Land-use decisions in developing countries and their representation in multi-agent
systems
PEPIJN SCHREINEMACHERS
University of Hohenheim
Postal address: University of Hohenheim (490 e), 70593 Stuttgart, Germany
Phone: +49-711 459 3615
Fax: +49-711 459 4248
[email protected]
THOMAS BERGER
University of Hohenheim
Postal address: University of Hohenheim (490 e), 70593 Stuttgart, Germany
Phone: +49-711 459 4117
Fax: +49-711 459 4248
[email protected]
Earlier version of a paper published in Journal of Land Use Science 1 (2006) 29 – 44
Land-use decisions in developing countries and their representation in multi-agent
systems
PEPIJN SCHREINEMACHERS* & THOMAS BERGER
University of Hohenheim, Germany
Recent research on land-use/cover change (LUCC) has put more emphasis on the
importance of understanding the decision-making of human actors, especially in
developing countries. The quest is now for a new generation of LUCC models with
a decision-making component. This paper deals with the question of how to
realistically represent decision-making in land use models. Two main agent
decision architectures are compared. Heuristic agents take sequential decisions
following a pre-defined decision tree, while optimizing agents take simultaneous
decisions by solving a mathematical programming model. Optimizing behavior is
often discarded as being unrealistic. Yet the paper shows that optimizing agents do
have important advantages for empirical land-use modeling and that multi-agent
systems (MAS) offer an ideal framework for using the strengths of both agent
decision architectures. The use of optimization models is advanced with a novel
three-stage decision model of investment, production, and consumption to represent
uncertainty in models of land-use decision-making.
Keywords: LUCC, agent behavior, mathematical programming, heuristics.
1
1
Introduction
The first generation of land-use/cover change (LUCC) models has been successful in
identifying the underlying causes of land-use change in developing countries (Lambin et
al 2001, Verburg et al 2004). Many studies have emphasized that people’s land-use
decisions depend on the economic opportunities and constraints as shaped by markets and
policies and mediated through institutions (Lambin et al 2001). So far, most LUCC
models have focused on land areas as the main unit of analysis and have not represented
the decision-making of farm households and landowners explicitly. According to
Verburg et al (2005), land-use modelers are aware of the mismatch between the unit of
analysis and the unit of actual decision-making. Within the second generation of LUCC
models, attention will therefore shift from pixels to agents (ibid.), which would bring
LUCC models and multi-agent systems (MAS) closer together.
MAS models of land-use/cover change (MAS/LUCC) couple a cellular
component that represents a landscape with an agent-based component that represents
human decision-making (Parker et al 2003). MAS/LUCC models have been applied in a
wide range of settings (for overviews see Janssen 2002; Parker et al 2002, 2003) yet have
in common that agents are autonomous decision-makers who interact and communicate
and make decisions that can alter the environment.
When moving from pixels to agents, the challenge becomes how to represent realworld land-use decision-making. Empirical MAS have accumulated much experience in
this field but little of this can be found in the LUCC literature as journal articles are often
too short to go into much detail. This paper meets a growing interest in a comparison of
alternative modeling approaches to represent land-use decision-making.
2
Agent decision-making in most abstract as well as empirical MAS has been
represented as behavioral heuristics, also called condition-action rules, stimulus-response
rules, or if-then rules. One simple example is a land-use rule that if subsistence needs are
not met then plant maize, but if met then plant coffee. Several studies justified the use of
heuristics on the grounds that the neoclassical model of utility maximization is unrealistic
or that empirical evidence has shown that people use simple heuristics to make decisions
(Parker et al 2003: 317; Jager et al 2000: 360). This paper argues that empirical land-use
modelers should be aware that there is much more of a continuum between heuristic and
optimizing behavior than what is suggested by the theoretically-oriented literature. The
paper shows that optimizing agents do have important advantages for empirical land-use
modeling and that MAS offer an ideal framework for using the strengths of both agent
decision architectures.
The paper is organized as follows. Section 2 gives a detailed discussion of
heuristic versus optimizing agent behavior and suggests a synthesis of both approaches.
Section 3 advances the suggested approach with a novel three-stage decision-making
model, which is suitable for representing decision-making under uncertainty and for
including rational and adaptive expectations. Section 4 concludes the paper.
