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

A Game Theore+c Approach for Managing Mul+-‐Modal Urban
Mobility Systems Christos Nikolaou Marina Bitsaki Alina Psycharaki George Koutras Transforma+on Services Lab Computer Science Department University of Crete 13/01/2015 nikolau @ tsl.gr 1

Table of Contents •  Collec&ve Adap&ve Systems • 
The ALLOW ENSEMBLES project •  The Strategic Ensemble Concept •  The FlexiBus Scenario •  Game Theory: Non-‐coopera+ve and coopera+ve games •  Future Work -‐ Publica+ons 13/01/2015 nikolau @ tsl.gr 2

Collec+ve Adap+ve Systems (CAS) •  “Collec+ve adap+ve systems consist
of many autonomous units that interact in a variety of ways over mul+ple scales”, h[ps://www.elec.york.ac.uk/research/intSys/cas.html •  Concept similar to: complex adap+ve 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 prolifera+on. •  Collec&ons of autonomous units (networks, hierarchies) are formed, o]en with compe&ng interests (for example for use of resources, of services, etc.). •  Various concerns (for example smarter energy use, empowering the pa&ent 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, nego&ate, develop strategies to achieve goals. 13/01/2015 nikolau @ tsl.gr 3

Examples of Collec+ve Adap+ve Systems 13/01/2015
nikolau @ tsl.gr 4 Smart Grid Smart Urban Mobility Smart Health Services

The Urban Mobility Scenario (Buses, FlexiBuses, Carpools, Taxis,
Passengers) 13/01/2015 nikolau @ tsl.gr 5

Table of Contents •  Collec+ve Adap+ve Systems • 

The ALLOW ENSEMBLES project (Funded by FET Proac+ve, 7FP,
EC) •  h[p://www.allow-‐ensembles.eu/ 13/01/2015 nikolau @ tsl.gr 7 Allow Ensembles develops new models, theories and algorithms that can: •  Autonomously form large-‐scale collec+ve adap+ve units (ensembles) that can ﬂexibly sa+sfy arbitrary goals in the real world environments. •  Improve the u&lity of ensembles by adap+ng the individual cells within an ensemble such that the overall system learns to get be[er at accomplishing goals. •  Make ensembles robust •  Evolve ensembles in order to promote beneﬁcial emergent proper+es and suppress detrimental emergent proper+es. •  Make ensembles secure and protect sensi&ve data by evolving security policies in unison with ensemble evolu+on.

Basic Concepts -‐ Cells •  Cell: a unique iden+fiable
building block represen+ng a concrete func+onality in a larger, mul+cellular system. •  Implemen+ng the func+onality may involve interac+ng 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 instan+a+ng cell archetypes 1 , or by other cells through the process of differentiation. (from “Terminology”, Internal Document, ALLOW ENSEMBLES consor+um). 13/01/2015 nikolau @ tsl.gr 8

Basic Concepts – Passenger Trip Booking Cell Archetype Example
13/01/2015 nikolau @ tsl.gr 9 (from “Terminology”, Internal Document, ALLOW ENSEMBLES consor+um).

Basic Concepts -‐ En++es •  En&ty: a physical or
virtual organiza+onal unit aggrega+ng a set of cells. •  Cells can either be unique in an en+ty, or they can be replicated by the en+ty by instan+a+ng the cell archetype as many +mes as necessary. However, each cell belongs to exactly one en+ty. •  Each en+ty has a context in which it operates, which is accessible by its cells. •  Furthermore, an en+ty has a set of goals that it a[empts to fulﬁll by ini+a+ng or par+cipa+ng in one or more ensembles. •  En+ty Examples: Bus Driver, Passenger, Route Manager and FlexiBus Manager. •  (from “Terminology”, Internal Document, ALLOW ENSEMBLES consor+um). 13/01/2015 nikolau @ tsl.gr 10

Basic Concepts -‐ Ensembles •  Ensemble: a set of
cells from diﬀerent en++es collabora+ng with each other to fulﬁll some of the goals of the en++es. •  Each ensemble is ini+ated and terminated by an en+ty, but more than one en++es are expected and allowed to join and leave through the ensemble’s life+me. •  Ensemble Example: The Bus Driver, Route Manager and the various Passenger en++es are par+cipa+ng in one Route ensemble •  (from “Terminology”, Internal Document, ALLOW ENSEMBLES consor+um). 13/01/2015 nikolau @ tsl.gr 11

