A Game Theoretic Approach for Managing Multi-Modal Urban Mobility Systems

A Game Theoretic Approach for
Managing Multi-Modal Urban
Mobility Systems
Christos Nikolaou
Marina Bitsaki
Alina Psycharaki
George Koutras
Transformation Services Lab
Computer Science Department
University of Crete
13/01/2015 nikolau @ tsl.gr 1

Table of Contents
• Collective Adaptive Systems
• The ALLOW ENSEMBLES project
• The Strategic Ensemble Concept
• The FlexiBus Scenario
• Game Theory: Non-cooperative and
cooperative games
• Future Work - Publications

Collective Adaptive Systems (CAS)
• “Collective adaptive systems consist of many autonomous units that
interact in a variety of ways over multiple scales”,
https://www.elec.york.ac.uk/research/intSys/cas.html
• Concept similar to: complex adaptive systems, cyber-physical systems,
service systems.
• Autonomous units could be (cyber and/or physical) systems and/or
humans.
• The Internet of Things (IoT) helps their proliferation.
• Collections of autonomous units (networks, hierarchies) are formed, often
with competing interests (for example for use of resources, of services,
etc.).
• Various concerns (for example smarter energy use, empowering the
patient to improve quality of life, environmentally friendly easy-to-use
urban mobility) could be addressed if:
– autonomous units (systems and/or humans) of CAS learn to cooperate and/or
compete, negotiate, develop strategies to achieve goals.

Examples of Collective
Adaptive Systems
Smart Grid Smart Urban Mobility
Smart Health Services

The Urban Mobility Scenario
(Buses, FlexiBuses, Carpools, Taxis, Passengers)

Table of Contents
cooperative games

The ALLOW ENSEMBLES project
(Funded by FET Proactive, 7FP, EC)
• http://www.allow-ensembles.eu/
Allow Ensembles develops new models, theories and algorithms that can:
• Autonomously form large-scale collective adaptive units (ensembles) that
can flexibly satisfy arbitrary goals in the real world environments.
• Improve the utility of ensembles by adapting the individual cells
within an ensemble such that the overall system learns to get better
at accomplishing goals.
• Make ensembles robust
• Evolve ensembles in order to promote beneficial emergent properties
and suppress detrimental emergent properties.
• Make ensembles secure and protect sensitive data by evolving
security policies in unison with ensemble evolution.

Basic Concepts - Cells
• Cell: a unique identifiable building block representing
a concrete functionality in a larger, multicellular
system.
• Implementing the functionality may involve interacting
with other cells through predefined protocols.
• Each cell is therefore defined in terms of its protocol
(exposed process fragments) and behavior (flow).
• Cells can be created either by instantiating cell
archetypes1, or by other cells through the process of
differentiation.
(from “Terminology”, Internal Document, ALLOW
ENSEMBLES consortium).

Basic Concepts – Passenger Trip
Booking Cell Archetype Example
(from “Terminology”, Internal Document,
ALLOW ENSEMBLES consortium).

Basic Concepts - Entities
• Entity: a physical or virtual organizational unit aggregating a set of
cells.
• Cells can either be unique in an entity, or they can be replicated by
the entity by instantiating the cell archetype as many times as
necessary. However, each cell belongs to exactly one entity.
• Each entity has a context in which it operates, which is accessible by
its cells.
• Furthermore, an entity has a set of goals that it attempts to fulfill
by initiating or participating in one or more ensembles.
• Entity Examples: Bus Driver, Passenger, Route Manager and FlexiBus
Manager.
• (from “Terminology”, Internal Document, ALLOW ENSEMBLES
consortium).

Basic Concepts - Ensembles
• Ensemble: a set of cells from different entities
collaborating with each other to fulfill some of the
goals of the entities.
• Each ensemble is initiated and terminated by an entity,
but more than one entities are expected and allowed
to join and leave through the ensemble’s lifetime.
• Ensemble Example: The Bus Driver, Route Manager and
the various Passenger entities are participating in one
Route ensemble
• (from “Terminology”, Internal Document, ALLOW
ENSEMBLES consortium).