2
Optimizing vs. heuristic behavior
Agent decision architectures fall into two broad categories of optimizing versus heuristic
agents (figure 1). This distinction overlaps with a more general debate between
economists advocating optimizing behavior and psychologists/cognitive scientists
3
advocating heuristic behavior. In psychology and cognitive science, heuristics are often
strongly contrasted against the concepts of rationality and utility maximization as used in
neoclassical economic theory.
[Insert figure 1 about here]
Optimizing agents are able to select the best decision from a range of feasible
alternatives while the selection process itself is assumed to be costless in terms of
computation. A key difference between optimizing and heuristic agents is that the latter
neither have the information to compare all feasible alternatives nor the computational
power to select the optimum.
Optimization can be used for both normative and positive purposes. Their
normative use is to re-allocate resources to attain a higher level of goal satisfaction by
eliminating inefficiencies, while their positive use is to replicate and simulate a realworld resource allocation. It is the latter use that is of interest for empirical LUCC
models. For this, the optimization model can be calibrated to observed behavior by
carefully representing all opportunities and constraints in the model. Further on in the
paper we will show that search and computation costs can be included in an optimization
model by using heuristics to constrain the range of perceived decision alternatives.
What follows is a reflection on the use of optimizing and heuristic behavior with a
focus on modeling land-use decisions. Before going into details, we make a short detour
into the issue of production and consumption functions, as these concepts define the
decision space for both types of agent behavior.
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2.1
Common building blocks: production and consumption functions
A production function is a physical relationship between combinations of inputs and
levels of output. Mathematically it can be expressed as: Q = f(X1, X2, …, Xn) in which Q
is the quantity of output (e.g. kilograms of maize) and Xi is the quantify of inputs with
i=1,2,..,n (e.g. land, labor, fertilizer, and cash). The function f defines a technology,
which can be approximated by different functional forms as shown in figure 2 for the one
input case. Linear functions and fixed input/output relations are generally seen as
unrealistic, while quadratic and Cobb-Douglas functions are more widely accepted (Rao
1989; Sadoulet and de Janvry 1995; Mundlak 2001). Production functions represent a
purely technical relation and not an economic relation as prices are not considered.
Production functions are hence independent of decision theories, being it heuristics or
microeconomics.
[Insert figure 2 about here]
Both heuristic and optimization-based approaches have used production
functions, though functional forms in the heuristic-based approach have typically been
simpler. For instance, Deadman et al (2004: 698) using heuristic agents in a LUCC model
for the Amazon considered the yield effect of only one input (soil quality); Huigen (2004:
14) using heuristic agents in a LUCC model applied to the Philippines assumed crop
yields as a function of years of experience in producing a crop; and Castella et al (2005)
using heuristic agents in an application to Vietnam used group discussions to obtain a
5
fixed crop yield/labor relation. The lack of variation in crop yields due to the use of
simple production functions is often compensated by introducing stochastic elements into
the model.
In MAS applied to developing country agriculture, consumption is often
considered explicitly as farm households consume a substantial part of their own crop
and livestock yield. Microeconomic theory confirms this intuitive fact and calls it the
non-separability of consumption and production decisions; this means that market goods
cannot be fully substituted for home produced goods if markets are imperfect or decisionmaking is subject to high levels of risk (Sadoulet and de Janvry 1995).
A consumption function quantifies the relation between expenditures on the one
hand and income, prices, and household characteristics on the other hand. Consumption
functions can be statistically estimated from household budget data (Sadoulet and de
Janvry 1995; Huang and Lin 2000). The above mentioned heuristic studies have included
relatively simple consumption functions often specified as minimum consumption levels
in relation to households size. Deadman et al (2004: 701/2) used a minimum requirement
of cash and of hectares of annual crops as a function of household size while correcting
for the difference between adults and children. Huigen (2004: 14) specified subsistence
needs in terms of cash and rice, both as a function of household size.
The choice of production and consumption function is not directly related to the
type of agent decision architecture. Both heuristic and optimizing approaches can use
realistic production and consumption functions. Such functions can be an important
source of agent heterogeneity, as agents can position themselves on different parts of
these functions. The use of non-linear functions is more realistic than the use of fixed
6
input/output relations or stochastic variables to introduce agent heterogeneity. Yet, how
can agents decide where to position themselves on these functions, that is, what and how
much to produce and consume?
2.2
The case for heuristic agents
Heuristics are relatively simple rules that guide humans in their decision-making.
Farmers typically use a large number of heuristics, perhaps because of the great
uncertainties of natural phenomena they are exposed to. For instance, Ghanaian farmers
have a rule that the rainy season starts after five days of consecutive rain, after which
they start cultivating their fields. Such rule of thumb often gives accurate predictions
without invoking complex computational models.
