
b)); and the payoffs of player
i∈ {B, B, b}at every strategy profile (sA
A, sA
a, sB
B, sB
b)SA
A×SA
a×SB
B×SB
bof each second-
stage subgame, are given by UB(FA(sA
A, sA
a), F B(sB
B, sB
b)). That is, every principal has the
same preferences as her agents on the game’s outcomes.
We employ the following standard equilibrium concepts.
Definition 1 A Nash equilibrium (NE) of the original game is a strategy profile:
sA,˜sB)SA×SBsuch that UA(˜sA,˜sB)UA(sA,˜sB)and UBsA,˜sB)UB(˜sA, sB),
for every sASA\ {˜sA}and sBSB\ {˜sB}.
Definition 2 A subgame perfect equilibrium (SPE) of the delegation game is a pair:
˜ω= (˜ωA,˜ωB) = (( ˜
FA;˜
SA
A,˜
SA
a),(˜
FB;˜
SB
B,˜
SB
b)) A×B,
and a vector:
7
sA
A(ω),˜sA
a(ω),˜sB
B(ω),˜sB
b(ω)) for each admissible ωA×B,
such that:
UA(FAsA
A(ω),˜sA
a(ω)), F B(˜sB
B(ω),˜sB
b(ω))) UA(FA(sA
A(ω),˜sA
a(ω)), F B(˜sB
B(ω),˜sB
b(ω))),
UA(FAsA
A(ω),˜sA
a(ω)), F B(˜sB
B(ω),˜sB
b(ω))) UA(FAsA
A(ω), sA
a(ω)), F B(˜sB
B(ω),˜sB
b(ω)))
for every sA
A(ω)6= ˜sA
A(ω), and sA
a(ω)6= ˜sA
a(ω); and
UA(˜
FAsA
A(˜ω),˜sA
a(˜ω)),˜
FBsB
B(˜ω),˜sB
b(˜ω))) UA(FAsA
A(ω),˜sA
a(ω)),˜
FBsB
B(ω),˜sB
b(ω))),
for every ω= (ωA,˜ωB)A× {˜ωB}\{˜ω}(respectively for players {B, B, b}).
While we rely on these solution concepts, we also try to provide a stronger version of our
results, i.e. require that the equilibrium notion meets additional criteria. Specifically, we
will sometimes demand that if a proper subgame is played by the agents along the path of
a SPE, then the agents’ decisions need to constitute a strict Nash equilibrium.
3.2 Discussion of the assumptions
According to the above formulation, the principal J ∈ {A,B} delegates part of the decision
to agent Jand another (possibly partly or totally overlapping) part of the decision to agent
j. Obviously, this is just a way to frame the problem that we are tackling and alternative
formulations would make as much sense, and lead to identical results. For instance, we
could have that the principal also participates in the decision making stage as in Rantakari
(2008).2The important modelling assumption that is crucial for the analysis is not related to
the identity of the players that participate in the second stage, but, instead, to the fact that
the principal can shape the rules of interaction of decision makers with similar preferences.
While we have assumed that the principal can “split” her decision in any arbitrary manner
(as long as surjective properties are satisfied), we need to note that in several applications
not all delegation strategies might be equally plausible/easy to implement. For instance,
when the strategy of a player in the original game can naturally be decomposed in a pair of
non-ovelapping decisions (e.g. the production decisions by different divisions of a firm), then
2Indeed, delegating the whole decision to a unique agent, is identical to not delegating at all. Given the
alignment of preferences, there is no substantial difference in deciding on your own or allowing somebody
else with identical preferences to make the choice. This modelling choice is made to keep notation to a bare
minimum, and the results would obviously remain unperturbed had we instead assumed that the principal
can participate himself in the second stage decision-making process.
8
delegating each of these decisions to a separate agent seems as the most obvious delegation
strategy, and organization structures such that the two agents interact in jointly shaping
both decisions might be harder to design/implement. For our main analysis, we abstract
from such issues, but in our subsequent application we show that delegation can have the
same positive effects even if principals are constrained to choose simple delegation strategies,
i.e. either decide on all issues on their own, or delegate each (non-ovelapping) decision to a
different agent.
We consider that agents have the same utility function as the principals, but we would
like to derive predictions that are robust to small misalignments in terms of preferences.
This is important because even if contracts compensate agents proportionally to the firm’s
profits, different individual preferences and/or other career concerns might make the agents’
and the principals’ interests diverge. Thus, if a result crucially depends on the preferences
of agents and principals being totally aligned (i.e. same ordinal preferences), and collapses
for the slightest misalignment, it is not as empirically relevant as a result that is robust in
that respect. This is why we are interested in equilibria that are strict (i.e. each player
has a unique optimal action) in the agents’ subgame: As long as the agents’ interests are
“sufficiently”–but not necessarily perfectly—aligned with those of the principal, the agents
have no incentives to deviate.3
4 Results
To prove our general results we assume that ΩJ⊆ QJfor every J ∈ {A,B}. That is, the
principals have access to every admissible organization structure. In the next section we
show that our results can hold even if the available organization structures are very few.
We begin by presenting an observation which will be the basis of the subsequent efficiency
properties and incentive-compatibility of delegating decisions to organizations of agents.
3Notice that our approach is more permissive than the notion of strict SPE, which requires that players
have a unique best response also in subgames off the equilibrium path (see, for instance, Kosfeld et al.
(2009)). As we show in our application (developed in Section 5), our results remain relevant in several
setups even if one employs this less permissive solution approach.
9
Lemma 1 Assume that the original game has a NE (˜sA,˜sB). Then, every subgame of the
six-player game admits a NE such that the payoffs of A,Aand aare UA(˜sA,˜sB)and the
payoffs of B,Band bare UB(˜sA,˜sB).