12
Conceptual Integration of the Project

Entities Interactions
• Entities interact in order to achieve
– Individual objectives
– Group objectives
• Interactions may:
– Help entities make decisions to achieve goals (gather info, learn, negotiate, optimize,
participate in games, form coaltions, etc.)
– Implement decisions made by entities (make payments, step in a bus, schedule a bus, etc.)
• Interactions result in the creation of
– (execution) ensembles in order to fulfill specific goals initiated by the entities
– Strategic ensembles in order to handle decision making and increase entities’
satisfaction expressed in utility terms

Table of Contents
cooperative games

The Strategic Ensembles Model
• A strategic ensemble model uses the entities’ utility-cells
– It is created before the execution ensemble
– It runs in parallel to the execution ensemble
– It affects the operations of the execution ensemble
• The objectives of a strategic ensemble include the following
– Impose constraints according to entity goals and preferences in order to
reduce the various choices of entities
– Assign utility to each entity when participating in an ensemble in order to
make the optimal choice
– Manage the negotiation among entities

Utility-cells
• Represent utility and game theoretic characteristics of entities
• The utility-cell of an entity has the following functionalities
– calculates the utility of an entity when participating in a given ensemble
– communicates with other cells and makes decisions/computes strategies of the
entity
– collects data from measurements (resource consumption, satisfaction, costs,
delays, prices, …) and passes them to the Evo(lutionary) Knowledge Data Base
– Consults EvoKnowledge (learns) about utility function parameters, external
conditions (for example changes in traffic patterns, special events in city, etc.).
– runs optimization algorithms to maximize entities’ utility or improve the
performance of ensembles

Strategic Ensemble
Exec-
cell
Utility-
cell
Utility-
cell
Exec-
cell
Exec-
cell
Exec-
cell
Utility-
cell
Exec-
cell
Exec
cell
Utility-
cell
Exec-cell
Utility-
cell
Entity 2
Entity 1
Entity 3
Entity 4
Entity 5
Entity 6

Passenger
Passengers
Utility-
CellUtility-Cell
Cell
Flexibus
Manager
Utility-
Cell
Example Strategic Ensemble
Route Planner
Cell
Cell
Utility-
Cell
Cell
Cell
Route Manager
Utility-
Cell
Cell
FlexiBus
Driver
routeInfo

Interactions
Exec
cell
Utility-cell
Utility-cell
Exec-
cell
Evo-cell
Route Planner
Strategic
Ensemble
Passenger
Evo-cell

Prior Art
• An efficient transportation system utilizes mass transit alternatives to the
automobile in order to reduce congestion and support ecological
solutions.
• Travelers make decisions based on timing, cost, comfort, safety and mode
of trips, while planners face policy questions such as frequency of routes,
itineraries, size, cost, environmental impact, etc.
• (Lam, Small, 2001): a method to value travel time and its reliability.
People had to choose between two parallel routes, one free but congested
and the other with time-varying tolls by maximizing a utility function (a
function of travel time, variability in travel time, cost, characteristics such
as time-of-day and car occupancy, and a random component).
• (Johansson et al., 2003): the labor market commuter behavior is analyzed
taking into account the observation that the willingness of an individual to
commute is different for short, medium and long time distances.

Prior Art (cont.)
• (Li, Huang, 2005): reliability of morning commuting in congested and uncertain
transport networks
• Other studies analyze the interactions between commuters and planners or
transport managers and examine how commuters choose their optimal routes and
trip modes using non-cooperative games.
• (Sun, Gao, 2007): a non-cooperative, perfect information, static game to describe
how travelers adjust their route choices and trip modes.
• (Anas, Berliant, 2010): the authors consider a commuting network consisting of a
finite set of nodes at which the commuters live or to which they commute or
through which they commute and a finite set of transport links between the nodes
(there exists only one mode of transportation). A non-cooperative game is
formulated consisting of a set of commuters who compete for routes.
• In our work, we investigate a dual problem facing both the commuters and the
transportation authority; the commuters choose their trip mode, while at the
same time the transportation company that provides a bus for example, makes
decisions on accepting or not travel requests dynamically.

