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Half-sandwich ruthenium(II)-arene complexes: synthesis, spectroscopic studies, biological properties, and molecular modeling
Developing an Integrated Land Allocation model based on
Linear Programming and Game Theory
farzam hasti ( farzam.hasti@gmail.com )
Gorgan University of Agricultural Sciences and Natural Resources
Abdolrasoul SalmanMahiny
Gorgan University of Agricultural Sciences and Natural Resources
Haydar Rouhi
Gorgan University of Agricultural Sciences and Natural Resources
Yousef Sakieh
LUT University - Lahti Campus
Ramtin Joolaei
Gorgan University of Agricultural Sciences and Natural Resources
Negin Pezhooli
Iran University of Science and Technology
Research Article
Keywords: Game theory, Land allocation, Linear programming, Geospatial information system (GIS)
Posted Date: January 20th, 2022
DOI: https://doi.org/10.21203/rs.3.rs-553638/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Version of Record: A version of this preprint was published at Environmental Monitoring and Assessment on March 21st,
2023. See the published version at https://doi.org/10.1007/s10661-023-11124-w.
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Abstract
Land use configuration in any given landscape is the result of a multi-objective optimization process, which takes into
account different ecological, economic and social factors. In this process, coordinating stakeholders is a key factor to
successful spatial land use optimization. Stakeholders need to be modeled as players who have the ability to interact
with each other towards their best solution, while considering multiple goals and constraints at the same time. Game
theory provides a tool for land use planners to model and analyze such interactions. In order to apply the spatial
allocation model and address stakeholder conflicts, an integrated model based on linear programming and game theory
was designed in the present study. For implementing such model, we conducted an optimal land use allocation process
through multi-objective land allocation (MOLA) and linear programming methods. Then, two groups of environmental and
land development players were considered to implement the optimization model. The game algorithm was used to select
the appropriate constraint so that the result was acceptable to all stakeholders. The results showed that in the third round
of the game, the decision-making process and the optimization of land uses reached the desired Nash Equilibrium state
and the conflict between stakeholders was resolved. Ultimately, in order to localize the results, a suitable solution was
presented in GIS environment.
1. Introduction
Land use planning is a complex process in which all land use types are evaluated simultaneously to set a systematic
framework that takes into account the conflicting goals and constraints of landowners (Kaiser et al. 1995; Guoxin et al.
2004; Ligmann‐Zielinska et al. 2008; Cao et al. 2011; Batty, 2018; Song and Chen 2018; Maleki et al. 2020). Spatial
optimization of land use is a complex decision-making problem with multiple antagonistic objectives from different
influential parties and proper coordination between land use conflicts is a major key to a successful spatial
optimization. The limited quantities of land resources and their suitability for different utilities are the main reasons for
such conflicts (Chen, 2007; Maleki et al. 2020). From a spatial point of view, land use conflicts can be considered as
competition of different land use types over a shared landscape to occupy land. However, in principle, such competitions
are mainly conflicts of interest between several stakeholders (Zhang Li and Fung 2012). Regarding land use management
and optimization, selecting a suitable alternative from the set of available options is a challenging task (Lund and Palmer
1997; Gu et al. 2021) since criteria are contradictory and hardly reconcilable, and any decision can cause objection from
one or multiple parties, who think their interests are neglected (Lee and Chang 2005) and it is often difficult to satisfy all
stakeholders with different interests, values and perspectives (Shields et al. 1999; Collins and Kumral 2020). Considering
land use challenges, the contradiction between the economic benefits of land use development (e.g. timber cultivation,
agricultural practices and recreational activities) and ecological values (e.g. water and soil conservation and
eutrophication reduction) has been well-documented in the literature (Lund and Palmer 1997; Jana et al. 2019). The
contradiction between the environmental approach of governmental decision-makers in the Zagros basins, Iran, and the
economic interests of local people living in these basins has led to the situation that majority of decision-makers are
trying to establish a balance between such conflicting goals. In this context, silo approaches and excluding influential
layers and parties in the region from decision making have only led to trade-off among different goals and negative
feedbacks and feedback loops among players (Raquel et al. 2007).
Many researchers have conducted extensive researches on land use optimization and allocation. Existing optimization
models can be roughly divided into the following three categories: linear programming models, cellular automation (CA)
models and intelligent algorithm models (Liu at al. 2015). Linear programming models can quickly detect the structure of
the optimal land use in response to specific goals and constraints (Arthur and Nalle 1997; Chuvieco 1993; Sadeghi et al.
2009). Automated cellular models are based on land use conversion principles and follow a bottom-up approach to
create different land use patterns under different conditions (Li and Yeh 2000, 2002). There are various machine learning
and artificial intelligence algorithms in the literature amongst which simulated annealing (Aerts et al. 2003), particle
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swarm optimization (Liu et al. 2012; Liu et al. 2012; Liu et al. 2012; Ye et al. 2021), ant colony (Li, Shi, He, and Liu 2011;
Liu, Li, et al. 2012; Tang et al. 2020) and genetic algorithm (Liu et al. 2015; Ozsari et al. 2021) are important
representatives to mention. Geographic information systems (GIS) play an important role in the application of intelligent
algorithms in spatial optimization of land use (Wu and Grubesic 2010). GIS is used to process and visualize spatial data
for these algorithms; however, these models do not take into account local land use conflicts and lack a coordinated
game-based mechanism for solving local land use competitions (Liu et al. 2015).