All proofs can be found in the Appendix.
The intuition of Lemma 1 is rather straightforward. If a strategy profile is part of an
equilibrium of the original game, this implies that there are no profitable deviations from
this strategy profile, including deviations along a reduced strategy sub-set of the original
set. When delegating decisions to organizations of agents whose strategy set constitutes a
sub-set of the original strategy set, there can therefore be no profitable deviation from the
strategy profile under consideration.
This first result, while easy to establish, is key for understanding the intuition behind
the analysis that follows. Among others, it guarantees that whenever the original normal
form game admits a Nash equilibrium, the corresponding extensive form game admits a
subgame perfect equilibrium. If we consider the very large sets of delegation strategies at
the disposal of the original players in the first stage of the six-player game, the importance
of this observation becomes apparent: when the original game possesses an equilibrium not
only are we sure that the extensive form game admits an equilibrium, but we also have a
lower bound of the maximum payoffs that can be achieved in a subgame perfect equilibrium.
All these allow us to state the following corollary to our first lemma.
Corollary 1 Assume that the original game has a Nash equilibrium. Then, a) every subgame
of the six-player game admits a Nash equilibrium, and, consequently, b) the six-player game
admits a subgame perfect equilibrium.
We now turn our attention to delegation, and try to understand if it may lead to superior
outcomes. We first present an intuitive, yet valuable observation.
Proposition 1 Consider any equilibrium strategy profile of the original game (˜sA,˜sB). If
there exists a strategy profile of the original game ( ˙sA,˙sB)such that UA( ˙sA,˙sB) = ˙
UA
UAsA,˜sB)and UB( ˙sA,˙sB) = ˙
UBUBsA,˜sB), with ˙
UJ> UJ(˜sA,˜sB)for some J, then
there exists a SPE in our six-player game with payoffs ˙
UAfor players A,Aand aand
payoffs ˙
UBfor players B,Band b.
10
To understand this result, observe first that from Lemma 1 we know that since (˜sA,˜sB)
is an equilibrium strategy profile of the original game, then every subgame of the six-player
game admits a Nash equilibrium guaranteeing players the same payoffs. Observe though
that player Acan always find an admissible delegation strategy such that the firm’s strategy
is ˙sAif at least one player chooses some strategy ˇs(which belongs both to SA
Aand to SA
a).
Under such a delegation strategy, if player A(a) expects that player a(A) will choose ˇs,
she is indifferent between ˇsand any other strategy, and both players playing ˇsis a mutual
best response. This is true also for the second firm. Hence, ( ˙sA,˙sB) is a Nash equilibrium
outcome of the subgame in which both principals choose the posited delegation strategy. To
then see why this may happen in a subgame perfect equilibrium, notice that in any subgame
in which at most one of the principals sticks to the given delegation strategy, there is a
Nash equilibrium with payoffs UAsA,˜sB) and UBsA,˜sB), which are (weakly) smaller than
UAand UBrespectively. Hence, any Pareto-superior outcome can be implemented by a
subgame perfect equilibrium when delegation is possible.4
4.1 Robust organizations
While the delegation strategy supporting this observation is simple and applies to general
settings with several agents and/or principals, it requires that the agents’ incentives are per-
fectly aligned with the principal’s in order to support the result (i.e. the ordinal preferences
of the principal and agents are the same). In real life settings, it is hardly ever the case that
an agent is indifferent between strategy ˇsand any alternative even if the firm’s profits (and,
hence, her pay) are not impacted by this choice. Agents build CVs, networks and reputation,
and all of their decisions are crucial in this respect, beyond their direct salary effects (e.g.
Williamson 1963, Cao et al. 2019). As such, the entire proof would then collapse if a player
had incentives to deviate from the stated equilibrium strategy, even though his deviation
does not directly alter the firm’s profits.
Second, the presented delegation strategy requires both agents in a firm to share (at
least part of) their strategy set, when in reality organizations more often than not clearly
delineate their agents’ action space in a manner that avoids such overlaps. That is, the above
4We thank a reviewer for proposing this elegant reasoning to us.
11
observation, while theoretically appealing, does not seem to be robust from an empirical
perspective.
To produce results that do not collapse once the perfect alignment assumption is relaxed,
we next investigate the existence of robust equilibrium organizations. That is, delegation
strategies that can support SPE with Pareto superior outcomes, such that all agents have
a unique best response in the relevant agents’ subgame. If such an equilibrium exists, then
it survives even if the agents’ incentives are not fully in line with the firm’s goals and/or if
they are not even observable by the principal, as long as any misalignment is slight/not too
large.5
Proposition 2 If there exists sA,¨sB)such that UA(¨sA,˙sB)<˙
UAand UB( ˙sA,¨sB)<˙
UB,
there exists a SPE in our six-player game with payoffs ˙
UAfor players A,Aand aand payoffs
˙
UBfor players B,Band b, such that the NE in the agents’ subgame along the SPE path is
strict.
This result proves that delegation to organizations of agents in certain contexts might
be both incentive compatible and payoff-increasing, even when agents’ preferences are not
fully aligned. That is, the original players might choose to delegate their decisions to players
with identical or sufficiently similar preferences as part of a subgame perfect equilibrium
play, and also enjoy larger payoffs compared to the no-delegation benchmark. The core
intuition of this result is that if there exists a strategy profile Pareto-dominating the Nash
equilibrium of the no-delegation game, and if there also exists a deviation strategy from the
Pareto-superior outcome that leaves the deviating party worse-off, then each of the original
players can design an organization of agents such that, when all delegates choose actions that
lead to the Pareto-superior outcome, the deviations of any agent will lead to the undesirable
outcome, leaving everybody strictly worse-off.
