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Game Theory and Territorial Game Theory and Territorial
IntelligenceIntelligence
Illustration Illustration fromfrom a Case a Case StudyStudy
Michel Carrard
National School of Engineering, Bourges
RESO-UMR 6590, Rennes 2 University
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The objective of this contribution is to The objective of this contribution is to
present the principles of a present the principles of a
methodological work that has methodological work that has
mobilized game theory to illuminate mobilized game theory to illuminate
a town and country planning issue a town and country planning issue
(Carrard, 2009):(Carrard, 2009):
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PLANPLAN
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22 Methodology: Game TheoryMethodology: Game Theory
33 The The ““Community GameCommunity Game””
44 Conclusion Conclusion and Prospectsand Prospects
ContextContext and and Study StakesStudy Stakes
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http://www.aeroport-grandouest.fr
ContextContext and and Study StakesStudy Stakes: : the transfer the transfer of Nantes Atlantique airportof Nantes Atlantique airport
Aéroport NDDL
5Dossier d’enquête préalable à la déclaration d’utilité publique, DGAC, 2006.
ContextContext and and Study StakesStudy Stakes: : thethe main components of NDDL airportmain components of NDDL airport
6Ernst&Young, CG d’Ille et Vilaine, 2006
ContextContext and and Study StakesStudy Stakes: : thethe impact of future NDDL airportimpact of future NDDL airport
Nantes: very high
impact
Rennes: high impactWestern and northern
Britain: no impact
NDDL airport: very high
impact
Zone of influence of
NDDL airport: high
impact
Rural area: low
impact
Secondary urban
centers: high impact
Nantes-Rennes: high
impact
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1) NDDL : « the largest airport in the West ? »
Resulting from competitioncompetition between airports
What statusWhat status for future NDDL airport ?for future NDDL airport ?
Two options were discussed during the Public Debate (2003):Two options were discussed during the Public Debate (2003):
or
2) NDDL : « the airport of the Great West ? »
Resulting from cooperation between airports
ContextContext and and Study StakesStudy Stakes: : problemsproblems
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PLANPLAN
11
22 Methodology: Game TheoryMethodology: Game Theory
33 The The ““Community GameCommunity Game””
44 Conclusion Conclusion and Prospectsand Prospects
ContextContext and and Study StakesStudy Stakes
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• Using game theory to analyze real situations
encounters two types of objection:
• 1) Game theory formalism is too restrictive to take the
complexity of reality into account.
• 2) Game theory does not “claim to say what is”, because
the assumptions of its models are too simplistic.
• Finally, the boundaries of game theory significantly
reduce its ability to help in decision making.
Methodology: Methodology: ReflexiveReflexive ModellingModelling
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• Choosing a method: reflexive modelling (Thépot,
1998)
• “Reflexive modelling claims to act further upstream on the
mental representation by which the decision maker
structures his schematic vision of reality” (Thépot, 1998, p.
8 and following )
• Reflexive modelling sets itself the objective of extracting
from the real “a few stylized facts from which other stylized
facts are deduced by using simple models of game theory
which will be submitted to the discretion of the decision
maker” (Thépot, 1998).
Methodology: Methodology: ReflexiveReflexive ModellingModelling
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Methodology: game theoryMethodology: game theory
“Reflexive modelling and normative modelling” in Thépot J., (dir.), 1998, Gestion et théorie des jeux. L’interaction stratégique dans la décision, ed. Vuibert
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• Reflexive modelling creates space for game theory and provides an objective as well as a methodology of work:
• An objective since this type of modelling claims to help the decision maker to clarify his strategic choices.
• A methodology as this approach only claims to describe the nature of the strategic interactions of players so as to draw logical implications and consequences.
• The aim is then less to determine the existence of solutions than to clarify the nature of the difficulties to reach them: coordination problems, conflicts of interest, impasses in cooperation, reputation effects, etc....
Methodology: Methodology: ReflexiveReflexive ModellingModelling
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Methodology: Game Theory and Methodology: Game Theory and
Prospective Prospective ApproachApproach
• Proximity can be found between the approach of prospective scenario and the solution concept of game theory.