Game theory, which was first introduced with the pioneering work of von Neumann and Morgenstern (1944), is the study
of mathematical models of conflict and cooperation between decision makers (Bočková et al. 2015). It is also a powerful
tool in determining the equilibrium among decision makers and it is used to analyze situations where stakeholders’
decisions affect those of others. Game theory has been used in various fields such as economics (Camerer, 1997) and
social sciences (Myerson, 1992), water resources management (Parrachino et al. 2006a, b; Carraro et al. 2007;
Homayounfar et al. 2010; Sobuhi, 2010; Liu at al. 2021; Mohammadifar et al. 2021), optimal groundwater consumption
(Mazandarani zadeh et al. 2010; Pourzand and Zibaei 2010; Nazari et al. 2020; Yazdian et al. 2021), wood market
(Mohammadi Limayi, 2006, 2007), paper market (Mohammadi Limayi, 2010), forest management (Rodriguez et al. 2009;
Shahi and Kant 2007; Ikonen et al. 2020) and watershed management (Lee, 2012; Moradi and Mohammadi Limaei 2018;
Adhami et al. 2020). The game theory can simulate the decision-making behavior of different stakeholders with
conflicting interests and facilitate reaching a consensus among them (Rasmusen, 2001; Zhang, 2004; Maleki et al. 2020).
The application of game theory in the context of land use change can be categorized into monitoring (Wu, Wu, and Shen
2005) multi-objective optimization (Lee, 2012), and resolving land use conflicts (Hui and Bao 2013; Maleki. et al. 2020)
studies. However, game theory methods are rarely associated with land use allocation models and in this research, we
have attempted to make a connection between land use optimization and conflict resolution to develop an informed
spatial allocation model. In this study, we first optimize different land use categories using the multi-objective land
allocation (MOLA) method and linear programming. Then, a contradiction is simulated during the land allocation process,
which will ultimately be resolved using the game theory algorithm. Despite much research on separate application of
game theory and linear programming in environmental studies, their integrated application for developing land allocation
models is a less noted attempt in the literature. Therefore, the main objective of this study is to develop an integrated land
allocation model to explore the potential of different land use optimization methods such as MOLA, game theory and
linear planning when combined together. In addition, this study provides a participatory basis to include the views of
different stakeholders during the decision-making process which supports application of the results and provides a
spatial decision support system, which helps decision makers to simulate and quantify the probable effects of strategies
adopted by influential parties in the region.
2. Material And Methods
The study site covers Gorgan and Kordkoy cities spanning over an area of 243921 hectares, located in Golestan Province,
northeastern Iran. Gorgan is located at 48° 28 ′ 54″ northern longitudes and 48° 49′ 36″ eastern latitudes and Kordkuy is
located at 47.88° 6′ 54″ northern longitudes and 30.12° 47′ 36″ eastern latitudes. The population size in Gorgan and
Korkoy is 462455 and 70244, respectively (Census Yearbook of Golestan Province 2013). Fig. 1 shows the geographical
location of the study area.
The trend of land use change in the study area shows that in 1984, forest cover accounted for more than 50% of the area,
while over time, their area has gradually declined, and by 2036, the area of forest cover is anticipated to be to less than
20% of its current total area (Asadollahi and SalmanMahiny 2017). Forest lands in this region have mainly been
transformed into land use categories such as agriculture and urban areas. Such land use conversions have been
occurring mostly based on economic interests with no respect to land potential and ecologically valuable ecosystems in
the region. Therefore, in order to protect forest and protected lands, and simultaneously, regulate land development plans
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in accordance with land capability of the area, governmental authorities need to find a balance between economic players
and environmental stakeholders whose interests are conflicting in the region. The environmental stakeholders include proenvironmental organizations and bodies, as well as pro-environmental people. The economic players include government,
land developers and private companies. Thus, in order to resolve conflicts between pro-environmental stakeholders and
land developers, a solution based on game theory and linear planning can be achieved, so that the results of land
management would be acceptable to all, which can later control unplanned and uncontrolled land use changes in this
area.
This study is conducted through three main steps to allocate land uses. In the first step, an initial multi-objective land
allocation model is presented using the MOLA method. The purpose of this step is to provide a model of primary land use
allocation based on the potential and natural characteristics of the region. In the second step, the initial land use
allocation model is updated according to higher goals such as the interests of pro-environmental stakeholders and land
developers (i.e. secondary land use allocation). Finally, in the third step, in order to implement the secondary land use
allocation, it is necessary to resolve the existing conflicts between the stakeholders with their conflicting interests, so that
the results of land use allocation are acceptable to all of them. To achieve this goal, we will use a designed game
algorithm. The general framework of the work is given in Fig. 2. First, we examined land suitability using the Multi Criteria
Evaluation (MCE) method for seven selected land uses. In the next step, we used the MOLA method for land allocation
and land use planning. Then, we used the multi-objective linear programming method to better optimize land uses and
improve the MOLA outputs. At this stage, to meet the needs of different stakeholders in the study area, two objectives of
minimizing runoff depth and maximizing profits from each land use were selected for land use optimization. Also,
restrictions were designed to implement the objectives according to the needs of each stakeholder group. Despite various
limitations, it was not possible to continue optimization process, and therefore. the game theory approach was
implemented to resolve the conflict. Finally, by resolving the conflict, based on the result of the game theory, one of the
constraints was selected as the constraint accepted by all stakeholders, and the multi-objective linear programming was
performed based on these constraints to optimize and upgrade MOLA outputs.
2.1. Land use optimization
The MOLA method was used to optimize different land use categories in the study area. In doing so, based on ecological
characteristics of the region, research objectives, experts' opinions and past studies, land use categories in the area were
defined as follows: warm and cold water aquaculture, agriculture, forestry, urban and rural developments, conservation
and rangelands. Then, the relevant data and map layers were collected and standardized. In the next step, using MCE for
each land use type, a suitability map was prepared, which fed into MOLA.