This result ensures that the Pareto-superior outcome can be implemented in equilibrium
even in contexts where the indifference-based delegation strategy supporting Proposition 1
5In the context of a finite game, a possible misalignment of preferences between the principal and agents
(or among the agents) would be to have the same ordinal preferences regarding the firm’s policy, but different
preferences regarding one’s own action. If the players assign a sufficiently small weight to the latter dimension,
then these preferences satisfy our description of slight misalignment.
12
cannot be applied (possibly due to a mild misalignment between the agents and the principal,
or exogenous restrictions). To better grasp this last point, consider the abstract payoff matrix
in Table 1 depicting the payoffs of two firms, Aand Bwhen each can choose an action from
{X,Y,X,Y}. If delegation was not a possibility so that the principals simultaneously decided
their firms’ strategies, the equilibrium strategies of this “original game” would be (Y,Y)
yielding payoffs of 2 to each firm. Allow next for delegation, considering that all the agents
are fully aligned with their principal, except for agent A. The payoff of agent Ais equal
to the firm’s profits plus a small reward if she chooses an action that could lead to a firm
decision Y, if player aalso selected an appropriate action. It is immediate to observe that
the delegation strategy proposed to support Proposition 1 does not enable firms to reach
the Pareto-superior outcome (X, X)because of the preference misalignment. If both agents
of firm Ause the strategy ˇswhich leads to firm policy X, and the other firm is expected to
choose Xtoo, then Ahas incentives to deviate to some ˇs0. Indeed, by the way that we have
defined ˇs, if Auses it, then her firm cannot choose Yindependently of the choice of player
a. Hence, if aplays ˇsand thus the firm’s policy is guaranteed to be X, then agent Ais
strictly better off by choosing an alternative strategy ˇs0, which could potentially lead to Yif
aalso properly modified her strategy (by the surjective properties that organizations have to
satisfy, such a strategy is guaranteed to exist). Therefore, agent awould also have incentives
to deviate away from ˇsto induce a firm decision Y, and the Pareto-superior outcome, (X, X ),
would not be attainable in SPE.
However, when each firm is managed by an alternative organization of two agents—one
deciding the letter of the firm’s strategy and one deciding whether it should be bold or not—,
then (X, X) is a SPE, as long as Acares to a sufficiently large degree about the firm’s profits.
Indeed, as suggested by Proposition 2, this organization leads to strict NE in the agents’
subgame along the SPE path. Hence, it is robust to small payoff asymmetries among the
participating agents.
Some important remarks are in order to qualify our result but also to underline the
implications and generality of our finding.
One should first note here that while delegating decisions to organizations might generate
Pareto-inferior Nash equilibria in certain subgames—not always, but this possibility cannot
13
Firm B
X Y X Y
X 3,3 3,2 2,2 1,4
Firm AY 2,3 2,2 2,2 1,4
X2,2 2,2 2,2 1,3
Y4,1 4,1 3,1 2,2
Table 1: An abstract example of strategic delegation in organizations.
be ruled out—, allowing principals to delegate decisions to organizations cannot give rise to
a subgame perfect equilibrium with a Pareto-inferior outcome, when off-the-equilibrium path
firms are expected to coordinate to the equilibrium outcome of the original game. This is so
because if one of the principals believes that by delegating to an organization she will end
up with a payoff that is inferior to the one that she would get in the original game, she can
deviate and delegate decisions to a single delegate. Since, this guarantees that her payoff will
be at least as high as in the original game, independently of the delegation strategy chosen
by the other original player, it is straightforward to conclude that delegation to organizations
might appear in such subgame perfect equilibria, only if it helps both principals reach Pareto-
superior outcomes.
Second, it is important to stress that along the equilibrium path, the potential existence
of multiple equilibria in the second stage of the game could be mitigated if one allowed a
more general set of possible organization structures, with principals being able to trim the
set of decisions that the agents are allowed to implement. While this could be valuable
in practical terms and would provide an unambiguous strengthening of our result from an
implementation perspective, it would arguably obscure the mechanism through which Pareto
improvements obtain: it is the delegation of the firm’s strategy to interacting multiple agents
that is responsible for the welfare improvements, and this obtains even if all possible strategies
can be reached.
One third crucial observation relates to the commitment of delegation contracts. In
the strategic delegation literature where organizations are seen as fixed, it has been shown
that secret renegotiation of contracts will typically jeopardize the commitment power of
delegation, thereby striping delegation contracts from their strategic commitment power
14
(e.g. Katz 1991). In our setting this is not the case. We have assumed that the agents’
payoffs are identical (or simply proportional) to the payoffs of the corresponding principals.
As it is trivial to observe, all our results remain true for agents’ payoffs that are monotonically
increasing in the principals’ payoffs, as in the contracts considered in Fershtman et al. (1991).
Since in our setting the commitment emerges from the design of the organization, our results
are robust to secret renegotiations of contracts/payoff-schemes between original players and
their agents in between stages (i.e. after the organizations are chosen but before agents make
their choices), provided we exclusively consider intuitive rewards (i.e. payoff-schemes that
are monotonically increasing in the principal’s payoff).6While it is not within the scope of
the paper to provide a full account of the potential dynamic considerations that arise in the
described agency context, our main theoretical argument seems to exhibit a certain degree of
robustness to secret renegotiations between firms and their delegates after the organizations
are set.
