Chapter 6 The Principal-Agent Problem and Incentives for Local Teams

Two timetables

Headquarters wants GMV to double this quarter and a return on investment next quarter. The local partner or country manager wants a steady income and a lasting reputation in the local business community: squeezing distributors or overdrawing influencer relationships to hit a volume target today means no one will work with you next year. This is not a matter of who is right, but of two timetables and two tolerances for risk. Economists call such problems principal-agent problems: the principal (headquarters) hands a task to an agent (the local team) whose effort it cannot fully observe and whose goals are not fully aligned with its own (Jensen and Meckling 1976; Holmström 1979).

A classic warning

In 1975 Kerr published a paper whose title says it all: “On the Folly of Rewarding A, While Hoping for B” (Kerr 1975). Organisations often reward what is easy to measure while hoping for what is hard to measure. Paying bonuses on GMV while hoping that the local team will protect the brand and long-term customer relationships is a textbook case.

Holmström and Milgrom turned this intuition into a rigorous model: multitask principal-agent theory (Holmström and Milgrom 1991). When an agent’s job contains several tasks that compete for the same time and energy, and some of them are hard to measure, strong incentives on the measurable task pull effort away from the unmeasurable ones. One of their conclusions is that in this situation optimal incentives are often weaker than a single-task model would suggest, sometimes even a fixed wage; only when the hard-to-measure task also gets some measure, even a noisy one, can the incentive on the measurable task be strengthened. Gibbons gives an accessible review of conclusions of this kind (Gibbons 1998).

A numerical model

Calculation

A local country manager divides effort between two tasks: short-term GMV (measured monthly, noise variance 1) and long-term partner and brand building (measurable only by a 12-month proxy such as the partner renewal rate or the share of repeat customers, noise variance 2; or not measured at all). Both tasks matter equally to headquarters, with diminishing returns; the parameter $s$ says how much the two tasks compete for time. The manager also values long-term relationships herself (her reputation in the local business community). She is risk-averse, with coefficient of risk aversion $r$ . Headquarters chooses the two incentive rates to maximise total surplus.

# Holmstrom & Milgrom (1991) multitask agency, numerically. A local country manager splits effort
# between t1 = short-term GMV (measured monthly, noise variance 1) and t2 = long-term partner and
# brand building, measured only by a noisy 12-month proxy such as partner retention or the share of
# repeat customers (noise variance 2), or not measured at all.
#   Value to headquarters:  2*sqrt(t1) + 2*sqrt(t2)   (both tasks matter, with diminishing returns)
#   Effort cost:            (t1^2 + t2^2)/2 + s*t1*t2  (s in [0,1): how much the tasks compete for time)
#   The manager also values t2 for its own sake (her standing with local partners): +0.2 per unit.
# Pay = fixed + b1*GMV + b2*proxy. CARA manager with risk aversion r; headquarters is risk-neutral and
# picks (b1, b2) to maximise total surplus, value - cost + 0.2*t2 - r/2*(b1^2*1 + b2^2*2);
# the fixed part then makes the manager just willing to sign.
import math

INTR = 0.2

def efforts(b1, b2, s):
    """Manager's best response: grad C = (b1, b2 + INTR), efforts non-negative."""
    g1, g2 = b1, b2 + INTR
    t1 = (g1 - s * g2) / (1 - s * s); t2 = (g2 - s * g1) / (1 - s * s)
    if t2 < 0: return g1, 0.0
    if t1 < 0: return 0.0, g2
    return t1, t2

def surplus(b1, b2, s, r):
    t1, t2 = efforts(b1, b2, s)
    cost = (t1 * t1 + t2 * t2) / 2 + s * t1 * t2
    return 2 * math.sqrt(t1) + 2 * math.sqrt(t2) + INTR * t2 - cost - r / 2 * (b1 * b1 + 2 * b2 * b2), t1, t2

def best(s, r, proxy):
    grid = [i / 100 for i in range(201)]
    return max(((*surplus(b1, b2, s, r), b1, b2) for b1 in grid for b2 in (grid if proxy else [0.0])),
               key=lambda x: x[0])