12 Conceptual Integration of the Project

En++es Interac+ons •  En++es interact in order
to achieve –  Individual objec+ves –  Group objec+ves •  Interac+ons may: –  Help en++es make decisions to achieve goals (gather info, learn, nego+ate, op+mize, par+cipate in games, form coal+ons, etc.) –  Implement decisions made by en++es (make payments, step in a bus, schedule a bus, etc.) •  Interac+ons result in the crea+on of –  (execu+on) ensembles in order to fulﬁll speciﬁc goals ini+ated by the en++es –  Strategic ensembles in order to handle decision making and increase en++es’ sa+sfac+on expressed in u+lity terms 13/01/2015 nikolau @ tsl.gr 13

The Strategic Ensembles Model •  A strategic ensemble
model uses the en++es’ u+lity-‐cells –  It is created before the execu+on ensemble –  It runs in parallel to the execu+on ensemble –  It aﬀects the opera+ons of the execu+on ensemble •  The objec+ves of a strategic ensemble include the following –  Impose constraints according to en+ty goals and preferences in order to reduce the various choices of en++es –  Assign u+lity to each en+ty when par+cipa+ng in an ensemble in order to make the op+mal choice –  Manage the nego+a+on among en++es 13/01/2015 nikolau @ tsl.gr 15

U+lity-‐cells •  Represent u+lity and game theore+c characteris+cs of
en++es •  The u+lity-‐cell of an en+ty has the following func+onali+es –  calculates the u+lity of an en+ty when par+cipa+ng in a given ensemble –  communicates with other cells and makes decisions/computes strategies of the en+ty –  collects data from measurements (resource consump+on, sa+sfac+on, costs, delays, prices, …) and passes them to the Evo(lu+onary) Knowledge Data Base –  Consults EvoKnowledge (learns) about u+lity func+on parameters, external condi+ons (for example changes in traﬃc pa[erns, special events in city, etc.). –  runs op+miza+on algorithms to maximize en++es’ u+lity or improve the performance of ensembles 13/01/2015 nikolau @ tsl.gr 16

Strategic Ensemble Exec-‐ cell U+lity-‐ cell U+lity-‐ cell
Exec-‐ cell Exec-‐ cell Exec-‐ cell U+lity-‐ cell Exec-‐ cell Exec cell U+lity-‐ cell Exec-‐cell U+lity-‐ cell En&ty 2 En&ty 1 En&ty 3 En&ty 4 En&ty 5 En&ty 6 13/01/2015 nikolau @ tsl.gr 17

Passenger Passengers U+lity-‐ Cell U+lity-‐Cell Cell Flexibus
Manager U+lity-‐ Cell Example Strategic Ensemble Route Planner Cell Cell tripRequest rankedRoutes tripRequest listOfRoutes U+lity-‐ Cell Cell Cell nego+a+ons Route Manager U+lity-‐ Cell Cell FlexiBus Driver routeInfo oﬀer

Interac+ons Exec cell U+lity-‐cell U+lity-‐cell Exec-‐ cell Evo-‐cell
Route Planner Strategic Ensemble Passenger Evo-‐cell

Prior Art •  An eﬃcient transporta+on system u+lizes mass
transit alterna+ves to the automobile in order to reduce conges+on and support ecological solu+ons. •  Travelers make decisions based on +ming, cost, comfort, safety and mode of trips, while planners face policy ques+ons such as frequency of routes, i+neraries, size, cost, environmental impact, etc. •  (Lam, Small, 2001): a method to value travel +me and its reliability. People had to choose between two parallel routes, one free but congested and the other with +me-‐varying tolls by maximizing a u+lity func+on (a func+on of travel +me, variability in travel +me, cost, characteris+cs such as +me-‐of-‐day and car occupancy, and a random component). •  (Johansson et al., 2003): the labor market commuter behavior is analyzed taking into account the observa+on that the willingness of an individual to commute is diﬀerent for short, medium and long +me distances. 13/01/2015 nikolau @ tsl.gr 20