Lastly, notice that we have conducted our analysis considering the smallest possible
interesting organization of agents: the one that is composed of two individuals. Given our
constraints (i.e. the principal does not trim the decisions that agents can implement and the
agents’ interests are fully aligned with those of the principal) it follows that our results cannot
be generated by a trivial organization of one individual. Moreover, the finding described in
Proposition 2 can easily be reformulated so that it applies to organizations composed of
more than two individuals, establishing that the crucial step is when we go from one to two
agents, and not when we further increase the size of the organization.
Overall, delegating decisions to organizations of agents with aligned incentives and in the
context of complete information has advantages (e.g. renegotiation-proofness) and disadvan-
tages (e.g. equilibrium multiplicity) when compared to delegating decisions to single agents
with misaligned incentives, but, more importantly, it constitutes an additional mechanism
in the hands of principals who wish achieve welfare improvements in strategic contexts.
6If we allow firms to secretly propose any contract to the delegates, including non-intuitive contracts with
rewards non-monotonically related to the original game’s payoffs, we can still obtain a qualified version of
our result: when the strategy profile (¨sA,˙sB) (see Proposition 2) of the original game “bankrupts” firm A
(i.e. gives zero profits to the firm owner), there always exists an equilibrium in our delegation game that
leads to higher payoffs compared to the standard game, which is also renegotiation-proof. Indeed, in such
instances the owner is unable to incentivize delegates to deviate from the Pareto-superior allocation.
15
5 An application to the Adaptation-Coordination trade-
off
Our theoretical framework demonstrates that firms may have incentives to delegate decisions
to agents that are endowed with the same “abilities” as the principal and whose preferences
are (almost) perfectly aligned to the principal’s. As such, considering a firm in a strategic (as
opposed to a decision theoretic) environment gives rise to a novel mechanism through which
a firm may benefit from decentralization: the independence of actions of one’s own dele-
gates/division managers. Our argument therefore appears relevant to the existing literature
that weighs the coordination benefits of centralization against the adaptation benefits of de-
centralization (e.g. Dessein and Santos 2006, Rantakari 2008) by emphasizing the potential
disadvantages of coordination in strategic contexts. In order to illustrate the added-value of
studying the firm’s organizational design in a strategic environment, we amend a standard
one-firm model used in that literature by considering two strategically interacting firms while
adapting the payoff functions.
We consider a setup with two firms denoted by J ∈ {A,B}, where each firm features a
namesake headquarters (principal). Firm A(B) has two divisions, A(B) and a(b), and in
the original game in which firms are run by their headquarters, each firm decides a binary
action per division. That is, SJ={0,1}2, with a typical element (sJ
J, sJ
j). In the delegation
game, the headquarters first choose an organization structure ωJJ={c, d}, where
ccorresponds to centralized decision making (i.e. for firm J ∈ {A,B},SJ
J=SJ, and
FJ(sJ
J, sJ
j) = sJ
J), and dto a decentralized organizational structure such that the decision
corresponding to each division is delegated to a namesake division manager (i.e. for firm
J ∈ {A,B},SJ
J=SJ
j={0,1}, and FJ(sJ
J, sJ
j) = (sJ
J, sJ
j)).
Each firm J ∈ {A,B} has a payoff function, UJ, which is defined as the aggregate profits
of its two divisions. For firm Athese profits are given by:
UA=PA
A+PA
a,
where
16
PA
A=βmax{sA
A, sA
a} − γ
sA
AsB
B
+δmax{sB
B, sB
b},
and
PA
a=βmax{sA
A, sA
a} − γ
sA
asB
b
+δmax{sB
B, sB
b}.
The profits of firm Bare defined in a similar manner.
The first term represents the firm’s coordination costs that are modelled as a weakest link
game (e.g. Riedl et al. 2016). This captures situations in which different divisions cooperate
for the production of the final product/service, and the ”weakest” division determines the
overall quality of the service/product.7The second term captures the firm’s adaptation
cost in a reduced-form modelization: we assume that for each division, a departure from
the opponent’s strategy reduces profits.8The last term—which is absent from the related
literature—represents the positive externalities of one’s own failure to coordinate divisions’
strategies on the competing firm. For instance, a non-coordinating firm may face higher
production costs, and thereby ceteris paribus give a strategic edge to the competitor.9
We will initially assume that the payoffs of headquarters Jand of the firm’s two division
managers Jand jare given by UJ. We later relax this assumption and allow that each
division manager cares more about the profits of its own division to better connect our
application to the related literature.
The timing of the game is simultaneous in the original game and we solve for the game’s
Nash equilibria. In the delegation game the timing is sequential: in Stage 1 the two firms’
respective headquarters simultaneously decide ωJ, and in stage 2 all players simultaneously
decide their strategies. We solve for the game’s subgame perfect equilibria, and we focus
7Imagine there are two restaurants in a location, and in every given restaurant there are two cooks: one
responsible for preparing the vegetables and another responsible for cooking the meat. The speed of meal
preparation—and, hence, profits—is determined by the slowest of the two.
8One could instead have assumed a more complex specification with adaptation requiring one’s own
strategy alignment with a market variable, that would itself be a function of all firms’ actions. Yet the
intuition of the mechanism is well captured with this simplified formulation. For our restaurant example,
this suggests that the vegetable (meat) cook of restaurant Acares to be as fast as the vegetable (meat) cook
of restaurant B: being slower induces reputation and other costs, and being faster requires costly effort that
is not properly compensated.
9Indeed, restaurant Adoes not only stand to gain by being fast, but also by restaurant Bbeing slow.
17
only on generic parameter configurations—that is, we exclude from our consideration the
cases in which β=γand 2β=γ—for presentation reasons.
The original game
For any pair (sB
B, sB
b), the best response of Ais given by:
sA
A=sA
a= 0 if γ < β
sA
A=sA
a= min{sB
B, sB
b}if β < γ < 2β
sA
A=sB
Band sA
a=sB
botherwise
.