2.1.1 Database preparation and multi-criteria evaluation
During the MOLA process, first a land suitability analysis for different land use categories is conducted. In this regard,
based on objectives of the study, local knowledge of the research location, data availability and former studies in the
region, hydrothermal aquaculture, cold-water aquaculture, agriculture, forestry, urban and rural development, conservation
and rangeland were selected as land use categories. The required factors for each land use were determined and a
suitability map for each land use was prepared using the MCE method. In this case, important factors including elevation,
slope, geographical aspect, geological characteristics, soil and erosion risk were obtained mainly from digital elevation
model (DEM) of the study area. The DEM of the area was acquired from National Cartographic Center (NCC) of Iran. In
addition, hydrographic map, plant type and vegetation, climate of the region, bedrock, percentage of vegetation density,
soil type and texture (including drainage conditions, soil depth and structure as well as fertility), distance from the road,
distance from residential areas, hydrological map of the study area were also prepared. The set of factor layers
implemented in this study were obtained from Goragn University of Agricultural Sciences and Natural resources, which is
the leading institute in conducting land use planning studies in the region.
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The MCE method evaluates land suitability in response to several environmental criteria. During the MCE process, several
map layers are standardized (i.e. fuzzified), weighted and combined to evaluate the suitability of the land for a specific
utility. In this regard, in the first step, the above-mentioned set of influential criteria on land suitability for targeted land use
categories in our study were identified. The set of criteria is divided into constraints and factors. Constraints include those
Boolean criteria that shows the suitability of the land in a 0 and 1 fashion. In other words, zero indicates absolute lack of
potential and one indicates suitability of the land for the desired land use. In contrast, factors represent the degree of the
land suitability in a continuous way, and therefore, the layers with continuous values are standardized using Fuzzy sets
theory. It is because each layer has a different measurement scale and it is necessary to standardize the layers to be able
to combine them into one single suitability map. The standardization process can be performed by fuzzy membership
functions on a scale of 0 to 1 or 0 to 255 (Drobne & Lisec, 2009). In addition, the relative weight of each factor layer is
determined based on Analytical Hierarchy Analysis (AHP) and finally layers are combined into one final suitability map
based on Weighted Linear Combination (WLC) method was used (Hasti et al., 2016). The WLC equation is presented as
follows:
where, Wi is the AHP-derived relative weight of the factor i, Xi is the standardized layer i, Ci is constraint i and ∏ is he
multiplication operator.
MOLA is an iterative allocation process through which a specific area threshold for each land use category is achieved
using the corresponding weight of the land use type. In the present study, the aim was to optimize land use categories
considering ecological conservation perspectives and economic interests. In case of ecological conservation, the
objective was minimizing the probability of runoff depth, and the economic goal was maximizing the profit from each
land use. In order to achieve the targeted goals and improve MOLA allocation behavior during spatial optimization
process, the multi-objective linear programming method was employed. A multi-objective linear programming model can
be defined as follows (Eq. 2):
Max (or Min)
s.t
Z(x) = [Z1(x), Z2(x), Z3(x), … , Zp(x)]
gj ≤ 0,
j = 1, 2, … , n
xk ≥ 0,
k = 1, 2, … , n
Eq. 2
where Z(x) is an objective function and [Z1(x), Z2(x), Z3(x), …, Zp (x)] is a set of objective functions Gi(x), j is the most
important constraint and xk, k is the decision variable. The goal of optimization is to find the best acceptable answer,
given the limitations and needs of the problem. For a problem, there may be different answers, and to compare them and
select the optimal solution, a function called the objective function is defined. The choice of this function depends on the
nature of the problem, for example, the objective function can be selected such as profit maximization, employment,
runoff minimization, erosion, environmental pollution, etc. Decision variables are variables that are used to write the
objective function, such as different types of land use. Constraints are factors that indicate what constraints exist or
should be applied to the execution of the objective function.
Land use optimization in watersheds using linear planning and geographic information systems is one of the appropriate
management methods to achieve optimal landscape configuration and maximum profit (Riedel, 2003); however, the
economic interests must be secured considering ecological and social sustainability aspects (Pfaff and Sanchez, 2004;
Ducourtieux et al. 2005). There are also other studies in the literature applying linear programming for land allocation
(Shabani, 2010; Chuvieco et al. 2004; Nikkami et al. 2002).
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In order to obtain the runoff depth probability of each land use type, the long-term hydrological impact assessment (LTHIA) model was used in Arc View software environment and the runoff depth probability was extracted. This model
provides an estimate of runoff changes, recharge and pollution of non-point sources due to past or predicted land use
change to provide a measure of the long-term effects of development on hydrological conditions (Bahadori et al. 2000;
Weng, 2001; Ma, 2004). This model was first developed for natural resource managers because they are familiar with
land use change in a particular area and have access to land use information and are often interested in studying
environmental impacts (Engel et al. 2003). In addition, economic data such as land use profit was retrieved from land use
planning database of Golestan Province, which was establish in 2014.
The purpose of this study is to integrate game theory into the land allocation process. At this stage, in order to simulate
contradictive perspectives during the land use allocation, two target categories can be considered for the implementation
of multi-objective linear programming. In other words, there are two categories of constraints for the implementation of
linear planning, which include constraints designed by stakeholders seeking environmental protection and land
developers trying to maximize economic interests. Therefore, with two sets of constraints, it is not possible to implement
land use allocation by linear programming. In this regard, each of the stakeholders wants to implement their goals, and at
this stage, game theory can be used to resolve the simulated conflict.
2.2. Game algorithm
At this phase, in order to resolve the simulated conflict, we can implement the general framework and the game algorithm
(Fig. 3).
