A PROPOSAL TO USE GAME THEORY TO ENHANCE STAKEHOLDER
ENGAGMENT IN THE FORMULATION OF
CATCHMENT FLOOD RISK MANAGEMENT PLANS
Unwin, D1.* Arthur, S2.
*...Sustainable Water Management Research Group, School of the Built Environment, Heriot Watt University,
Edinburgh, EH14 4AS, Scotland, U.K.
1.
[email protected]
2.
[email protected]
Abstract: This paper reports on the initial phases of novel research undertaken at
Heriot-Watt University which forms a key part of the transnational Interreg IVB
project, Strategic Alliance for Integrated Water Management Actions (SAWA). The
research presented in this paper focuses on developing a sound methodology in
applying multi-dimensional and majority rule Game Theory techniques to analyse
and inform the selection processes used when deploying adaptive flood risk
management measures in a real world case study located within a catchment of the
river Wandse, in Hamburg, Germany. The paper documents how cooperative,
Pareto-optimised, conflict resolution techniques and simultaneous one dimensional
voting strategies can be used to support how decisions are made. The paper reports
on the benefits that may be gained through assessing how different stakeholder views
are to be accommodated, through an approach to structure, analyze, and understand
strategic scenarios.
The methodology presented will further develop the existing collaborative nature
within the SAWA project to increase overall project benefit, through enhanced
stakeholder communication, and improved coordination. The game structures
employed are of cooperative and simultaneous form and will provide fully traceable
outcomes which will ultimately provide a useable tool in the form of a Decision
Support System (DSS).
Key Terms: Game Theory, Pareto-Optimization, Conflict Analysis/Resolution
Introduction: The Strategic Alliance for Integrated Water Management Actions
(SAWA) is a pan-European 8.2 million Euro project involving more than 20 partners
in five countries. The project aims to investigate “adaptive” flood risk management
within the context of the EU Floods and Water Framework Directives. The project
will focus on the engineering, social and capacity issues associated with Flood Risk
Management Plans (FRMP), and is defined by three interlinked work-packages,
namely:
•
WP1, which is primarily concerned with implementing the Flood Directive
(FD). Learning from experience, with regards to catchment management
conflicts resulting from implementing the Water Framework Directive
(WFD) and FD. In addition to addressing the issue accommodating Water in
the urban environment, through holistic consideration of flood hazard (not
•
•
flood risk) and community cohesion through bottom-up governance
approaches.
WP2, Supporting the Flood Risk Management Decision Making Process. To
ensure that the correct flood risk management decisions are reached. It is
important to understand what data should be considered by engineers,
planners, the public and politicians. Currently, decisions are often based
predominately on flood extent data derived from hydraulic models calibrated
using limited data. Therefore it has been identified that there is considerable
scope for studying how data is collected during an event; in terms of direct
(e.g. depth, extent, properties effected) and indirect (e.g. health impacts,
habitat loss) impacts. Key to this proposed work would be the philosophy that
some social groups are more vulnerable to flooding than others and that it is
important to add a social dimension to any subsequently developed DSS
WP3, Education projects in integrated water management. Education is
identified as a key dissemination route for SAWA. For this to be effective, it
must be integrated throughout the project as a whole and be tailored to meet
the needs of the different recipients.
The research presented in this paper, which is linked primarily to WP2, details the
development of a trans-national Game Theory (GT)/Pareto-Optimization (PO)
approach to provide a Decision Support System (DSS) methodology. The
methodology proposed was hypothesised to be optimal as it addressed the needs of
the Floods Directive (and by implication, the three SAWA work packages) directly
in addition to considering such key drivers as, target groups, areas of operation,
desired outcomes and informational demand - both pre and post DSS development.
The methodology is based on a governance approach, in the SAWA project, and it is
envisaged that this will form a pivotal link between the three work-packages. In that,
in addition to stakeholders and project funders, the DSS will also consider social
aspects in the “bottom-up” development of Catchment FRMP.