Table of Contents
cooperative games

The FlexiBus Scenario: Assumptions
• A route is a set of predefined pick-up points
• We consider two phases in the lifecycle of a route:
– The pre-booking phase: a route is going to be executed if a
certain number of requests is reached until a certain
deadline
– The execution phase: the route is bound to start or it has
already started
• The pick-up points of a route are bound to change at
the execution phase
– Add a pick-up point due to a new request
– Remove a pick-up point after a cancellation

Time-line
End of
Route
Pre-booking
phase
Preparation phase
Initialization
Running phase
Execution Ensemble
Strategy Ensemble
Booking phase

Entity’s Utility
• Entity’s utility
– Utility accrued when participating in a specific
ensemble
– Calculated by the entity according to
• Her preferences (that are publicly known)
• Private information
• According to the entity’s utility the winning
route may be different from the one resulted
by the evaluation of the other members of the
ensemble (e.g. the route manager).

Entity Utility (Example)
• Consider Peter sending the request (Destination: Piazza Duomo, arrival time: 21.30)
to Urban Mobility System with preferences
– Pay with credit card (desired)
– Non-smoking bus (demanded)
– Window seat (desired)
• Consider the following candidate routes
– Route A (at a cost of 10 Euros): non-smoking bus, pay with credit card, window seat
– Route B (at a cost of 12 Euros): non-smoking bus, pay with credit card, aisle seat
– Route C (at a cost of 7 Euros): non-smoking bus, pay with credit card, aisle seat
• Route A has higher value to Peter than Route B but not clear for Route C (it depends
on how Peter values money)

Table of Contents
cooperative games

Game theoretic models
• Analyze models that:
– show the strategic interactions among various
components
• my decisions affect others’ decisions
– derive equilibria so that utility/profit is maximized
• Nash equilibrium

Nash Equilibrium
• Nash equilibrium is an outcome of a game in which each
player is assumed to know the equilibrium strategies of the
other players, and no player has anything to gain by changing
only his own strategy unilaterally
– In a game of two players A and B, the pair of strategies (s, g) is a Nash
equilibrium if s is optimal for A given g and g is optimal for B given s

Nash Equilibrium (Example)
• Consider two players A and B
• Strategies for player A  {Top, Left}
• Strategies for player B  {Left, Right}
• Nash equilibria: (Top, Left), (Bottom, Right)
B
A
Left Right
Top 2,1 0,0
Bottom 0,0 1,2

Non-cooperative Games
• Static games
– all players' decisions are made simultaneously
– players receive payoffs that depend on the actions just chosen
• Dynamic games
– each player can consider his plan of action not only at the beginning of the
game but also whenever he has to make a decision
– perfect/imperfect information
• At each move the player with the move knows the full history of the play thus
far
• Games of complete/incomplete information
– Each player’s payoff function is common knowledge among all players

A Non-cooperative Game of Complete
Information
• Objective: model the interactions of entities when a new
request arrives in a route that is being executed and
compute their optimal choices (strategies) based on
utilities
• Problem description
– We consider a route to be a set of fixed pick-up points and the
respective estimated travel times between pick-up points
– When a new request arrives, the various entities make
decisions:
• route planner: accept or reject the request (in case of accept send
conditions (travel time, cost)
• new passenger: accept or reject offer
– We formulate these interactions as a game
• Are there equilibrium strategies?