Fig. 2 shows the game algorithm designed for this study. As shown in the figure, after the initial (MOLA) and the second
(linear programming) land allocation, we have two sets of constraints according to the different needs of the
stakeholders (environmental and economic), and therefore, the optimization process will stop (conflict). According to the
various scenarios and strategies that are designed, which we will explain in the following, we will use game theory to
resolve this conflict and select one of the limitations to continue the optimization process. This algorithm shows that in
each stage of the game, if the result is Nash equilibrium, which is acceptable to all players, the created conflict will be
resolved. The result of resolving the conflict is selection of one of the limitations for implementing linear programming
and final land allocation.
Once the game algorithm has been designed, it is necessary to devise strategies for each step of the algorithm to
simulate decision conditions and selection of players. Specifically, there are different categorizations of games. Games,
in terms of format, can be divided into two forms of strategy or normal and wide or tree. Strategy games are a compact
form of a game in which players simultaneously coordinate their strategy. Extensive games can also be referred to as a
set of normal games (Hasti et al. 2016). Each game contains three main elements including i) players, which is the factor
that makes decisions in the game., ii) actions, which is a set of actions defined for each player, and iii) final result,
function or preferences, which is the result of each player from his decision according to the rules and scenarios of the
game (Hasti et al. 2016). In the present study, the idea of a prisoner puzzle game (non-zero outcome), which is a wellknown example of normal games, was undertaken and the wide form of the game was used to implement it. The conflict
is created in such a way that each player accepts his own restrictions and has designed restrictions according to his
goals. The designed goal for players in the game is to meet their designed constraints. In other words, the choice of
constraints designed by them is more important. In the next stage, game scenarios for each player were determined
according to experts’ knowledge and the designed goal. The game scenario in the first iteration is presented in Table 1.
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Table 1 Game scenario descriptions in the first iteration
Player
Strategy
Economic (EC) player
Environmental (En) player
If selects Ec, constraints = 5
If selects En, constraints = 5
The first strategy
If selects Ec, constraints = 10
If selects Ec, constraints = 3
The second strategy
If selects En, constraints = 3
If selects En, constraints = 10
The third strategy
If selects En, constraints = 2
If selects Ec, constraints = 2
The fourth strategy
To better understand Table 1, for example, the first strategy shows that if the environmental player chooses his
constraints (En constraints), he will get 5 points. Also, if the economic player selects his designed constraints (Ec
constraints), he gets 5 points. Therefore, Table 1 shows the strategies that each player can choose and the points that he
will receive from each choice.
Then, the game model was designed in Gambit 13.1 software and the game results were determined, which included the
balance of the game and the usefulness (points) obtained for each player as a result of solving the game. The results
show that players have selected their own restrictions and the desired conflict is still present, and consequently, the game
enters the second iteration. In the second phase of the game, the objective for each player was to achieve the
environmental and land development interests as well as respecting constraints designed by other players. In other words,
each of the constraints designed by each group achieves the maximum value of the objective function (minimizing the
probability of runoff depth and maximizing the profit from each land use). To do this, the environmental objective
function was first implemented based on constraints separately designed in response to environmental conservation and
economic benefits. Then, the same procedure was repeated for economic function. In the next step, based on the experts’
opinion and according to the results of the multi-objective linear programming for objective functions (based on the
constraints designed by each player separately), game scenarios were introduced for each decision of the players. Table
2 shows the game scenario in the second iteration.
Table 2 Game scenario descriptions in the second iteration
Player
Strategy
Economic (Ec) player
Environmental (En) player
If selects Ec, constraints= 6
If selects En, constraints = 6
The first strategy
If selects Ec, constraints= 10
If selects Ec, constraints= 4
The second strategy
If selects En, constraints = 4
If selects En, constraints = 10
The third strategy
If selects En, constraints = 2
If selects Ec, constraints= 2
The fourth strategy
The land use allocation game model was implemented with the second iteration in Gambit 13.1 software. The results of
the game including the desirability of the players in each decision and the balance of the game were obtained. Given the
nature of the game theory (Nash Equilibrium concept) in predicting player’s decisions and game resolution results, it
shows that each player selects his or her own constraints as the final decision. Due to outcome of the game, the conflict
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has not yet been resolved and it is not possible to continue the process of optimization and land use allocation.
Therefore, due to the nature of the game theory in bargaining and repetition, the game will enter its third phase. In the
third phase of the game, more emphasis was placed on the bargaining power of the game theory, and the goal of the
players in making decisions was set accordingly. To resolve the conflict, the players' goal was to satisfy the other side
based on their required area and needs. To do this, both environmental and land development objective functions were
implemented simultaneously with the designed constraints of the ecologists and economists in the WINQSB software. In
the next step, based on the results of the implementation of the multi-objective linear programming model (i.e. area
allocated to each land use), the goal of each player, the opinion of experts and game decision scenarios were designed
(Table 3).
Table 3 Game scenario descriptions in the third phase
Player
Strategy
Economic (Ec) player
Environmental (En) player
If selects Ec, constraints= 3
If selects En, constraints = 8
The first strategy
If selects Ec, constraints= 3
If selects Ec, constraints= 2
The second strategy
If selects En, constraints = 5
If selects En, constraints = 10
The third strategy
If selects En, constraints = 4
If selects Ec, constraints= 3
The fourth strategy
The results of the game solution show that the Nash Equilibrium is at the stage where both players choose the designed
constraints related to the environment. By negotiation between the players and satisfying each other, the result indicates
that the conflict has been resolved and the process of land use allocation continues. In this way, spatial optimization with
constraints designed by environmentalists can be implemented in a way that it is acceptable to all stakeholders based on
the results of the game algorithm. Due to the nature of game theory, the game can enter other stages until the decisionmaking process finally reaches the Nash Equilibrium. The essence of the game theory is that each player selects a
strategy, but the end result depends on the choice of all players. Therefore, each player, to some extent, can control the
outcome of the game. The end result varies from person to person, with one player being the best and the other the worst.