As stated, the specific aim of the DSS is to support the formulation of FRMP(s) by
meeting the identified need to involve stakeholders throughout the development
process. This is key as failure to engage with stakeholders will mean that the
development of the FRMP will be constrained as the full range of Non Structural
Measures (NSM) cannot be considered. Therefore, fundamental to the philosophy is
the following questions:
‘How can education and communication be improved to optimally integrate stake
holders on all levels?’
•
Such as within cooperative planning forums or “Learning and Action
Alliances” in this project (LAA).
Also,
‘In applying the concept of flood risk management plans, how can local decision
making be an integral part of catchment based planning in applying the concept of
flood risk management plans?’
•
•
Particularly in respect to ‘playing’ with different solution possibilities
(measure types or their combinations) for addressing flooding hazard.
Understanding how the solution possibilities, their implementation, pros, cons
and conflict potential are sensitive to changeable stakeholder viewpoints.
By including stakeholders, project funders and public bodies as key decision makers
within the DSS, in a culture that is detached from any hierarchical constraints, it is
hypothesised that the methodology will provide the necessary transparency for
successful, effective, dissemination of results, to end users, practitioners and project
evaluators alike.
The approach presented in this paper is to be applied to a real world case study area
in Hamburg, Germany. The case study area relates to a catchment of the River
Wandse which is shown in Figure 1 by the dark line running approximately from
North-East to Centre, as highlighted by the arrows. The catchment itself is
approximately 89.7 km2 in area and consists of a predominantly (sub)urban
development. Secondary and tertiary phases of the development and implementation
of the methodology will see case studies from Sweden, Norway, the Netherlands and
the United Kingdom (the other SAWA membership countries), being undertaken, as
part of the development of a generally applicable DSS and user interface.
Figure 1 River Wandse (Hamburg)
Figure 2(a) shows the four phase structure of a LAA. The stakeholders analysed in
Phase 1 of this particular case study area including local municipal authorities (water
management, urban development, civil defence), infrastructure suppliers, NGOs,
political and public bodies. Phase 2 deals with the selection of flood hazard
management measures to be applied, with both Structural and Non Structural
Measures (NSM) being considered. Phases 3 and 4 as highlighted in Figure 2(a) are
where the methodology presented in this paper will be applicable. To ensure a
continuous collaborative decision making process, all stakeholders, professionals and
public are to be involved right from the start and throughout the four phases of the
LAA. This process then contributes to successful engagement of all parties and
‘moves’ each respective group up the ladder of (citizen) participation from the
‘steps’ of tokenism to those of empowerment, as shown in Figure 2(b).
Figure 2(a) Learning and Action Alliance Structure
2(b) Ladder of (citizen) Participation
Based on these considerations, the proposed methodology to be applied to the case
study area initially will use Pareto techniques, where the purpose is to choose the
‘best trade-offs’ among all the defined and conflicting objectives and to search for
possible equilibrium solution points. Or to identify regions where coalitions may be
formed between stakeholder groups, where a majority acceptance of an objective can
be sought. This is discussed fully in the following section.
Methodology (Conflict Analysis): The methodology presented here provides details
of the strategy to be used in terms of identifying (potential) conflict resolution and
providing an additional stability assessment. For example, let X and Y be two
dimensions of a single, interrelated issue, say, installation cost (X) and estimated
whole life cost (Y), with an individual (or group) ideal response being defined over
X0, X0.01....X1.0 (preference indicator) and Y0, Y0.01....Y1.0 with the M(m, n) matrix G
= [αi,j]i=1,...,m; j=1,...,n representing each players ideal response combination for the
interrelated parameters XY. By plotting the information from the matrix G as a series
of points and assigning a ‘range’ (v) to a third parameter Z. Represented by the M(m,
1) column vector H = [βi]T i=1,...,m; with the value of v being dependent upon each
players distance from a point representing the (median) status quo, say N, as shown
in Figure 3A. It can be assumed that the parameter Z, when plotted as a circle of
radius v, represents an indifference curve of each player to the related XY
dimensions. The ‘fuzzy’ nature of defining the intangible, individual or group
indifference in relation to the median of the XY dimensions. Has been applied
successfully in areas such as coalition formation at governmental level, and as such
is deemed to be suitable for application here in the selection of potentially conflicting
responses to flood hazard management solutions. The alternative being that each
stakeholder indifference curve is ‘fitted’ independently through expert consultation.