Most heuristics build on the concept of bounded rationality (Simon 1957), which
refers to the limited cognitive capabilities of humans in making decisions. Simon
described bounded rationality as a search process guided by rational principles, what he
called satisficing -- a word created by blending satisfying with sufficing (Gigerenzer and
Goldstein 1996). Satisficing is a decision-process that goes on until an aspiration level is
reached (Selten 2001). For instance, each time a farmer wants to plant maize he does not
endlessly shop around to find the best maize variety (with best defined as a weighted
calculation of all relevant criteria: yield, maturity, disease resistance, tolerance, fodder
quality, etc.). It is more likely that the farmer contacts the outlet where he always goes to
and buys the seed that he bought last year.
This example also points to another key difference between heuristics and
optimization in that the former is not only concerned with the decision outcomes but
7
especially with how these decisions are made in the human mind (hence the shared
interest of psychologists, cognitive scientists, and biologists in behavioral heuristics).
Behavioral heuristics are implemented in MAS using decision trees. Figure 3
shows an example based on Deadman et al (2004: 702) in the previously mentioned
application to land-use change in the Amazon rainforest using the LUCITA model. This
decision tree is implemented at the plot level. For each plot the agent evaluates whether
subsistence needs have been met; if not, the agent checks the availability of labor and
cash; if the availability is enough then annual crops are planted and if not, then the plot is
left fallow. Correspondingly, if subsistence needs have been met, then the agent first
evaluates the pH of the plot and then checks if there is enough labor and cash. The
structure of decision trees in most MAS/LUCC applications is fairly simple. For instance,
Jager et al (2000) in a theoretical application used six decisions; Becu et al (2003) in an
empirical application to Thailand used 13 decisions; and Castella et al (2005) used 24
decisions. These last two applications also use continuous loops.
[Insert figure 3 about here]
The use of decision trees, and heuristics in general, is intuitive. Agent behavior is
straightforward to follow from the structure of a decision tree. Because they are
transparent, they are easy to validate by interacting with farmers and experts. The
researcher can, for instance, consult with farmers whether they believe these rules are
valid or not (Castella et al 2005). Constructing a decision tree is, however, not easy. The
researcher needs to identify not only the most important decisions, but also in the correct
8
sequence. Furthermore, appropriate conditions (e.g. saturation levels) need to be set, e.g.
determining what is ‘enough’ cash and labor in the above example.
Decision trees can be parameterized using sociological research methods (e.g.
Huigen 2004), data-mining techniques applied to survey data (e.g. Ekasingh et al 2005),
participatory modeling and role-playing games (e.g. Barreteau et al 2001; Becu et al
2003; Castella et al 2005), laboratory experiments (e.g. Deadman 1999), group
discussions (e.g. Castella et al 2005), and expert opinion.
2.3
The case for optimizing agents
Economists are often accused of seeing human decision-makers as rational optimizers
with perfect foresight as described in undergraduate textbooks in economics. Optimizing
agents would be cognitive supermen able to process large amounts of information on all
feasible alternatives and always select the best one. For this ability, optimizing behavior
is frequently criticized and ridiculed as unrealistic and not describing the way real people
think (e.g. Todd and Gigerenzer 2000). Applied models in developing country agriculture
are, however, much different from textbook examples and can, for instance, include risk
and uncertainty, limited information, and non-profit goals. To understand where the idea
of optimizing farm households came from we make a brief historical detour.
Until the 1960s, small-scale farmers in developing countries were viewed as
obstacles rather than promoters of agricultural development. Development efforts focused
on industrial-based growth, while several developing counties experimented with largescale collective agriculture to accelerate modernization (e.g. Vietnam, Tanzania, China).
This view was challenged in 1964 by Theodore W. Schultz who put forward the
9
hypothesis that small-scale farming is ‘poor but efficient’ (Schultz 1964). Schultz saw
farmers as making efficient use of their resources but their productivity was constrained
mostly by their knowledge and access to improved technologies. The general acceptance
of Schultz’ hypothesis opened the way for applying concepts and methods of neoclassical
microeconomics to small-scale farming in developing countries. Although many studies
since Schultz have shown wide inefficiencies in small-scale (as well as large-scale)
agriculture, the point has remained that farmers do try to use their limited resources in the
best possible way and that poverty reduction in rural areas can only be achieved by
enhancing the productivity of small-scale farmers.