Thus, the fundamental question is, given the different outcomes for individuals, how does game theory resolve conflict
(Samsura et al. 2010) There are different approaches to game theory, however the concept of Nash Equilibrium is often
used (Aumann, 1985). Nash Equilibrium can be introduced as a strategy choice for each player such that no player is
willing to change and the strategy chosen by each player is the best response to the strategy chosen by other players. The
best means that changing this strategy will not increase the result (Samsura et al. 2010). The following equation shows
the Nash Equilibrium in a game:
Ui(a*) = Ui(a1*, a2*, … , an*) ≥ Ui(a1*, a2*, … , an*)
Eq. 2
In this regard, Ui is the utility of the i-th player and the actions of each player in different situations. According to the
above explanations, by reaching the Nash Equilibrium, the result of the game is accepted by the majority, and the
objective functions were performed with environmental constraints.
For model sensitivity analysis, it is also necessary to examine the expected outputs by changing the model inputs used in
this research. As explained, the purpose of this study is to improve land allocation results from the MOLA analysis with
objectives such as minimizing runoff depth and maximizing profits using linear programming, and therefore, the result of
linear planning changes land allocation areas. For sensitivity analysis of the model, we implemented the L-THIA model
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once with the initial land allocation map (MOLA) as the input land use layer and once with maps from linear
programming (one time with environmental stakeholder constraints and one time with economic stakeholder
constraints). Finally, we examined the sensitivity of the model and changes in runoff depth in response to changes in
land allocation (Table 8).
3. Results
First, for each of the seven land uses selected in the study area, we obtained the land suitability surface through the MCE
method. Then, we used the MOLA method for the initial optimization. Fig. 4. shows the MCE-derived land suitability
output for each land use category.
The input data feeding objective functions during for MOLA allocation process were standardized in a range between 50
and 255. Table 4 shows the environmental and the economic objective functions.
Table 4 Environmental and economic objective function
Objective function
Object function type
Row
Min = 241aa+50ac+50aw+255ad+109ar+109ap
Minimizing runoff
depth
1
Maximizing land
use profits
2
+137ff+109fp+50cc+241wa+50ww+255wd+109wr+255dd+241ra
+50rc+255rd+109rr+109rp+137pf+109pr+109pp
Max = 152aa+255ac+254aw+255ad+101ar+100ap+152ff+100fp+255cc
+152wa+254ww+255wd+101wr+255dd+152ra
+255rc+255rd+101rr+100rp+152pf+101pr+100pp
In Table 4, (aa) represents agricultural lands, (ff) forest lands, (cc) cold-water aquaculture lands, (ww) hydrothermal
aquaculture lands, (rr) rangelands, (pp) protected areas and (dd) urban and rural development. Other decision variables
represent the conversion of one land use to another, e.g., (aw) is agricultural land that can be converted into hydrothermal
aquaculture and (ra) is rangeland land that can be converted into agriculture.
According to Table 4, the objective functions of minimizing runoff depth and maximizing land use profits indicate that in
order to optimize the MOLA-derived land use map with the aim of reducing the depth of runoff and increase profits, it is
important to consider which land use is likely to convert to another and if these land uses are converted, how much runoff
will be produced and how much profit is generated.
Then, each of the environmental groups and land developers designed their own constraints. Each group accepts its own
constraints to continue the multi-objective linear planning process and rejects the other party's constraints. This conflict
prevents the continuation of the land allocation process and stops the algorithm. Therefore, game theory was used to
resolve the conflict. Table 5 shows the designed constraints of each group.
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Table 5 Limitations of each group
Constraint
Player
Row
(1):aa+ac+aw+ad+ar+ap+ff+fp+cc+wa+ww+wd+wr+dd+ra+rc+rd+rr+rp+pf+pr+pp=1895000;
(2):Aa+ac+aw+ar+ap=285000; (3):Ff+fp=460000; (4):Wa+ww+wd+wr=30000;
(5):Pp+pf+pr=910000; (6):pp<810000; (7):pp>805000; (8):ff<400000; (9):ff>390000;
(10):cc<14000; (11):cc>12000; (12):pf+pr<100000; (13):pf+pr>90000; (14):aa<270000;
(15):aa>200000; (16):rr<160000; (17):rr>150000; (18):Ww<25000; (19):ww>20000;
(20):dd=30000; (21):ac<=12307; (22):aw<=60000; (23):ad<=230000; (24):ar<=51000;
(25):ap<=45000; (26):fp<=334000; (27):wa<=60000; (28):wd<37000; (29):wr<60000;
(30):ra<=512000; (31):rc<=15000; (32):rd<=243000; (33):rp<=118000; (34):pf<=334000;
(35):pr<=118000;
Environmental
1
(1):aa+ac+aw+ad+ar+ap+ff+fp+cc+wa+ww+wd+wr+dd+ra+rc+rd+rr+rp+pf+pr+pp=1895000;
(2):Aa+ac+aw+ar+ap=285000; (3):Ff=460000; (4):Wa+ww+wd+wr=30000;
(5):Pp+pf+pr=910000;
Economic
2
(6):Pf<100000; (7):pf>80000; (8):Pr<100000; (9):Pr>80000; (10):Rr<135000; (11):Rr=130000;
(12):Rc+rd+ra<30000; (13):Rc+rd+ra>25000; (14):Ww=15000; (15):Wd<=15000;
(16):Cc=15000; (17):Aa=270000; (18):ac<=12307; (19):aw<=60000; (20):ad<=230000;
(21):ar<=512000; (22):ap<=45000; (23):wa<=60000; (24):wd<37000; (25):wr<60000;
(26):ra<=512000; (27):rc<=15000; (28):rd<=243000; (29):rp<=118000; (30):pf<=334000;
(31):pr<=118000;
Here A indicates agricultural use, F is forestry, R is rangeland, D is urban and rural development, W is hydrothermal water
use, C is cold water aquaculture and P is conservation. Other variables indicate the conversion of one land use to another.