• “A scenario is not the prospective reality but a means to represent it with
a view to illuminating the present action in the light of possible and
desirable futures” (Godet, 2004, p. 10)
• The solution concept refers to the conditions imposed on the strategies of players, which if they are verified, become the solutions of the game (Guerrien, 2002).
• The solution to a game, when it is reached, suggests the existence of “a viable social order”, that is to say, such a state of the world that the mutual interest of players ensures its stability.
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• "Game theory can, on intuitive bases, ultimately identify some socially possible futures among the many conceivable
scenarios” (Schmidt, 1999, p. 56).
• Three situations may come up which can help the futurist to identify scenarios (Schmidt, 2000):
– The first, when the solution to a game is an empty set, then the related scenario must be abandoned.
– The second, when the solution is unique, then the scenario identified is the only stable state, and should be analyzedcarefully.
– Finally, a game may sometimes have several solutions. This can lead the futurist to make recommendations based on criteria thatare external to the game itself.
Methodology: Game Theory and Methodology: Game Theory and
Prospective Prospective ApproachApproach
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• "The intelligence of a social situation is scarcely reduced to the understanding of a single game" (Schmidt, 2000, p. 258).
• In our study, we developed three games, which each in their own way, have approached an aspect of the interactions between the players concerned by the future airport:
– The focus is on the institutional dimension of the players in the “Community Game”
– In the other two games, the «Airport / Airlines Game» and the « Airport in the Metropolitan Loire-Bretagne Area game (EMLB)” attention is focused on airports and their interactions with airlines.
Methodology: Game Theory and Methodology: Game Theory and
Prospective Prospective ApproachApproach
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• This multiplication of games is the opportunity to refine the analysis of certain types of interactions.
• Each game is an independent model but none is completely cut off from the other two.
– the players are the same from one game to the other
– the solution to a game can affect the next game, etc...
• All three games can be seen from a future oriented approach, as a metagame (Howard, 1971, Schmidt, 2000) which includes such games as many sub-games.
Methodology: Game Theory and Methodology: Game Theory and
Prospective Prospective ApproachApproach
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PLANPLAN
11
22 Methodology: Game TheoryMethodology: Game Theory
33 The The ““Community GameCommunity Game””
44 Conclusion Conclusion and Prospectsand Prospects
ContextContext and and Study StakesStudy Stakes
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The The ““Community GameCommunity Game””
Means used:
- Non-cooperative game for 2 players
- Solution concept used : Nash equilibrium and
Schapley value
A – Objective:
Reflecting on the conditions for cooperation between
Nantes and Rennes airports
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A – The players
A and B:A and B: two communitiestwo communities
� A has an airport leader
(interregional calling)
� B has a local airport (local
calling)
Objectives for A and B:Objectives for A and B:
� Increasing access through their
airports
� Maximize their attractiveness
The The ““Community GameCommunity Game””
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A – the game
The The ““community gamecommunity game””
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AA
BB BB
A – Community Game Tree
Scenario 1ScenarioScenario 11
Negotiated
Management
Scenario 2Scenario Scenario 22
Challenged Challenged
LeadershipLeadership
Scenario 3Scenario Scenario 33
Hierarchical
Relationship
Scenario 4Scenario Scenario 44
Competitive
Management
Cooperation
Cooperation Cooperation
Competitive
Competitive Competitive
The The ““Community GameCommunity Game””
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A – Preference order
(3 , X) (3 , X) (2 , X) (2 , X)
(0 , X)(0 , X)(1 , X) (1 , X)
The payoff matrix for A
Assumption
The The ““Community GameCommunity Game””
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A – Preference order
(X , 0) (X , 0) (X , 1)(X , 1)
(X , 2)(X , 2)(X , 3)(X , 3)
The payoff matrix for BAssumption
The The ““Community GameCommunity Game””
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A – The position of players with non-cooperative strategies
(1 , 3)(1 , 3) (0 , 2)(0 , 2)
(3 , 0) (3 , 0) (2 , 1)(2 , 1)
Nash equilibrium
The payoff matrix
Assumption
The The ““Community GameCommunity Game””
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Playing thePlaying the ““Community GameCommunity Game””
• In the context of reflexive modelling of the
situation, Rennes and Nantes players were offered
to participate in the “community game”
• This was, initially, to assess their preferences for
the scenarios from political, economic and social
criteria. Then, they were asked to play the game.