Agricultural economists will agree that farm households in developing countries
do not perform complex algebra to make optimal decisions. Yet the assumption of
optimal decision-making clears the way to focus on the hypothesized sources of
inefficiency: lack of physical infrastructure, failing institutions, market imperfections,
and limited information flows, all of which have clear policy relevance. This points us to
a key difference between the heuristics and optimization approach in that the latter seeks
to identify inefficiencies not in the limited cognitive capacity of the human mind but in
structural factors external to the decision-maker, which may be addressed through policy
intervention.
Optimizing agents have been implemented in MAS using a variety of
optimization approaches. For instance, Balmann (1997), Berger (2001), Becu et al
(2003), and Happe (2004) used mathematical programming and Manson (2005) used
genetic programming to optimize land-use decisions. Neural networks could also be used
to optimize land-use decisions but the authors are unaware of any such empirical
10
application. Since mathematical programming is the most widely used approach, we
focus on this in the following.
Mathematical programming. Mathematical programming (MP) is a computerized
search for a combination of decisions that yields the highest objective function value.
Different form the heuristic approach, MP requires the explicit specification of an
objective function. In applications to farm households in developing countries, objectives
of agents usually include cash income, food, and leisure time, which can be either
specified in monetary units or in terms of utility. It is noted that heuristic approaches
commonly use the same objectives (e.g. Deadman et al 2004).
An example. The use of optimization is illustrated by formulating the decision
tree of figure 3 as a MP model. This example optimizes cash income while satisfying the
agent’s food consumption needs expressed in calories. A MP problem can be presented as
a system of equations but is clearer when presented as a so-called tableau as shown in
figure 4. The first row of the tableau shows seven decision variables Xn (with
n=1,2,…,7). Each decision variable is associated with an element in the price vector
depicted in the second row of the tableau. In this example only perennial crops and
pasture add to the cash income. The objective function is specified as the product of the
decision vector and the price vector.
Each column of the tableau is called an activity and each row is called a
constraint. A constraint is the product of the decision vector with each separate row. The
value of this product must or must not top the value specified in the right-most column,
11
which is called the right-hand-side and which puts lower or upper bounds on the
constraints. For instance, the first constraint tells that the selected amount of land of pH
greater or equal than 5.5 cannot exceed 4 hectares (1*X2+1*X4+1*X5 ≤ 4). This simple
example has seven constraints in total; the first four indicate that the agent cannot use
more land, labor, and cash than is available; the fifth indicates that the agent cannot
consume more annual crops than produced; and the final constraint ensures that
subsistence requirements are met before perennial crops are planted. All decision
variables are furthermore constrained to positive values only.
The example assumes that the agent has a subsistence energy need of 9 Million
calories (the right-hand side in the seventh constraint), which is about equivalent to a
household of two adults and three small children. It is further assumed that 1 ton of
annual crops contains 2 Million calories of food energy, and hence the agent has to
produce 4.5 tons. This example shows that not all objectives need to be converted in a
single currency and included in the objective function. Subsistence requirements can also
be included in the constraints, in which case they have a clear resemblance to satisficing
rules.
Optimization of the tableau is called solving. Different solving algorithms are
available (e.g. simplex, interior point) depending on the complexity of the tableau. This
particular problem is small and can be solved in Microsoft Excel. The optimal solution is
125 for X3=1, X4=1.5, X5=2.5, and X7=4.5.
This simple example can easily be expanded to include more detailed production
and consumption functions instead of fixed input/output relations. When included in
MAS, heterogeneity of decision-making can be introduced by making right-hand side
12
values and crop yields agent-specific. Modern solving algorithms can include a very large
number of activities and constraints. For instance, Berger (2001) included 240 activities
and 120 constraints, while forthcoming work by Schreinemachers (2006) includes 2320
activities and 553 constraints.
[Insert figure 4 about here]
Relation to heuristics. The above example showed the great similarity between a
decision tree and a MP model. The branches and nodes of a decision tree have their
analogs in the activities and constraints of a MP model. Following Brandes (1989) one
can even argue that it boils down to a semantic question whether observed goal-oriented
behavior is satisficing or optimizing. Satisficing can be seen as a special case of
optimizing with explicit search costs, be it cognitive or financial, which limits the
gathering and processing of all information. Likewise, optimization can be seen as a
special case of satisficing in which search costs are neglected and aspiration levels are
very high. Other than these similarities, there are also clear differences between both
approaches. In the following we discuss three main advantages of MP for empirical landuse modeling.