Considering environmental constraints, constraints (1) to (5) relate to area limitations. Constraint No. (1) relates to the
amount of required area (cell) from the entire study location. Constraint No. (2) indicates the amount of areas that should
be converted to agriculture that have the required area (same as the area obtained from MOLA) and constraint No. (3)
refers to areas that should be converted to forests that have the required area (area obtained from MOLA). Restriction No.
(4) shows areas that need to be converted to hydrothermal aquaculture that have the required area (MOLA area) and
restriction No. (5) is that areas should be converted to conservation that has the required area (MOLA area)
constraint. Other limitations relate to environmental and technical constraints. In terms of economic constraints,
constraints No. (1), (2), (4), (5) are related to area constraints and other constraints are related to economic, social and
technical constraints. Table 5 shows that there should be constraints to achieve the desired objective functions. The unit
of all of them is area (cell). The pixel size of each of the maps used in this research is 30 meters by 30 meters.
In this research, the prisoner puzzle game was used for the land use allocation game. Based on game elements, action A
indicates the choice of its designed constraint and action B indicates the choice of the constraint designed by the other
player. The third element of the game is the payoff of each player at each stage of the game. After running the game in
Gambit 13.1 software, a stage of the game called Nash Equilibrium was achieved (Fig. 3). The concept of Nash
Equilibrium indicates each player makes rational decisions, meaning that each player seeks to maximize his profit. In
other words, Nash Equilibrium is a point at which if a player changes his game, his profit does not change (assuming the
rest of the game is fixed). In the second game, the goal for each player was primarily to achieve environmental and
economic goals and then to select the constraints designed by the players. To do this, first environmental objective
function was implemented based on environmental and economic constraints separately designed in WINQSB
software. Then, the same procedure was repeated for the economic function. Table 6 shows the results of the objective
functions in the WINQSB software. The numbers in Table 6 show only the value of the objective function and are unitless.
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Table 6 Results of objective functions based on designed constraints
With economic
constraints
261944992
252247296
With economic
constraints
256186992
Object function type
The objective function
Minimizing runoff
volume
Environmental objective
function
Maximizing user profit
Economic goal function
251552304
In the next step, the players make decisions according to the designed scenarios. The results of the game indicate that
each player has chosen his own designed restrictions (Fig. 3). In the third game, the players' goal was to satisfy the other
side based on the required areas and needs of the other side. To do this, both environmental and economic objective
functions were implemented simultaneously with the designed constraints of the environment and in another stage with
the designed economic constraints in WINQSB software. The results of performing the objective functions are presented
in Table 7. The pixel size of each of the maps used in this research is 30 meters by 30 meters.
Table 7 Results of execution of objective functions in WINQSB software
Land use
Changing the area of land uses based
on socio-economic constraints (cell)
Changing the area of land uses based on environmental
constraints (cell)
Agriculture
Agriculture (270000 cells), Agriculture
to cold water aquaculture (12307),
Agriculture to hydrothermal
aquaculture (2693 cells)
Agriculture (215000 cells), Agriculture to cold water
aquaculture (12307 cells), Agriculture to hydrothermal
aquaculture (47693 cells), Agriculture to urban and rural
development (10000 cells),
Forestry
Forestry (460,000 cells)
Forestry (400000 cells), Forest to protection (60000 cells)
Cold water
aquaculture
Cold-water aquaculture (15000 cells)
Cold-water aquaculture (15000)
Hydrothermal
aquaculture
Hydrothermal aquaculture (15000
cells), Hydrothermal aquaculture to
urban development And rural (15000
cells)
hydrothermal aquaculture (20000 cells), hydrothermal
aquaculture for urban and rural development (10000 cells)
urban and
rural
development
urban and rural development (30000
cells)
urban and rural development (30000 cells)
rangeland
rangeland (140000 cells), rangeland
to urban and rural development
(25000 cells)
rangeland management (165000 cells)
Protection
Protection (710000 cells), Protection
to forestry (100,000 cells), protection
to rangeland (100000 cells)
Protection (810000 cells), Protection to forestry (100000
cells)
After running the game in Gambit 13.1 software, the third stage of the game was obtained under the Nash Equilibrium
state. At this stage, each player selects the constraints designed by the environment, and the payoff is the environmental
player ten and the economic player five. Due to the solution of the game, the environmental player is declared as the
winner of the game, and with this result, the conflict is created, and then, it is possible to resolve and continue the process
of allocating land use. Accordingly, land use optimization continues throughout the multi-objective linear programming
process with constraints designed by environment (Fig. 4).
Page 11/27
Linear programming is not an originally spatial method and the results are in the form of changing the area of each land
use and converting one land use to another, for the final optimization according to the defined set of goals. Locations that
have the least suitability for the initial land use and the highest suitability for the converted land use should be changed.
In order to find these areas, the map layers were cross-tabulated. In the next step, there were different solutions for
locating these areas. In this regard, we extracted the land use whose area needs to be changed and then we ranked the
MOLA-derived map and extracted the desired area from this layer. These areas were then reclassified based on land use
category, and finally overlaid with MOLA map. This process was implemented for the results of multi-objective linear
planning and the final land use optimization map was configured using goal programing and GIS. Table 8 shows the
comparison between new MOLA areas and the initial optimization areas and the probability of runoff depth of each land
use based on old and new MOLA maps with L-THIA method.