It is thus immediate to deduce that the equilibrium in the original game is described by
the following optimal strategies and payoffs for J= (A,B):
If γ < β, then ˜sJ
J= ˜sJ
j= 0,and ˜
UJ= 0,
If β < γ < 2β, ˜sJ
J= ˜sJ
j=χ∈ {0,1},
and ˜
UJ= 2(δβ)χ
Otherwise,˜sA
A= ˜sB
B=χ1∈ {0,1},˜sA
a= ˜sB
b=χ2∈ {0,1},
and ˜
UJ= 2(δβ) max{χ1, χ2}.
The delegation subgame
If ωA=c, for any pair (sB
B, sB
b), the best response of Ais defined as in the original game,
namely:
sA
A=sA
a= 0 if γ < β
sA
A=sA
a= min{sB
B, sB
b}if β < γ < 2β
sA
A=sB
Band sA
a=sB
botherwise
If ωA=d, for any 3-ple (sA
a, sB
B, sB
b), the best response of Ais defined as:
18
sA
A=
sA
aif γ < 2βand sA
asB
B
sB
Botherwise
,
and sA
ais defined likewise.
Using these best responses, we can then deduce the Nash equilibria for all possible second-
stage subgames:
Fully centralized subgame: (ωA, ωB) = (c, c)
Observe first that a fully centralized setup is equivalent to our original game and the
equilibrium payoffs are thus defined as above.
Partially centralized subgame: (ωJ, ω−J ) = (c, d)
If one firm adopts a decentralized organization, while its competitor opts for a centralized
organization, it is immediate then to observe that the equilibrium outcomes will be exactly
the same to the ones under full centralization.
Fully decentralized subgame: (ωA, ωB)=(d, d)
The last possible subgame is such that both firms decentralized decisions to the managers
in charge of their respective divisions. The equilibrium of this subgame is then described by
the following optimal strategies and payoffs:
If γ < 2β, ˙sJ
J= ˙sJ
j=χ∈ {0,1},and ˙
UJ= 2(δβ)χ
otherwise,˙sA
A= ˙sB
B=χ1∈ {0,1},˙sA
a= ˙sB
b=χ2∈ {0,1},
and ˙
UJ= 2(δβ) max{χ1, χ2}.
Having fully characterized the equilibria for all possible subgames, we can next solve for
the game’s first stage. Observing that the payoffs under full decentralization are always at
least as high as under the other organizational structures provided δ > β, we can deduce the
following proposition:
19
Proposition 3 If δ > β > γ, then the game admits a SPE such that ˙ωJ=d, for every
J={A,B}, which Pareto-dominates the fully-centralized solution and which involves a
strict NE in the agents’ subgame along the SPE path.
This stylized application captures well the intuition driving a principal’s incentives to
delegate decisions to an organization of agents when firms interact strategically. In the pa-
rameter space β > γ, the coordination costs to the firm’s headquarters (i.e. the principal)
are higher to the costs of adaptation. Given the assumed weakest link technology character-
izing the adaptation costs of a firm, the headquarters have incentives in coordinating both
departments’ strategies on the value generating the lowest possible cost, namely on 0. Since
the headquarters of both firms reason likewise, the firms end up being fully coordinated
and adapted to their competitors’ strategy, thence implying that at equilibrium no firm
would benefit from its opponent’s potential positioning away from the location minimizing
coordination costs.
Under a partial decentralization scenario, the division managers in the decentralized
firms can only reduce coordination costs if their own department is the one with the highest
“location”. Thence, their incentives to choose 0 are the same to the centralized firm only if
their own action is higher than the one of the other department of their firm. Otherwise,
the division manager cannot influence coordination costs, and therefore seeks to minimize
adaptation costs. Since, however, the strategy of the centralized firm is not affected by its
competitor in this parameter space, and thus locates all its departments’ actions in 0, both
departments of the decentralized firm will adapt to their competitor by acting likewise.
Under full decentralization, we are facing a game with a coordination problem since
all four departments have incentives in coordinating their actions on the department whose
location is closer to 0. As such, all four division managers choosing 1 is an equilibrium, hence
implying that there exists an equilibrium where all departments employ the same strategy
featuring a strictly positive value. Interestingly, while firms minimize their adaptation costs,
the coordination costs may nevertheless be strictly positive since the chosen actions may
depart from the cost-minimizing location. This, in turn, implies that firms will enjoy positive
externalities from their competitors’ failure to minimize coordination costs, which—if large
enough—will leave all decision-makes (headquarters and division managers) strictly better-
20
off than under full centralization or partial decentralization.
The gist of the fully decentralized subgame’s solution is the mechanism driving our main
theoretical result: by decentralizing decisions the headquarters (principal) reduces the de-
viation possibilities available to the division manager (agent) who is unable to reduce co-
ordination costs beyond the other department’s strategy. The parallel with our theory is
that under delegation, when the competing firms are expected to employ play ˙sA= ˙sB(in
our application (1,1)), firm Acan only reach ¨sA(in our application (0,1), or (1,0)) by the
means of an individual deviation of a division manager, with UAsA,˙sB)< U ( ˙sA,˙sB) (in our
application 2(δβ)γ < 2(δβ)). Hence, while a centralized structure would have jointly
localized the two departments’ actions at 0 so as to cut coordination costs (i.e. the analogue
to playing ˜sAin our theory), a division manager proves unable to do this unilaterally, thence
incentivizing him to opt for the minimization of the adaptation costs instead. Whether these
outcomes are preferable to the centralized and partially decentralized solutions eventually
depends on the values of the parameters (i.e. whether ˙
UA> U(˜sA,˜sB)).10
Observe that a necessary condition for Proposition 3 to hold (i.e. ˙
UA> U(˜sA,˜sB)) is that
δ > β, which in essence implies that the positive externalities enjoyed when the competitor
mis-coordinates his divisions’ strategies are larger to the own costs of mis-coordination.