(a) Heterogeneity in input and output decisions. Farm households in developing
countries are observed to grow many different crops, to attain widely different levels of
crop yields, and to use widely different levels of land, labor, and variable inputs. For
instance, farm households surveyed in two village communities in Uganda grow about 13
13
crops in as many intercropping combinations in two seasons and each with different
levels of labor on different qualities of soil (Schreinemachers 2006). This variation can be
captured in empirical production functions as discussed above, which define output levels
for each level and combination of input. Reducing this variation to uniform input-output
relations is unrealistic, yet capturing this variation in a heuristic approach is practically
infeasible for the large number of conditions and actions that need to be specified. Even if
labor and land were the only inputs, if farm household used only three different levels of
labor input, and if there were only three qualities of soil, the researcher would still have
to specify at least 468 rules (13 × 2 × 2 × 3 × 3) to capture each possible land-use
decision. The MP approach has the practical advantage that additional decisions can be
included relatively easy, which allows the decision model to represent detailed
production and consumption functions more easily.
The use of relatively simple decision trees can create abrupt shifts in simulation
experiments that give unrealistic dynamics. For example, a rule that defines agents to
expand their agricultural land area into the forestland after three years of bad weather
would make all agents in the population simultaneously switch to forestland, which
would appear as a structural break or an emerging behavior but which is in fact a model
artifact. The same problem can be caused by using agent categories with a single set of
heuristics, as these artificial groups tend to behave much alike.
The implementation of detailed production and consumption functions in
MAS/LUCC is therefore a straightforward way of representing heterogeneity as agents
can produce and consume at any point of the function depending on their household
composition, resource endowments, location in the landscape, and level of knowledge.
14
(b) Capturing economic trade-offs in resource allocation. A heuristic-based approach
cannot adequately capture trade-offs in the allocation of scarce resources in space and
time. Farm households and landowners have only limited amounts of land, labor, and
cash available. Land allocated to maize cannot be used to grow vegetables at the same
time. When a farm household considers growing maize, it compares the expected benefit
from maize with the expected foregone benefit from other competing land-uses, which is
called the opportunity cost of maize. If the expected benefit from growing maize
outweighs its opportunity costs, then the household will most likely choose to grow
maize.
This reasoning is difficult to implement in a heuristic approach. For instance,
Deadman et al (2004) and Quang Bao Le (2005) use algorithms that order all alternative
decisions in descending order by level of goal satisfaction, add a random choice element,
and then sequentially choose decisions from the top of the list until, for example, all
available land is planted. This approach does not consider trade-offs in resource
allocation as only fixed prices but not opportunity costs are used. Yet, it would be
unrealistic to assume that farmers do not do any economic reasoning. The reason why
economic trade-offs cannot be fully captured using heuristics is that this method relies on
pre-determined conditions that are sequentially and independently evaluated whereas the
MP model uses an objective function that allows agents to consider decisions
simultaneously and in coherence. This simultaneous consideration is important as
opportunity costs are not absolute and exogenous for a farm household but are a function
of the relative scarcity of each resource. This relative scarcity is expressed as the shadow
15
price, which is defined as the possible increment in the agent’s goal satisfaction from one
additional unit of a resource.
To exemplify, imagine two farm households: one has a small area of land but
much household labor, while the other has a large area of land but only little household
labor. Land is relatively dear for the household with less land but more labor, i.e. it has a
high shadow price of land and a low shadow price of labor; this household will aim to be
very efficient in its land use by choosing high-yielding crops such as vegetables. The
household with more land and less labor will do the opposite and make extensive use of
its land perhaps by grazing cattle or planting trees.
Most heuristic-based approaches therefore assume land-use independent of
relative resource endowments, thereby contradicting a large amount of empirical
literature showing its importance (e.g. for discussions on the farm size--productivity
debate, see Cornia 1985; Singh 1988; Heltberg 1998; Dorward 1999).
(c) Assessing the quantitative impact of policy interventions. Whereas the heuristic
approach addresses inefficiencies in the limited cognitive capacities of the human mind,
the optimization approach addresses inefficiencies in structural characteristics external to
the decision-maker such as market imperfections, limited information, and lacking
physical infrastructure. This focus on structural sources of inefficiency has clear policy
relevance as policy interventions can be tailored to overcome these structural issues.