print("competition s | risk aversion r | 12-month proxy | best b1 (GMV) | b2 (proxy) | efforts t1, t2 | surplus")
for s in (0.0, 0.5, 0.8):
    for r, proxy in ((1.0, False), (1.0, True), (3.0, True)):
        v, t1, t2, b1, b2 = best(s, r, proxy)
        print(f"{s:13.1f} | {r:15.1f} | {'used' if proxy else 'none':14s} | {b1:13.2f} | {b2:10.2f} |"
              f" {t1:5.2f}, {t2:5.2f}   | {v:7.2f}")
print("a GMV-only bonus when tasks compete strongly (s = 0.8, r = 1, no proxy):")
for b1 in (0.2, 0.5, 1.0, 1.5):
    v, t1, t2 = surplus(b1, 0.0, 0.8, 1.0)
    print(f"   b1 = {b1:.1f}: GMV effort {t1:.2f}, relationship effort {t2:.2f}, surplus {v:.2f}")
# competition s | risk aversion r | 12-month proxy | best b1 (GMV) | b2 (proxy) | efforts t1, t2 | surplus
#           0.0 |             1.0 | none           |          0.63 |       0.00 |  0.63,  0.20   |    2.10
#           0.0 |             1.0 | used           |          0.63 |       0.42 |  0.63,  0.62   |    2.52
#           0.0 |             3.0 | used           |          0.40 |       0.22 |  0.40,  0.42   |    2.09
#           0.5 |             1.0 | none           |          0.27 |       0.00 |  0.23,  0.09   |    1.48
#           0.5 |             1.0 | used           |          0.60 |       0.42 |  0.39,  0.43   |    2.03
#           0.5 |             3.0 | used           |          0.37 |       0.19 |  0.23,  0.27   |    1.66
#           0.8 |             1.0 | none           |          0.21 |       0.00 |  0.14,  0.09   |    1.31
#           0.8 |             1.0 | used           |          0.59 |       0.40 |  0.31,  0.36   |    1.84
#           0.8 |             3.0 | used           |          0.37 |       0.18 |  0.18,  0.23   |    1.49
# a GMV-only bonus when tasks compete strongly (s = 0.8, r = 1, no proxy):
#    b1 = 0.2: GMV effort 0.11, relationship effort 0.11, surplus 1.31
#    b1 = 0.5: GMV effort 0.50, relationship effort 0.00, surplus 1.16
#    b1 = 1.0: GMV effort 1.00, relationship effort 0.00, surplus 1.00
#    b1 = 1.5: GMV effort 1.50, relationship effort 0.00, surplus 0.20

The results agree with the conclusions of Holmström and Milgrom. A few are worth pointing out:

When the tasks do not compete for time ( $s = 0$ ), the optimal GMV rate is 0.63 with or without a long-term measure; with the measure, effort on relationship building rises from 0.20 to 0.62 and total surplus from 2.10 to 2.52.
When the tasks compete strongly and there is no long-term measure ( $s = 0.8$ ), the optimal GMV rate falls to 0.21. The last lines of the program show why: once the GMV bonus reaches 0.5, the manager cuts relationship effort to zero, and total surplus falls.
Finding a long-term measure, even a very noisy one, allows the GMV incentive to be strengthened again (from 0.21 to 0.59 at $s = 0.8$ ), and both tasks get effort. This is the economic basis of “balanced scorecard” practices: the question is not whether to give incentives but that incentives must cover the competing tasks together.
The more risk-averse the manager ( $r$ rising from 1 to 3), the lower both rates should be and the larger the fixed part. In the model this fits a local partner’s preference for a steady base salary: for a risk-averse person, a high commission is an expensive way to pay, because you must pay for the risk she bears.

Note

Limits of the model. It assumes that headquarters knows all the parameters, whereas in reality headquarters often knows neither the local team’s risk preferences nor how far the two tasks actually substitute for each other. It also ignores psychological effects such as incentives crowding out intrinsic motivation; treating the local team’s regard for long-term relationships (the intrinsic return in the program) as a fixed number is a simplification.

Let partners choose: a contract menu

Headquarters often does not know whether a local partner intends to stay for the long term or may leave within a year or two. One answer is a contract menu that lets different types of partner choose the contract that suits them, revealing their type through the choice. Information economics calls this screening.

Calculation

Two types of partner: long-horizon (expects to stay three years or more, monthly discount factor 0.995, risk aversion 1.0) and short-horizon (leaves with probability 6 % a month, monthly discount factor 0.98, risk aversion 2.0). Two contracts: A, “salary”, a fixed 8 a month plus a 2 % share; B, “partner”, a fixed 5 a month plus a 4 % share and a deferred payment of 150 at month 36, forfeited on leaving.

# A contract menu that lets local partners sort themselves (screening). Two kinds of partner apply:
#   long-horizon  - expects to stay 3+ years, monthly discount factor 0.995, risk aversion 1.0
#   short-horizon - may leave within a year (leaves with probability 0.06 a month), discount 0.98,
#                   risk aversion 2.0
# Monthly revenue the partner influences: mean 100, SD 40 (illustrative units, e.g. thousand MYR).
# Menu, 36 months:
#   A 'salary'  : fixed 8 a month + 2 % of revenue
#   B 'partner' : fixed 5 a month + 4 % of revenue + a deferred tranche of 150 paid at month 36
#                 to a partner who is still there (forfeited on leaving)
# Each type's value = expected discounted pay - risk premium (CARA, r/2 * variance of monthly pay).
def value(contract, beta, leave, r):
    fixed, share, tranche = contract
    v, alive = 0.0, 1.0
    for m in range(1, 37):
        alive *= 1 - leave
        monthly = fixed + share * 100 - r / 2 * (share * 40) ** 2
        v += alive * beta ** m * monthly
    return v + alive * beta ** 36 * tranche