While this may appear to be a demanding condition, one can show that it is met in standard
oligopoly models, e.g., an appropriate version of Cournot.
In the organizational design stage, for the parameter restriction δ > β > γ, both firms
decentralizing decisions is essentially the unique most reasonable prediction. Indeed, this fol-
lows directly from the fact that the subgames with fully decentralized firms generate (strictly)
Pareto superior outcomes, and that subgames with partial delegation admit a unique equilib-
rium which is welfare equivalent to the no-delegation outcome. Hence, firms have unilateral
incentives in decentralizing their own organization because in the event the competitor re-
tains a centralized structure the equilibrium in the partially decentralized subgame would
have been the same to the one obtained under full centralization, while if the competitor
decentralizes his own organization, the focal firm’s headquarters could only increase their
10The SPE that we characterize is essentially a strict SPE, since all players have a unique best response
in all subgames, both on and off the equilibrium path.
21
own payoffs.
The fact that the employed natural delegation strategy supports strict equilibria in the
agents’ subgame is also noteworthy, since it guarantees that our results are indeed robust to
preference misalignments between the headquarters and their division managers.11 In fact,
one can also verify that Proposition 3 remains unperturbed if division managers’ payoffs are
highly misaligned, as is typically assumed in the adaptation-coordination literature. Con-
sider a variant of our application where the headquarters’ payoffs are defined as above, while
division manager J’s payoff is instead given by UJ
J=PJ
J+αP J
j, with α[0,1], and define
similarly UJ
j. Such a conceptualization enables our application to cover a wide range of pref-
erences, spanning from perfect alignment (α= 1) to cases where division managers are only
concerned about their own division’s utility (α= 0). Moreover, assume the headquarters
have the choice between taking all decisions on their own (centralization), and decentralizing
decisions as above. It is quite immediate to show—and we thus omit the technical exposi-
tion for space concerns—that the exact same result contained in Proposition 3 would then
obtain, thus providing further support to the robustness of our mechanism to preferences’
misalignment.
It is interesting at this stage to go beyond the pure relevance of our theory in the above
context, and to compare the results of our model with the ones that would obtain absent
strategic interaction, i.e. in a decision-theoretic setup. Since the competitor’s strategies
would then be fixed, the positive externalities would then be the same irrespective of the focal
firm’s choice of organizational structure and positioning strategies. Thence, it is only obvious
to deduce that it would always be optimal for the headquarters to centralize decisions, and
implement the best responses described earlier. Hence, this simplified framework partially
inspired from Dessein and Santos (2006) and Rantakari (2008) reveals the essence of the
mechanism underlying our theory. Moreover, the same firm that would have adopted a
centralized organization of tasks when operating in a decision-theoretic environment, may
11To better grasp the importance of this result, imagine that we had instead envisaged a delegation strategy
(i.e. a surjective function F(.)) such that both division managers would face the same strategy set, and such
that both divisions’ actions would be 1 if at least one division manager chose a given strategy (i.e. the
surjective function considered in the proof of Proposition 1). It is then immediate to observe that, while a
Pareto-improving subgame Nash equilibrium of this modified game would still exist, it would nevertheless
not involve a strict NE in the agents’ subgame.
22
be incentivized to decentralize decision-making when operating in a strategic environment.
As explained, the intuition of the mechanism is the same to the one underlying our theory in
sections 3 & 4: strategic delegation enables firms to commit not to deviate from a possible
strategy by reducing the strategy set available to each DM/delegate as compared to the
company’s full strategy set.
In the context of the example we develop, this commitment via the very design of the
organization enables a firm to replicate the profits that would obtain under a centralized
scheme, while potentially increasing profits if the competitor also decentralizes decisions.
Indeed, with both firms strategically delegating decisions, Pareto-superior profits that would
have been subject to deviations with centralized organizations, are now equilibrium outcomes
given the added constraint on possible deviations. Thence, strategic delegation enables firms
to commit to a less aggressive strategy that eventually benefits both firms.
As a last point, it is interesting to observe that empirical studies establish a causal effect of
increased product market competition on decentralization of decisions inside the firm (Bloom
et al. 2010, Meagher and Wait 2014). These findings have been rationalized by scholars
studying the trade-off between increased decentralization, that enables firms to adapt to local
market conditions, vs increased centralization which allows improved coordination across the
firm’s various activities (e.g. Dessein and Santos 2006, Rantakari 2008). Yet, since product
market competition is by construction absent in these studies, increased competition has
therein been associated to reduced (profit) margins (e.g. Alonso et al. 2015), which in turn
affect the optimal delegation structure. While these findings are certainly very instructive,
our contribution highlights that in strategic settings firms can have an additional incentive
to decentralize decisions so as to commit to milder competition.
6 Conclusion
In this paper we have explored the incentives for firms to strategically delegate decisions to
organizations of agents when firms operate in strategic setups. Our findings reveal that max-
imizing the firm owner’s payoff does not necessarily require drafting elaborate agreements,
and that by carefully designing the organization, Pareto-efficient payoffs can be attained even
23
with extremely simple contracts where compensations are proportional to the organization’s
performance.
The argument behind our finding is rather intuitive: complexifying the structure of an
organization operating in a strategic environment by delegating decisions to agents with a
predefined set of rules shaping their interactions, expands the set of equilibrium outcomes.