Even more so, an optimization-based approach can ex-ante simulate the impact of policy
interventions (Berger et al 2006).
16
In the heuristic approach this is more difficult to accomplish. Heuristics define
currently or previously observed behavior and are environment-specific. The researcher
would have to specify which of these heuristics would change in response to a particular
policy intervention that alters this environment. The optimization-based approach
circumvents this problem by specifying an objective function based on microeconomic
theory; the exact decision behavior of farm households does then not need to be known.
This brings greater flexibility in representing human behavior as objectives can
realistically be assumed more or less constant but decision rules not.
2.4
Synthesis
LUCC and MAS models have traditionally been multi-disciplinary approaches in which a
large variety of theories and methods co-exist. This also holds for the representation of
agent decision-making in these models. There is no superior decision-model. The choice
of decision model depends as much on the research question as on the taste and scientific
background of the researcher. Table 1 synthesizes the main points of discussion.
[Insert Table 1 about here]
The heuristic approach works especially well in abstract and experimental
applications or in empirical applications where the objective is not to quantify change
but, for instance, to support collective decision-making processes (e.g. d’Aquino et al
2003). In group discussions it is much easier to present a decision tree than to explain a
MP model. If the objective is to quantitatively support policy intervention and to get
17
detailed knowledge about different agricultural land-uses, then a MP model including
detailed production and consumption functions is perhaps the more suitable method.
One advantage of MAS is the flexibility to combine and integrate different
decision models. The use of one type of agent decision-making does certainly not exclude
the use of other types and the above examples have shown that some heuristic models can
easily be formulated in terms of a MP model and vice versa. When using an optimization
approach, heuristics can additionally be used to capture many other aspects of household
decision-making. These heuristics can either be directly included in the MP model or
implemented in the source code. We define four categories of heuristics:
1. Behavioral heuristics directly related to production and consumption decisions of
farm households: For instance, crop rotation requirements or the observation that
vegetables are only grown close to the farmstead. These rules should be included as
constraints in the MP model as they constrain production decisions.
2. Behavioral heuristics indirectly related to production and consumption decisions: For
instance, Berger (2001) in a MP-based application to Chile included a rule that if the
income of an agent is below the opportunity cost of labor then the agent migrates out
of the region. Such rules should be implemented outside the MP in the MAS source
code because they do not constrain production decisions but are an evaluation of
decision outcomes.
3. Behavioral heuristics of agent interaction: For instance, the communication of
information among agents. These rules should be implemented outside the MP as
they go beyond the decisions of an individual agent.
18
4. Behavioral heuristics related to exceptional circumstances: For instance, how to reallocate the land if an agent’s last household member deceases, and what to do if the
household agent does not produce enough food and income to sustain itself? In the
case where no household members are left, the rule should be implemented outside
the MP as the agent seizes to exist. Yet, when the agent does not immediately seize to
exist, as is the case when income is not enough for subsistence, the rule is best
handled inside the MP.
3
Uncertainty and expectation formation
Decisions in agriculture and forestry are rather unique because of relatively long timespans between implementation and outcomes and a high level of uncertainty in these
outcomes due to the vagaries in weather, pests, and diseases. Nobody can predict the
future perfectly, and farm household even less so. In the case of land-use decisions of
farm households, the three main areas of uncertainty are price uncertainty, yield
uncertainty, and uncertainties in resource supply.
The undergraduate textbook model of perfect foresight is of course highly
unrealistic and MAS modelers have a wide range of more realistic alternatives at their
disposal. Uncertainty can be introduced in MAS by limiting the foresight of agents and
using learning algorithms possibly in combination with some stochastic elements. A
discussion of different algorithms is out of scope of the present paper. Instead we suggest
a pragmatic approach of how to combine optimizing agent behavior with imperfect
foresight and agent learning (see Schreinemachers 2006 for details).
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3.1
A three-stage agent decision model
MP models typically optimize all decisions simultaneously. For instance, the tableau in
figure 4 optimized both production and consumption decisions at once. This is a strong
simplification of decision-making because at the time of planting, agents cannot know the
harvest, and hence cannot know how much of it they will consume. This problem can be
circumvented by dividing the year into stages and formulating and solving a MP model at
each stage. To do this, we conceptualize farm decision-making as an annual cycle of
three sequential decisions on investment, production, and consumption (figure 5). The
same MP model is optimized at each stage in the decision-making process but with
different time horizons and constraints, and solutions are partly carried over from one
stage to the next. This procedure allows expected outcomes to deviate from realized
outcomes although the extent of this depends on the type of learning algorithm
implemented.