Assumptions
• All passengers have the same destination
• Current passengers do not negotiate for the new
conditions (resulted by the new passenger) of the route
• The route planner has to take into account that any violation
of his past commitments will affect negatively his utility
• We consider a game of complete information
• The route planner provides private information of current
passengers to the new passenger
• The utility functions of all actors are common knowledge

Assumptions
• We consider a dynamic game
• Decision points: request arrivals
• new strategies have to de derived each time a new request arrives
(thus a new game is formulated)
• All these games across the route have to be synchronized in order to
derive optimal profits for the FlexiBus company and the passengers
• Each game is sequential
• The new passenger makes a request
• The route planner calculates his strategy (accept or reject) based
on request
• The new passenger calculates his strategy based on planner’s
strategy

Game Formulation
• Set of players:
– current passengers (1,…,n)
– new passenger (np)
– route planner (rp)
• Strategy profile:
(ti : travel time)
ti , i=1,…n are fixed and known
𝑠 = (𝑡1, 𝑡2,…, 𝑡 𝑛, 𝑡 𝑛𝑝 , 𝑡𝑟𝑝 )

Game Formulation
Profits:
– Current passengers:
– New passenger:
G: the profit gained by alternative solution
f: function that incorporates the risk of adding future passengers
– Route Planner:
g: function that incorporates the risk of losing future passengers
𝑝 = (𝑝1, 𝑝2, … , 𝑝 𝑛 , 𝑝 𝑛𝑝 , 𝑝 𝑟𝑝 )
𝑝𝑖 =
0, 𝑡𝑖 < 𝑡 𝑟𝑝
𝑢𝑖 𝑡 𝑟𝑝 , 𝑡𝑖 ≥ 𝑡 𝑟𝑝
𝑝 𝑛𝑝 =
𝐺, 𝑡 𝑛𝑝 < 𝑡 𝑟𝑝
𝑢 𝑛𝑝 𝑡 𝑟𝑝 − 𝑓(𝑡 𝑛𝑝 ), 𝑡 𝑛𝑝 ≥ 𝑡 𝑟𝑝
𝑝𝑟𝑝 = 𝑢 𝑟𝑝 𝑡𝑟𝑝 + 𝑝𝑖
𝑖≠𝑟𝑝
− 𝑔(𝑡𝑟𝑝 )

37
Set of
Processes
Subsystem architecture
Process/Flow Engine
Utility Module
Set of
Processes
services.tsl.gr
Set of
Processes
Fragments
(Parts of
Meta-cells)
Set of
Processes
Set of
ProcessesSet of
Services
Design Time
Run Time

Entity Hierarchies
• Entities can form hierarchies (of entities):
– For example: people and systems participate in a
department entity, which in turn may participate in a
division entity, which in turn may participate in a
corporation entity.
• Utility of higher-level entity could be defined as the
sum of the utilities of the entities one level below (and
so on recursively),
• But, optimal utility of a higher-level entity is NOT
necessarily the sum of the optimal values of the
utilities of the immediate lower-level entities.
• … a number of interesting research questions…

Role of utility in Evolution
• Utility function with incorrect (or partially correct) parameters
– may result in wrong selection of ensembles
– e.g., use of incorrect travel duration etc.
Execution
Context
EvoKnowledge
Monitor Utility
Evolve
Utility function selects the proposed
solution with highest utility taking
into account goal, context and user
preferences (measured utility)
1
Ensemble with
high utility is executed
2
Parameters of utility function are
adjusted according to past executions and
the calculated utility and monitored utility
in a given context
3
Utility Functions

Specialization tree
Goal
……... specialization ………
Ensemble N
Utility Functions

Example
Goal: Reach a
destination
Car sharing
Non-Public
Transportation
Public
Transportation
Rent car
U1 (t,c)
U2 (t,c,r,d)
t: travel time
c: cost
r: reliability
d: walking distance

Example
(in Collaboration with IPVS)
t: travel time
c: cost
r: reliability
d: walking distance
Goal: Reach a
destination
Non-Public
Transportation
Public
Transportation
Train Flexibus
U1 (t,c)
U2(t,c, r,d)

Cooperative Games
• In cooperative game theory, interest is on outcomes of coalitions
of players rather than actions of individual players
– focus in cooperation games is on coalitions that will be formed and on
the sharing of value or cost incurred among members of the
coalition.
• Cost allocation problem in which players perform a joint task and
allocate its cost among them
• Why use cooperative games
– Helpful tool if performance of an intelligent system and its entities can
be improved when several players cooperate
• Dynamic cooperative game (??)
• Implementation issues:
– get information on game parameters and data from EvoKnowledge (?),
– test game and obtain results in ALLOW Ensembles platform, ….