New equilibria arise in such instances due to the limited impact of individual choices on the
firm’s policy, when multiple agents interact in shaping it. If this expanded set of equilib-
ria includes an equilibrium Pareto-dominating the one(s) of the game without delegation,
this Pareto-superior equilibrium is then a subgame perfect equilibrium of the game with
delegation.
To better fix the ideas, we develop an application inspired by the strand of the literature
that identifies adaptation and coordination needs as the backbone of firms’ organizational
structure. Our simplified application shows that if the mis-coordination of a firm’s de-
partments generates strong positive externalities on the competitor, as when a firm gains
a strategic edge because of the miscoordination among the competitor’s departments, a
Pareto-superior decentralized equilibrium can emerge endogenously. Strategic delegation in
the context of this application enables firms to commit not to deviate from Pareto-superior
outcomes, when centralized organizations would have deviated and would have implemented
strategies producing smaller positive externalities on each other, and eventually resulting in
lower equilibrium profits to all firms.
Our theory brings new insights on the firm’s organizational design. We have deliberately
kept the model’s structure to a bear minimum to demonstrate the advantages of strategic
delegation in the cleanest possible way. In future research it would be interesting to further
elaborate these initial findings by, e.g., considering incomplete information, refining the
structure of contracts, or specifying the type of market competition under consideration.
24
A Appendix
A.1 Proof of Lemma 1
Proof. In the first stage of the game, an original player, J ∈ {A,B}, decides a delega-
tion strategy, (FJ;SJ
J, SJ
j), such that FJ: (SJ
J, SJ
j)SJ. Hence, for every admissible
pair of delegation strategies, (FA;SA
A, SA
a) and (FB;SB
B, SB
b), there exists (˜sA
A,˜sA
a,˜sB
B,˜sB
b)
SA
A×SA
a×SB
B×SB
bsuch that FAsA
A,˜sA
a) = ˜sAand FB(˜sB
B,˜sB
b) = ˜sB. Given that (˜sA,˜sB)
is an equilibrium of the original game it follows that UAsA,˜sB)UA(sA,˜sB) for ev-
ery sASA, and UB(˜sA,˜sB)UB(˜sA, sB) for every sBSB. But since UAsA,˜sB) =
UA(FAsA
A,˜sA
a), F B(˜sB
B,˜sB
b)) and FA(sA
A, sA
a)SAfor every (sA
A, sA
a)SA
A×SA
a, it is the
case that UA(FAsA
A,˜sA
a), F B(˜sB
B,˜sB
b)) UA(FA(sA
A,˜sA
a), F BsB
B,˜sB
b)) for every sA
ASA
Aand
UA(FAsA
A,˜sA
a), F B(˜sB
B,˜sB
b)) UA(FAsA
A, sA
a), F BsB
B,˜sB
b)) for every sA
aSA
a. Similarly, we
have that UB(FAsA
A,˜sA
a), F B(˜sB
B,˜sB
b)) UB(FAsA
A,˜sA
a), F B(sB
B,˜sB
b)) for every sB
BSB
Band
UB(FAsA
A,˜sA
a), F B(˜sB
B,˜sB
b)) UB(FAsA
A,˜sA
a), F B(˜sB
B, sB
b)) for every sB
bSB
b. That is, every
subgame of the four-player game admits an equilibrium such that the payoffs of A,Aand a
are equal to UAsA,˜sB) and the payoffs of B,Band bare equal to UBsA,˜sB).
A.2 Proof of Proposition 2
Proof. We prove this proposition by focusing, explicitly, on a class of admissible delegation
strategies that lead to the desired result. This is similar to Fershtman et al. (1991) who also
prove by construction that contract-design can lead to any Pareto-superior outcome (i.e. by
limiting attention to a specific class of contracts—the target-compensation schemes).
Assume that ( ˙sA,˙sB) is a strategy profile of the original game that Pareto dominates the
equilibrium (˜sA,˜sB). That is, it is a strategy profile of the original game that gives weakly
larger payoffs to both original players—strictly larger payoffs to at least one of them—
compared to the payoffs corresponding to the equilibrium (˜sA,˜sB). Then, consider the fol-
lowing delegation strategy of player A: player Achooses an element from SA
A={u, d}and
player achooses an element of SA
a=SA.
If player Achooses sA
A=uthen FA(sA
A, sA
a) = sA
aexcept when sA
a= ˙sA. In that case
25
FA(sA
A, sA
a) = ¨sA. If player Achooses sA
A=dthen FA(sA
A, sA
a) = ˙sA
aif player achooses
sA
a= ˙sAand FA(sA
A, sA
a) = ¨sA
aotherwise. Notice that according to this simple delegation
strategy: a) all strategies in SAcan be reached, and b) {d, ˙sA}is a strict Nash equilibrium
of the two-player restriction of the second-stage subgame to FB(sB
B, sB
b) = ˙sB. That is, the
subgame in which Auses the posited delegation strategy and Ba similar delegation strategy
that leads to ˙sBwhen the play of Aand aare expected to lead to ˙sA
a, admits a strict Nash
equilibrium with payoffs UAfor players A,Aand aand payoffs UBfor players B,Band b.
If in all other subgames the original players believe that they will end up in equilibria with
payoffs UAsA,˜sB) and UBsA,˜sB), the existence of which is guaranteed by Lemma 1, then
employing the described delegation strategies in the first stage of the game is part of a strict
subgame perfect equilibrium.
References
[1] Ricardo Alonso, Wouter Dessein, and Niko Matouschek. When does coordination require
centralization? American Economic Review, 98(1):145–179, 2008.
[2] Ricardo Alonso, Wouter Dessein, and Niko Matouschek. Organizing to adapt and com-
pete. American Economic Journal: Microeconomics, 7(2):158–87, 2015.