MENU = {"A salary": (8, 0.02, 0), "B partner": (5, 0.04, 150)}
TYPES = {"long-horizon": (0.995, 0.0, 1.0), "short-horizon": (0.98, 0.06, 2.0)}
for t, (beta, leave, r) in TYPES.items():
    vals = {c: value(k, beta, leave, r) for c, k in MENU.items()}
    pick = max(vals, key=vals.get)
    print(f"{t:13s}: " + ", ".join(f"{c} {v:6.1f}" for c, v in vals.items()) + f"  -> picks {pick}")

# Expected cost to headquarters per hire (undiscounted, with each type's chance of staying):
for c, (fixed, share, tranche) in MENU.items():
    for t, (beta, leave, r) in TYPES.items():
        stay = sum((1 - leave) ** m for m in range(1, 37))
        cost = stay * (fixed + share * 100) + (1 - leave) ** 36 * tranche
        print(f"cost of {c} for a {t} partner: {cost:6.1f} over 36 months "
              f"(still there at month 36: {(1 - leave) ** 36:.0%})")
# long-horizon : A salary  318.0, B partner  378.9  -> picks B partner
# short-horizon: A salary  103.7, B partner   79.2  -> picks A salary
# cost of A salary for a long-horizon partner:  360.0 over 36 months (still there at month 36: 100%)
# cost of A salary for a short-horizon partner:  139.8 over 36 months (still there at month 36: 11%)
# cost of B partner for a long-horizon partner:  474.0 over 36 months (still there at month 36: 100%)
# cost of B partner for a short-horizon partner:  142.0 over 36 months (still there at month 36: 11%)

Each type chooses the contract designed for it: the long-horizon partner takes the partner contract (worth 378.9 against 318.0), the short-horizon partner the salary contract (103.7 against 79.2). The deferred payment and the higher share appeal more to long-horizon partners, who are more likely to collect the deferred payment and mind monthly fluctuations less. The cost is that, for a long-horizon partner, the partner contract costs more in total (474.0) than the salary contract (360.0). That extra cost is the price headquarters pays to separate the types and keep long-term partners; whether it is worth paying depends on how much more value a long-term partner creates, which the model does not compute.

Hypothesis · not established

The contract-menu screening hypothesis (not yet established). When recruiting local partners or country managers in Southeast Asia, if both “higher fixed income” and “lower fixed income + higher share + deferred payment” contracts are offered, those who choose the latter will show clearly higher three-year retention and partner renewal rates than those who choose the former, and the difference will not be fully explained by characteristics observable beforehand (age, experience, family situation). If retention does not differ, or the difference is fully explained by prior characteristics, the hypothesis is weakened.

What options and equity do

Many companies going abroad give core local partners equity or options. In this chapter’s models their role is to write the value of long-term tasks into pay: the value of an option depends on the firm’s value some years later, which includes brand, channels and relationships that are hard to measure month by month. But options have costs too. They shift the firm’s risk onto local partners who are often more risk-averse than headquarters; in many Southeast Asian countries, the legal, tax and settlement arrangements for a foreign parent’s options granted to local staff are complicated; and if the firm’s valuation is driven mainly by headquarters’ decisions, local partners will see the options as “headquarters’ lottery ticket” rather than a reward for their own effort. The checklist in Chapter 8 therefore requires incentive arrangements to be reviewed together with the residual-control matrix.

Summary

Most of the misalignment between headquarters and local teams is not a matter of anyone’s character, but of different timetables, tolerances for risk and measurability. The multitask model shows that rewarding only measurable short-term indicators draws effort away from long-term tasks, and that finding even a noisy measure for long-term tasks lets short-term incentives be strengthened again. A contract menu lets different types of partner sort themselves. The next chapter leaves the models for a while and returns to classical texts of Chinese strategy and the Western covenant tradition.

References

Gibbons, Robert. 1998. “Incentives in Organizations.” Journal of Economic Perspectives 12 (4): 115–32.

Holmström, Bengt. 1979. “Moral Hazard and Observability.” Bell Journal of Economics 10 (1): 74–91.

Holmström, Bengt, and Paul Milgrom. 1991. “Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design.” Journal of Law, Economics, and Organization 7: 24–52.

Jensen, Michael C., and William H. Meckling. 1976. “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure.” Journal of Financial Economics 3 (4): 305–60.

Kerr, Steven. 1975. “On the Folly of Rewarding a, While Hoping for b.” Academy of Management Journal 18 (4): 769–83.

Fan, Y. (2026). Cross-Cultural Contracts, Real Options and Game Theory of Southeast Asian Market Entry: Relational Contracting, Optimal Stopping Thresholds and Institutional Distance, Read Beside the Art of War [跨文化契约、实物期权与东南亚出海博弈论] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23753261 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).