A methodology that is subject to potentially significant variation. Therefore it is
possible to plot the resulting data from the tangible dimension parameters recorded in
G and the intangible indifference recorded in H onto a two dimensional XY
quadrant, as shown in Figure 3(a). For application of this methodology, the authors
used the Mathworks Matlab®, (version 7, release 2009A) software package due to its
vector and matrix formulation being suited to the data capture within the case studies
of the SAWA project.
Figure 3(b) shows that by further plotting a convex hull around the points A – C, a
Pareto region is formed where any point, of solution inside the region is preferable to
those outside the region.
Figure 3(a) 2 player’s Indifference
3(b) Three Player’s Pareto Region
Figures 3(a) and 3(b) also show regions where the indifference curves overlap to
form ‘winset’ regions, or ‘lensing’, where common ground between players can be
‘assumed’. However, from Laver and Shepsle (1996) defining solutions according to
‘winsets’ alone can result in a non-stable solution that is particularly sensitive to
cycling (i.e. players switching allegiance in order to gain alternative benefit). In order
to overcome this sensitivity it is preferential to identify points within the boundary of
the Pareto region where there is an intersection of ‘lattice’ lines, as shown by the
arrow in Figure 3(b). These intersecting ‘lattice’ lines form a challenge to the status
quo (point N), if they fall within the Pareto region and within a ‘winset’. However in
the randomly generated example shown in Figure 3(b) point N, the median,
represents the stable solution as no ‘lattice’ line intersection falls within a ‘winset’
region.
As can be seen from Figures 3(a) and 3(b) it is possible to quickly identify the areas
of the quadrant where conflict between players can be resolved (stable solutions),
through identification of points within the region where there is occurrence(s) of
‘lattice’ intersect within a ‘winset’ region. In addition to identifying player strategy
choices where direct conflict will arise i.e. with no region overlap and no ‘lattice’
intersections occurring. Scenarios where (strong) conflict arises could then be
subject to further analysis in order to attempt to draw a solution through reevaluation of player response functions. The model tested by Laver and Shepsle is
particularly suitable for application within the SAWA project, in terms of analysing
potential stakeholder conflict. As the model is deemed to be more robust when
explaining coalitions where there is a large central stakeholder, such as a municipal
authority, with additional smaller, ‘satellite’ stakeholders, than when applied to
coalition formation of entirely small to medium, totally diverse stakeholder groups.
Therefore by expanding the methodology to include additional stakeholder groups
and applying it to alternatively proposed flood hazard management solutions, each
with identical pairs of key related dimensions, for example:
•
•
Installation Cost – Whole Life Cost
Environmental Impact – Adaptability to Climate Change
•
Social Impact – Recreational Benefit...etc etc
It can be assumed that the methodology can rapidly assess aspects of a proposed
solution where conflicting interests may/may-not occur. These solutions may then be
subjected to a form of simultaneous one dimensional voting strategy in order to
determine a solution to be implemented. This is covered in the following section.
Methodology (Voting): The previous section discussed the analysis of player
responses to series of specific inter-related dimension sets of an issue and how the
information can be used to identify aspects of such proposed solutions where levels
of conflict/coalition occurs. As stated in the Abstract and throughout this paper, the
methodologies employed are termed as simultaneous and cooperative in nature. A
cooperative culture was promoted as the foundation to both phases of the DSS
methodology for development within the project and beyond, as cooperation has
been shown to be highly beneficial following emergence, either spontaneously or
through rational thought. Even between groups of (possibly) antagonistic ‘players’ of
a game due to the realisation or belief that player groups may meet again under
similar circumstances. A situation which is encountered where practitioners are
developing catchment flood risk management plans. Or within broader context of a
transnational project such as SAWA. In the specific context of game theory,
cooperative behaviour results in binding agreements between players being formed.