[3] Michael R. Baye, Keith J. Crocker, and Jiandong Ju. Divisionalization, franchising, and
divstiture incentives in oligopoly. American Economic Review, 86(1):223–236, 1996.
[4] Gary S. Becker and Kevin M. Murphy. The division of labor, coordination costs, and
knowledge. Quarterly Journal of Economics, 152(4):1137–1160, 1992.
[5] Nicholas Bloom, Raffaella Sadun, and John Van Reenen. Does product market compe-
tition lead firms to decentralize? American Economic Review: Papers & Proceedings,
100:434–438, 2010.
[6] Jordi Brandts and David J. Cooper. A change would do you good. . . an experimental
study on how to overcome coordination failure in organization. American Economic
Review, 96(3):669–693, 2006.
26
[7] Bernard Caillaud, Bruno Julien, and Pierre Picard. Competing vertical structures:
Precommitment and renegotiation. Econometrica, 63(3):621–646, 1995.
[8] Xiaping Cao, Michael Lemmon, Xiaofei Pan, Meijun Qian, and Gary Tiane. Political
promotion, ceo incentives, and the relationship between pay and performance. Man-
agerment Science, 65(7):2947–3448, 2019.
[9] Gary Charness and Matthew O. Jackson. Group play in games and the role of consent
in network formation. Journal of Economic Theory, 136:417–445, 2007.
[10] Gary Charness and Matthias Sutter. Groups make better self-interested decisions. Jour-
nal of Economic Perspectives, 26(3):157–76, 2012.
[11] Fangruo Chen. Decentralized supply chains subject to information delays. Management
Science, 45(8):1076–1090, 1999.
[12] Luis C. Corchon. Oligopolistic competition among groups. Economics Letters, 36:1–3,
1991.
[13] Wouter Dessein. Incomplete contracts and firm boundaries: New directions. Journal of
Law, Economics, and Organization, 30(suppl 1):i13–i36, 2014.
[14] Wouter Dessein, Luis Garciano, and Robert Gertner. Organizing for synergies. American
Economic Journal: Microeconomics, 2:77–114, 2010.
[15] Wouter Dessein, Desmond Lo, and Chieko Minami. Coordination and organization
design: Theory and micro-evidence. Unpublished mansucript.
[16] Wouter Dessein and Tano Santos. Adaptive organizations. Journal of Political Economy,
114(5):956–995, 2006.
[17] Ramon Faul´ı-Oller and Magdalena Giralt. Competition and cooperation within a mul-
tidivisional firm. Journal of Industrial Economics, 43(1):77–99, 1995.
[18] Chaim Fershtman, Kenneth L. Judd, and Ehud Kalai. Observable contracts: Strategic
delegation and cooperation. International Economic Review, 32(3):551–559, 1991.
27
[19] Chaim Fershtman and Ehud Kalai. Unobserved delegation. International Economic
Review, 38(4):763–774, 1997.
[20] Bengt Holmstr¨om. On Incentives and Control in Organizations. PhD thesis, Stanford,
1977.
[21] Bengt Holmstr¨om and Paul Milgrom. Multitask principal-agent analyses: Incentive
contracts, asset ownership, and job design. Journal of Law, Economics & Organization,
7:24–52, 1991.
[22] Michael L. Katz. Game-playing agents: Unobservable contracts as precommitments.
RAND Journal of Economics, 22(3):307–328, 1991.
[23] Jeongbin Kim and Thomas R. Palfrey. An experimental study of 2 ×2 games played
by teams of players. mimeo, California Institute of Technology, 2021.
[24] Jeongbin Kim, Thomas R. Palfrey, and Jeffrey R. Zeidel. Games played by teams of
players. American Economic Journal: Microeconomics, forthcoming.
[25] Levent Kockesen and Efe A. Ok. Strategic delegation by unobservable incentive contract.
Review of Economic Studies, 71:397–424, 2004.
[26] Michael Kosfeld, Akira Okada, and Arno Riedl. Institution formation inpublic goods
games. American Economic Review, 99(4):1335–1355, 2009.
[27] Kieron J. Meagher and Andrew Wait. Delegation of decisions about change in orga-
nizations: The roles of competition, trade, uncertainty, and scale. Journal of Law,
Economics and Organization, 30(4):709–733, 2014.
[28] Stephen Polasky. Divide and conquer: On the profitability of forming independent rival
divisions. Economics Letters, 40:365–371, 1992.
[29] Heikki Rantakari. Governing adaptation. Review of Economic Studies, 75:1257–1285,
2008.
[30] Heikki Rantakari. Organizational design and environmental volatility. Journal of Law,
Economics, and Organization, 29(3):569–607, 2013.
28
[31] Arno Riedl, Ingrid M. T. Rohde, and Martin Strobel. Efficient coordination inweakest-
link games. Review of Economic Studies, 83:737–767, 2016.
[32] Metin Sengul. Advances in Strategic Management: Organization Design, chapter Orga-
nization Design and Competitive Strategy: An Application to the Case of Divisional-
ization, pages 207–228. Emerald Publishing Limited, 2018.
[33] Steven D. Sklivas. The strategic choice of managerial incentives. RAND Journal of
Economics, 18(3):452–458, 1987.
[34] John Vickers. Delegation and the theory of the firm. Economic Journal, 95:138–147,
1985.
[35] Bernhard von Stengel and Daphne Koller. Team-maxmin equilibria. Games and Eco-
nomic Behavior, 21:309–321, 1997.
[36] Oliver E. Williamson. Managerial discretion and business behavior. American Economic
Review, 53:1032–1057, 1963.
29
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