The General Idea of an Algorithm
for Cooperative Games
• Game (𝑁, 𝑐)
• Specify set 𝑁 = {1, … , 𝑛} of potential users involved (𝑛 = |𝑁|).
• Specify cost function 𝑐: 2 𝑁 → ℝ of a route, where 𝑐(𝑆) is the joint cost of
the route used by the set 𝑆 ⊆ 𝑁 of users (𝑐 ∅ = 0).
• A required property for 𝒄:
• Subadditive cost: For every two disjoint sets of users the cost of the route
if they merge is smaller than or equal to the costs of the route they would
incur if used separately (𝑐 𝑆1 ∪ 𝑆2 ≤ 𝑐 𝑆1 + 𝑐 𝑆2 , 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑆1, 𝑆2 ⊂ 𝑁).
• In a subadditive game: 𝑐(𝑁) ≤ 𝑖𝜖𝑁 𝑐( 𝑖 ). If this condition holds with
strict inequality then the game is called essential (each player gains from
cooperation).
• If subadditivity property does not hold, coalitions other than the grand
coalition might be possible.
• Cost should reflect:
– Services required by the operator, Infrastructure costs, Payments, …

Algorithm (cont.)
• Allocate 𝑐(𝑁) among the users in 𝑁.
• Specify an allocation rule 𝑥: 𝑥 𝑐 =
𝑥1, … , 𝑥 𝑛 𝑠. 𝑡. 𝑖𝜖𝑁 𝑥𝑖 = 𝑐(𝑁) (such as Shapley
value for fairness or core for stability).
• 𝑥 is an imputation of game (𝑁, 𝑐) if the following
hold:
– 𝑖𝜖𝑁 𝑥𝑖 = 𝑐 𝑁 1 feasibility of the grand coalition
(costs are reimbursed) and
– Pareto efficiency: 𝑥𝑖 ≤ 𝑐 𝑖 ∀𝑖𝜖𝑁 2 no player pays
a higher price in the grand coalition than he would do
independently

Table of Contents
cooperative games

Future Work
• In the case of one route
– Permit actions such as adding pick-up points in order
to serve new passenger requests or removing pick-up
points in case of cancelations
– Perform negotiations with current passengers when a
new request arrives
• Consider multiple routes for one request as part
of the decision mechanism
• Design routes according to a decision making
mechanism that takes into account traffic
demand

Some recent related publications
• “A Game Theoretic Approach for Managing Multi-Modal Urban Mobility
Systems”, Vasilios Andrikopoulos, Marina Bitsaki, Antonio Bucchiarone,
Santiago Gómez Sáez, Dimka Karastoyanova, Frank Leymann, Christos
Nikolaou, Marco Pistore, 2th International Conference on the Human Side
of Service Engineering Human Factors and Ergonomics, 2014/7/19,
Kraków, Poland: CRC Press/Taylor & Francis
• "Utility-based Decision Making in Collective Adaptive Systems.“,
Proceedings of the 4th International Conference on Cloud Computing and
Services Science (CLOSER’14), Andrikopoulos Vasilios, Marina Bitsaki,
Santiago Gómez Sáez, Dimka Karastoyanova, Christos Nikolaou, and Alina
Psycharaki. (2014).
• “Towards Modelling and Execution of Collective Adaptive Systems”. A. V.
Andrikopoulos, A. Bucchiarone, S. Gomez Saez, D. Karastoyanova, and C.
Antares Mezzina. 9th International Workshop on Engineering Service-
Oriented Applications (WESOA 2013), In conjunction with ICSOC 2013,
December 2nd 2013, Berlin, Germany.

A Game Theoretic Approach for Managing Multi-Modal Urban Mobility Systems

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