[Insert figure 5 about here]
Investment decisions (stage 1). Land-use investments are those productive activities
with a gestation period between first input use and total output of more than one year.
This includes most forms of animal husbandry, perennial crops including forestry, and
infrastructure. The difference between investment decisions and current production
decisions is the time horizon of the decision-maker.
20
In the investment stage, the agent optimizes investment decisions by comparing
future and annual costs and revenues, which are based on the agent’s yield and price
expectations and the long-run expected household labor supply. How these expectations
can be formed is discussed below. Production and consumption decisions are considered
in the investment stage by a simultaneous optimization of all three decisions. This means
that the agent considers the trade-off between future benefits and current needs when
deciding how much to invest.
The results of the optimal investment plan are then added to the resource
endowments of the agent. For instance, if the agent had three cows at the start of the
period and invests in two more cows, then the resource endowment is updated to five
cows of different vintages while the agent’s savings are reduced with the purchasing
price of two cows.
Production decisions (stage 2). After deciding on investments, the agent decides on the
current land-use in the production stage. This includes the decisions what crops to grow,
on which plots, using which variable inputs, and in what quantities. Like in the
investment stage, these decisions are based on the agents’ expected yields and prices for
the present period. Consumption needs are considered by simultaneously optimizing the
production and consumption decisions.
All new investment decisions, such as purchasing new livestock, acquiring more
land, or planting additional trees were already taken in the previous stage and cannot be
reversed at the production stage. Livestock can, however, be sold and trees be cut down if
needed at this stage. For this, previous investment decisions are split into two
21
alternatives: one is to sell or cut at the end of the period based on the present expected
costs and benefits, while the other is to value the future expected costs and benefits. If
present net benefits exceed the expected future annual net benefits, then the investment
will be sold or cut at the end of the present period.
Consumption decisions (stage 3). In the third and last stage of the yearly decisionmaking process, the agent sells and consumes products based on actual yields and prices.
Investment and production decisions cannot be reversed in the consumption stage. Actual
prices replace the expected prices and actual crop yields, as simulated from actual input
levels in the production stage, enter the MP to replace expected yields. The results of the
consumption stage can be used to quantify the economic well-being and food security of
the agents and the agents’ resources are updated to serve as a starting point for the next
period.
3.2
Agent expectation formation
Taking up the example of production functions, we briefly discuss how crop yield
expectations can be implemented in a MAS/LUCC model. Our point of departure is
microeconomic theory, which offers two concepts for modeling agent expectations:
rational expectations and adaptive expectations. First, rational expectations imply that
decision-makers use all relevant pieces of information and make optimal land-use
decisions based on stochastic foresights. Positive and negative unexpected events cancel
out over time, so that expectations on average are accurate (see Arrow 1987). For the
implementation in MAS, rational expectations mean that the agents’ expectations have to
22
be consistent with the production function in the crop yield model. In other words, the
‘internal model’ the agents use for their land-use decisions is in line with the ‘true model’
of crop yield that the model builder has implemented. In terms of coding, model agents
first evaluate the consequences of their land-use choices by consulting the crop yield
model, then implement their decisions, and finally the crop yield model is run with some
random error term so that agent decisions might turn out incorrect in some periods but
optimal over time.
Second, adaptive expectations imply that decision-makers base their views about
the future only on past trends and experiences, ignoring newly available and potentially
relevant information. Various learning algorithms (e.g. reinforcement learning) can be
used to specify how expectations are adapted. The theoretical justification for this rather
myopic form of behavior is that access to and processing of new information might be
too costly. In terms of coding, model agents base their yield expectations on the yields of
the previous year while correcting them for past forecasting errors, then implement their
land-use decisions, and finally the crop yield model is run to simulate actual yields.
Although rational expectations might be implemented in MAS for the case of crop
yield expectations, this concept is little appealing when it comes to expectations
concerning the outcomes of non-market interactions, such as agent interaction on
common grazing lands. For these cases, heuristics can certainly better capture agent
expectations. Yet the point is that MAS can integrate alternative forms of expectations. In
many practical cases a combination of different types of expectations will be required.