Table 8 sensitivity analysis and comparison of runoff area and depth probability with old and new MOLA maps
C runoff
depth (cm)
B runoff
depth (cm)
A runoff
depth (cm)
C area
(cell)
B area
(cell)
A area
(cell)
Land use
Row
1896.5
1587.5
1644.7
370000
215000
285000
Agriculture
1
754.3
743.4
754.3
460000
500000
460000
Forestry
2
647.2
508.1
508.1
130000
165000
165000
Rangeland
3
2732.4
2237.4
2197.7
119000
50000
30000
Urban and rural
development
4
0
0
0
52000
67693
30000
War water
aquaculture
5
0
0
0
34000
27307
15000
Cold water
aquaculture
6
453.6
498.2
508.1
730000
870000
910000
Protection
7
1895000
1895000
1895000
Sum
In Table 8, A means the initial MOLA land use map that has been used as the input of the L-THIA model. In addition, B
and C are the land allocation maps resulted from linear programming model, once with the constraints of environmental
stakeholders and once with the constraints of economic players.
The L-THIA model was implemented again with an end-use allocation map to determine the effect of the objective
function (minimizing the probability of runoff depth) on reducing runoff depth. The results are presented in Table 8 and
Fig.5.
Figure 6 shows the game elements and the form of games played during the execution of the algorithm.
The elements of the first game were as follows:
Players = (EN, EC).
Action = (A1, B1).
Action profile = (A1, A1), (A1,B1), (B1,A1), (B1,B1)
Utility = the profit of each player in choosing each action of the game’s steps is as follows:
Page 12/27
UEn = (A1, B1) = 10, UEc = (A1, B1) = 5 (Step A of the game)
UEn = (A1, A1) = 5, UEc = (A1, A1) = 5 (Step B of the game) (Nash equilibrium)
UEn = (B1, B1) = 2, UEc = (B1, B1) = 2 (Step C of the game)
UEn = (B1, A1) = 3, UEc = (B1, A1) = 10 (Step D of the game)
According to elements of the game, action A indicates the choice of its own designed constraint and action B indicates
the choice of the other constraint designed by the player. The third element of the game is the payoff of each player at
each stage of the game. The elements of the game in the second stage are as follows:
Players = (EN, EC).
Action = (A1, B1).
Action profile = (A1, A1), (A1, B1), (B1, A1), (B1, B1)
Utility = the profit of each player in choosing each action of the game’s steps is as follows:
UEn = (A1, B1) = 10, UEc = (A1, B1) = 4 (Step A of the game)
UEn = (A1, A1) = 6, UEc = (A1, A1) = 6 (Step B of the game) (Nash equilibrium)
UEn = (B1, B1) = 2, UEc = (B1, B1) = 2 (Step C of the game)
UEn = (B1, A1) = 4, UEc = (B1, A1) = 10 (Step D of the game)
Finally, the elements of the game in the third stage were defined as follows:
Players = (EN, EC).
Action = (A1, B1).
Action profile = (A1, A1), (A1, B1), (B1, A1), (B1, B1)
Utility = the profit of each player in choosing each action of the game’s steps is as follows:
UEn = (A1, B1) = 10, UEc= (A1, B1) = 5 (Step A of the game) (Nash equilibrium)
UEn = (A1, A1) = 8, UEc = (A1, A1) = 3 (Step B of the game)
UEn = (B1, B1) = 3, UEc = (B1, B1) = 4 (Step C of the game)
UEn = (B1, A1) = 2, UEc = (B1, A1) = 3 (Step D of the game)
After running the game, the step A of the game obtained the game’s balance. At this stage, each player selects the
constraints designed by the environmentalists, and the payoffs are the environmental player ten and the economic player
five. According to the solution of the game, the environmental player is declared as the winner of the game, and with this
result, it is possible to resolve the conflict and continue the process of land use optimization. Accordingly, land use
assessment continues with constraints designed by the environmentalists. Each stage of the game had its own Nash
Equilibrium, but it should be noted that once the game reaches the Nash Equilibrium, the player does not change his
strategy in any way. In the first and second games, stage B of the game, each of the stakeholders selects his own
Page 13/27
designed constraints (Fig. 6). The output of this stage of the game was the Nash Equilibrium but the game conflict was
still unresolved and it was not possible to continue the process of land use optimization. Fig. 7 shows the final land use
map of the study area using the land allocation model based on linear programming and game theory.
4. Discussion
In the third phase of the game, more emphasis was placed on the bargaining power of the game theory, and the goal of
the players in making decisions was grounded on this basis. Table 7 shows the results of the execution of the objective
functions with their corresponding constraints. Each player must first prioritize the needs of the other party based on the
required area, which is accordingly translated as a constraint. With environmental constraints, 70,000 cells should be
allocated from agricultural to aquatic use and hydrothermal and cold water use and rural-urban development. With this
result, attention has been paid to the needs of the economic players considering production of labor, increasing profits
and reducing the initial cost of establishing each land use. Under such designed limitations, the economic player of
15,000 cells from agriculture should be allocated to aquaculture, cold water and hydrothermal applications.