• As the proposal failed to reach its end, we will
present some results obtained with the test group
(8 participants).
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B - Experimental game
1 - Political criterion Reelection of politicians
2 - Economic criterion The growth of GDP per capita
Employment (unemployment)3 - Social criterion
Assumption: Three criteria weigh the same (1 / 3) in the choice of strategies
Three decision criteria for A and B
Playing thePlaying the ““Community GameCommunity Game””
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1st rank 4th rank
(2,75 , 4,5) (2,75 , 4,5) ((--3 , 4,5) 3 , 4,5)
(5,25 , (5,25 , --1) 1) (1 , (1 , --2) 2)
(0,25 , 4,75) (0,25 , 4,75) ((--3 , 3,25) 3 , 3,25)
(4,25 , (4,25 , --3) 3) (4,5 , 1) (4,5 , 1)
B – Experimental game
Nash Equilibrium
Playing thePlaying the ““Community GameCommunity Game””
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1st rank 4th rank
(2,75 , 4,5) (2,75 , 4,5) ((--3 , 4,5) 3 , 4,5)
(5,25 , (5,25 , --1) 1) (1 , (1 , --2) 2)
(0,25 , 4,75) (0,25 , 4,75) ((--3 , 3,25) 3 , 3,25)
(4,25 , (4,25 , --3) 3) (4,5 , 1) (4,5 , 1)
B – Experimental game
Playing thePlaying the ““Community GameCommunity Game””
Differential between rankings Differential between rankings constitute margins from constitute margins from
which players can mutually adjust to (example 1)which players can mutually adjust to (example 1)
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1st rank 4th rank
(2,75 , 4,5) (2,75 , 4,5) ((--3 , 4,5) 3 , 4,5)
(5,25 , (5,25 , --1) 1) (1 , (1 , --2) 2)
(0,25 , 4,75) (0,25 , 4,75) ((--3 , 3,25) 3 , 3,25)
(4,25 , (4,25 , --3) 3) (4,5 , 1) (4,5 , 1)
B – Experimental game
Differential between rankings Differential between rankings constitute margins from constitute margins from
which players can mutually adjust to (example 2)which players can mutually adjust to (example 2)
Playing thePlaying the ““Community GameCommunity Game””
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PLANPLAN
11
22 Methodology: Game TheoryMethodology: Game Theory
33 The The ““Community GameCommunity Game””
44 Conclusion Conclusion and Prospectsand Prospects
ContextContext and and Study StakesStudy Stakes
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Conclusion Conclusion and Prospectsand Prospects
• If Game Theory concepts are not easily transferable to
real cases, Reflexive Modelling offers interesting
prospects to address situations in which the
interactions between actors are strong.
• Reflexive Modelling does not seek to determine an
optimal strategy for a decision maker but rather to
guide him in his decision making
• Reflexive Modelling requires a dialogue between the
decision maker (s) and the modeller.
• We also recalled that game theory allows a futurist
reading in so far as it allows to select the scenario
among a set of scenarios.
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Conclusion Conclusion and Prospectsand Prospects
• Finally, with respect to the subject of this conference,
it appears that territorial intelligence can fully benefit
from the contributions of game theory.
• We will give two examples:
- The first, we have experienced in our study, relies on
game assessment by the players themselves with a view
to clarifying their preferences, beliefs, etc... (Reflexive
modelling).
- The second, is related to the development of evolutionary
games which, together with information technology tools,
allow simulations of cooperation and competition
between economic actors (Berro, Leroux, 2006).
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Thank you Thank you for for your your
attentionattention