23
4
Conclusion
Although heuristics and optimization are often strongly contrasted in the theoreticallyoriented literature, the differences are not as large as they appear. Both approaches
assume goal oriented behavior and become more realistic when using detailed production
and consumption functions. Heuristic decision trees can be converted into optimization
problems and vice versa. For land-use modeling, the use of optimization models has
certain advantages: (1) Multiple input and output decisions can be included in a
straightforward way, which better captures agent heterogeneity. (2) Economic trade-offs
can be considered by simultaneous solving the decision problem whereas heuristics relies
on a sequential decision problem and is not well able to capture economic trade-offs. (3)
The outcomes of optimization models have a clearer policy relevance than those of
heuristic models because optimization models focus on structural factors as the main
sources of inefficiency (institutions, markets, information, physical infrastructure)
whereas heuristic models focus on the limited cognitive capacities of the human mind as
the main sources of inefficiency.
Still, there is no objectively preferable decision-model. The choice of decision
models in MAS much depends on the research question as well as on the personal
preferences and background of the researcher. Heuristic and optimization-based
approaches can complement one another. One pragmatic approach is a three-stage
sequential optimization procedure of investment, production, and consumption decisions
as presented in this paper.
24
5
Acknowledgment
This paper greatly benefited from discussions with Nicolas Becu and Marco Huigen and
the excellent comments of three anonymous reviewers. We gratefully acknowledge the
financial support of the Robert Bosch Foundation and of Senator Dr. Hermann Eiselen
who endowed the Josef G. Knoll Visiting Professorship at Hohenheim University.
6
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Figure 1: Types of agent decision-making
Agent decision-making
Optimizing agents
Heuristic agents
e.g. satisficing
Normative use
Positive use
Re-allocating resources
Representing an
to improve a situation
actual situation
30
31
Quantity of output
Figure 2: Alternative functional forms for an agricultural production function
Quadratic
Linear
Cobb-Douglas
Fixed input/output relation
Quantity of input
32
Figure 3: Decision tree to simulate land-use changes in the Amazon
Are subsistence
requirements met?
yes
no
Enough cash and
Soil pH < 5.5
no
yes
yes
no
labor for annuals?
Enough cash and
Enough cash and
labor for perennials?
labor for pasture?
no
yes
no
yes
Leave
Plant
Leave
Plant
Leave
Plant
fallow
annuals
fallow
perennials
fallow
pasture
Source: based on Deadman et al (2004: 702)
33
Figure 4: Mathematical programming model to simulate land-use changes in the
Amazon
Decision vector
Price vector
X1
X2
0
0
Leave
fallow (ha)
pH
<5.5
1
2
3
4
5
7
Land pH ≥ 5.5 (ha)
Land pH <5.5 (ha)
Labor (mandays)
Cash ($)
Annuals (ton)
Calories (Mcal)
1
pH
≥5.5
1
X3
X4
0
0
Plant
annuals (ha)
pH
<5.5
1
25
10
-1.5
X5
X6
X7
50
10
0
Plant
Plant Calorie
Reperen- pasture supply sources
(ha) (Mcal)
pH nials
(ha)
≥5.5
1
1
4
≤
1
2
≤
25
15
5
≤ 100
10
10
5
50
≤
-2.0
1 =
0
2 ≥
9
34
Figure 5: Conceptual model for a three-stage decision-making process
Investment:
Production:
Consumption:
Timing:
Price & yield
expectations:
Resource
expecatations:
Investment
stage
Production
stage
Consumption
stage
take
consider
consider
take
consider
take
Decisions made at the beginning of the period
… and at the end
of the period
Expected yields & expected prices
Actual yields &
actual prices
Expected future
resource supply
Actual current resource supply
35
Table 1: Comparison of approaches
Criterion
1 Focus
Heuristic agents
Optimizing agents
Decision process as much as
Decision outcomes
decision outcomes
2 Sources of
inefficiency
3 Strengths
Internal: the limited cognitive
External: imperfect markets,
capacity of the mind
physical infrastructure, etc.
•
•
•
Simulating broad land uses
5 Calibration
Representing agent
(e.g. pasture/fallow/crops)
heterogeneity through detailed
Inclusion of multiple
crop choices and input levels
stakeholders
•
Capturing economic trade-offs
Validation through
•
Providing quantitative policy
stakeholder interaction
4 Data needs
•
support
High for well-designed and
High for well-designed and
detailed heuristics
detailed optimization models
Relatively quick and easy
Time consuming, especially for
a detailed model
6 Data source
Laboratory experiments, role-
Surveys, crop-yield experiments,
playing games, surveys, expert
expert opinion
opinion
36