Environmental constraints have also improved economic landscape of the area by changing agricultural land uses, while
not reducing forest and natural ecosystems, which play a key role in reducing runoff and erosion. In addition, in the
second stage, with this change in agricultural use, the concerns of environmentalists for protecting forests are also taken
into account. With the limitation of the environmental player, about 60,000 cells should be allocated to forest protection,
and consequently, proper attention has been paid to such environmental aspects. But according to designed limitations,
the economic player of forestry will remain intact. Namely, more attention has been paid to the economic aspects of
forestry than to the environmental needs of the other side. Cold-water aquaculture will remain unchanged in both
constraints. 10,000 cells of hydrothermal water use should be allocated to urban and rural development based on the
designed constraints of the environment (considering socio-economic aspects through changing economic uses). 15,000
cells of this land use should be converted to urban and rural development according to the designed constraint of
economic domain. The use of urban and rural development will remain unchanged in both constraints. Due to its role in
reducing runoff and erosion, as well as its economic aspects such as forage production, livestock grazing and
beekeeping, the use of rangeland habitat will remain unchanged in the designed environmental constraints. But with the
economic constraints, 25,000 cells of this land use must be allocated to urban and rural development. Therefore, less
attention has been paid to the needs of the other side and most of the socio-economic aspects are considered. Finally,
with the designed environmental constraints, 100,000 cells should be allocated from conservation land use to forestry.
With this allocation, attention has been paid to both socio-economic and environmental aspects of forestry. Forestry use
will reduce runoff and erosion, and also provides shelter and habitat for wildlife. On the other hand, 200,000 protection
cells should be allocated for rangeland and forestry use. Therefore, the area of environmental protection activities will be
reduced, and less attention will be paid to the needs of the other party.
In stage B of the third game, each player will choose their own designed restrictions. According to the rules of the game,
the environmental player will get 8 points and the economic player will get 3 points assuming that the environmental
player will not change his game, if the economic player wants to change his game and choose the designed
environmental constraints (moving from stage B to stage A of the game). In this case, his score will increase from 3 to 5
points. Therefore, according to the definition of Nash Equilibrium, stage B of the game cannot maintain the equilibrium
state.
In stage A of the game, each player will choose the designed environmental constraints. Based on game scenarios, the
environmental player gets 10 points and the economic player gets 5 points. Assuming that the environmental player is
not willing to change his game, if the economic player wants to change his game (move from stage A to stage B) and his
score will be reduced from 5 to 3; so refuses to change his game. Also, assuming the economic player is fixed, if the
environmental player wants to change his game and chooses the economic constraint (moving from stage A to stage C
Page 14/27
of the game), then his score will be reduced from 10 to 3 and the environmental player will not be willing to change his
game. As mentioned, because none of the players are willing to change their game, stage A of the game will be
considered as the equilibrium state and steps C and D, as defined by Nash, cannot reach the Nash Equilibrium.
The preferences of the environmental player on each of the outputs in the third phase of the game are as follows:
Step A > Step B > Step C > Step D.
The preferences of the economic player on each of the outputs in the game with the third repetition are as follows:
Step A > Step C > Step B > Step D.
Given the players' preferences for each output, it is clear that the strategy of designed environmental constraints is
strongly dominant as an action; because it takes into account both environmental and socio-economic aspects (through
environmental economics) and the results are practical. In contrast, the strategy of choosing the constraint designed by
the economic player is selected as a strongly defeated action since the other side is highly dissatisfied due to its low
score in the game scenarios.
5. Conclusion
We applied a game with environmental and economic constraints for land use optimization. For this, multi-objective
linear programming with environmental constraints was adopted and the result was fed into the MOLA process.
Comparing the optimal output areas of the multi-objective linear programming model and game theory with the initial
land use areas showed the need for changing the current area and configuration land use categories in the region. The
results of the integrated model suggested a reduction of 6,300 hectares from agricultural land use, to achieve the
environmental objectives such as possible reduction of runoff depth and soil erosion. Around 3,600 hectares were added
to forest land use to address the needs of the environmental and socio-economic sectors. The area of warm and cold
water aquaculture as well as urban and rural land uses were increased during the optimization process to meet socioeconomic goals. Eventually, 3,600 hectares were reduced from protected areas and allocated to forestry. Forestry plays an
important role in safeguarding the environmental objectives (reducing the potential runoff depth and the erosion
likelihood), and on the other hand, it helps achieving the socio-economic goals. According to the studied socio-economic
parameters, the desirability of forestry is far greater than the protected areas, which could provide an interesting topic for
further studies in the region. Future studies can evaluate the potential of ecologically-friendly activities such as forestry
and recreation in improving socio-economic status of the region, while protecting its valuable ecological functions and
ecosystem services. Future models can also quantify the role of tourism and its interaction with other land use categories
in the region to establish a spatial decision support system for informed and multi-objective land use planning. By
referring to Table 8, the sensitivity in changes of the runoff depth can be understood by changing the inputs of the L-THIA
model using different inputs such as different land use maps. It is clear that with different land allocation maps, runoff
outputs were expected to be commensurate with them. Also, by comparing the runoff depth of each land use, it can be
found that the final land allocation map in this study will provide a more acceptable runoff depth.
This research is one of the first attempts in combining game theory with MOLA and linear programming models and
according to the results, the model can lead to conflict resolution between different stakeholders. The integrated model
suggested in this study, is less complex and the results are easier to interpreted compared to similar studies based on
application of game theory, genetic algorithm and fuzzy sets theory (mentioned in the introduction). Therefore, as a topic
of further research, the mode can be further implemented in other research areas with different sets of land use
categories and influential stakeholders to evaluate the potential of such integrative studies in conflict resolution and
sustainable development plans.
Page 15/27
Declarations
Data Availability:
The datasets generated during and/or analyzed during the current study are available from the corresponding author on
reasonable request.
Conflict of Interest Statement:
The authors undertake that there is no conflict of interest to declare.
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Figures
Figure 1
The geographic location of the study area
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Figure 2
Research flow chart
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Figure 3
General study framework and game algorithm for land use allocation
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Figure 4
Land suitability derived from the MCE method
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Figure 5
Execution of L-THIA model with initial and final optimization results
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Figure 6
Elements and form of the games
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Figure 7
Final land allocation
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