Therefore, considering these contexts, it may be hypothesised that a degree of
foresight is not necessary for the development of cooperation, though it may in some
cases help. Therefore the strategies chosen now are more significant in terms of the
effect that they have upon future decision outcomes. In terms of overcoming the
dilemma faced by player groups as to whether mutual cooperation will develop
through successive strategy choices, or as to whether a particular player (usually
themselves) will be less beneficial than others. The overcoming of this particular
dilemma requires that the individual player groups have sufficient belief that they
will meet again and thus have a stake in their future interaction, as alluded to in
Figure 2(b), the ladder of (citizen) participation. This, then leads to the situation
where cooperation, based upon some levels of reciprocity achieves a high degree of
stability, even under differing strategy selections, and is proven resistant to attempts
by outlying individuals/groups attempting to employ less cooperative strategic
choices (votes), for essentially short term, minority gains. By promoting beneficial,
frequent, future interactions and organised practice.
Thus under the simultaneous/cooperative culture outlined and with the results of the
Pareto optimisation the voting phase of the methodology will employ a Binary
Agenda approach to remove solutions which are subject to high levels of potential
conflict. A simple example of a Binary Agenda is given in Figure 4.
Figure 4 Binary Agenda
A binary agenda may be formally defined in that and agenda is binary if at every
stage of the process along the (simultaneous) timeline a player can vote in favour of a
strategy in an available set (i.e. D in the first ballot) or vote for an alternative strategy
(i.e. B in the first ballot) within the available set. Solutions to the game are then
derived from the game sub-sets.
For example:
If in the first ballot the majority of the stakeholders or in unanimity
select B in preference to D, then option D is eliminated from this and
all future ballots.
The available solutions to each ballot (game) sub-set are: “equilibrium” or “weakly
un-dominated”, where:
• Equilibrium solutions represent a unanimous vote. In that if all stakeholders
vote in favour of a particular outcome, then no single player can benefit from
or affect the outcome of the stage of the ballot by changing their respective
vote.
• Weakly dominated solutions represent voting results where a ‘stable’
majority is achieved, from Caplin and Nalebuff’s equation of:
Where:
m* = majority required
n = number of players (stakeholders)
However as this project deals with a diverse, real-world stakeholder group often
comprising of opposing viewpoints we shall restrict further applications to weakly
un-dominated solutions.
Discussion: From the methodology presented it is reasonable to provide a brief
discussion, for the purpose of clarity, of the research methodology presented in this
paper into the four bullet points below:
•
•
•
•
As is the case with other catchments, it has been recognised that unless all
stakeholders can be engaged in producing a FRMP for the River Wandse
catchment, the plan may not reach its full potential.
The Methodology proposed to be used on a real world case study is hypothesised
to be applicable in a multi-disciplinary, trans-national culture’s
As management options evolve during formulation of the FRMP, the novel game
theory approaches outlined in this paper ‘flex’ to accommodate new parameter
sets.
o Complexity and detail can be accommodated by the methodology, to suit
case studies from alternative regions.
Case studies from single properties to whole developments can be considered
without significant changes to the application of the methodology.
Progression: The two novel stages of Optimization and Voting methodology
presented in this paper will be further developed and applied by the authors to a
series of real world case study areas within the SAWA membership countries. This
will results in the verification of the approach and development of a generally
applicable DSS and user interface that can be confidently used by end users practitioners, planners and educators. The authors will also seek to employ the
methodology further through collaboration with other ongoing projects in the fields
of flood resilience, urban flood risk management planning and projects dealing with
societal and regional, economic issues.
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