Prior Art (cont.) •  (Li, Huang, 2005): reliability
of morning commu+ng in congested and uncertain transport networks •  Other studies analyze the interac+ons between commuters and planners or transport managers and examine how commuters choose their op+mal routes and trip modes using non-‐coopera+ve games. •  (Sun, Gao, 2007): a non-‐coopera+ve, perfect informa+on, sta+c game to describe how travelers adjust their route choices and trip modes. •  (Anas, Berliant, 2010): the authors consider a commu+ng network consis+ng 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 transporta+on). A non-‐coopera+ve game is formulated consis+ng of a set of commuters who compete for routes. •  In our work, we inves&gate a dual problem facing both the commuters and the transporta&on authority; the commuters choose their trip mode, while at the same +me the transporta+on company that provides a bus for example, makes decisions on accep+ng or not travel requests dynamically. 13/01/2015 nikolau @ tsl.gr 21

The FlexiBus Scenario: Assump+ons •  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 un+l a certain deadline –  The execu+on 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 execu+on phase –  Add a pick-‐up point due to a new request –  Remove a pick-‐up point a]er a cancella+on

Time-‐line End of Route Pre-‐booking
phase Prepara+on phase Ini+aliza+on Running phase Execu+on Ensemble Strategy Ensemble Booking phase

En+ty’s U+lity •  En+ty’s u+lity – U+lity accrued when
par+cipa+ng in a speciﬁc ensemble – Calculated by the en+ty according to •  Her preferences (that are publicly known) •  Private informa+on •  According to the en+ty’s u+lity the winning route may be diﬀerent from the one resulted by the evalua+on of the other members of the ensemble (e.g. the route manager).

En+ty U+lity (Example) •  Consider Peter sending the request
(Des+na+on: Piazza Duomo, arrival +me: 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)

The ALLOW ENSEMBLES project •  The Strategic Ensemble Concept •  The FlexiBus Scenario •  Game Theory: Non-‐coopera&ve and coopera&ve games •  Future Work -‐ Publica+ons 13/01/2015 nikolau @ tsl.gr 27

Game theore+c models •  Analyze models that: – show
the strategic interac+ons among various components •  my decisions aﬀect others’ decisions – derive equilibria so that u+lity/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 op+mal for A given g and g is op+mal for B given s

Nash Equilibrium (Example) •  Consider two players A and
B •  Strategies for player A → {Top, Le]} •  Strategies for player B → {Le], Right} •  Nash equilibria: (Top, Le]), (Bo[om, Right) B A Le] Right Top 2,1 0,0 Bo[om 0,0 1,2

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

A Non-‐coopera+ve Game of Complete Informa+on •  Objec+ve:
model the interac+ons of en++es when a new request arrives in a route that is being executed and compute their op+mal choices (strategies) based on u+li+es •  Problem descrip+on –  We consider a route to be a set of ﬁxed pick-‐up points and the respec+ve es+mated travel +mes between pick-‐up points –  When a new request arrives, the various en++es make decisions: •  route planner: accept or reject the request (in case of accept send condi+ons (travel +me, cost) •  new passenger: accept or reject oﬀer –  We formulate these interac+ons as a game •  Are there equilibrium strategies?

Assump+ons •  All passengers have the same des+na+on
•  Current passengers do not nego+ate for the new condi+ons (resulted by the new passenger) of the route •  The route planner has to take into account that any viola+on of his past commitments will aﬀect nega+vely his u+lity •  We consider a game of complete informa+on •  The route planner provides private informa+on of current passengers to the new passenger •  The u+lity func+ons of all actors are common knowledge

Assump+ons •  We consider a dynamic game • 
Decision points: request arrivals •  new strategies have to de derived each +me a new request arrives (thus a new game is formulated) •  All these games across the route have to be synchronized in order to derive op+mal proﬁts for the FlexiBus company and the passengers •  Each game is sequen+al •  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 Formula+on •  Set of players: – 
current passengers (1,…,n) –  new passenger (np) –  route planner (rp) •  Strategy proﬁle: (ti : travel +me) ti , i=1,…n are ﬁxed and known = (1 ,2 ,…, , , )

Game Formula+on Proﬁts: –  Current passengers:
–  New passenger: G: the proﬁt gained by alterna+ve solu+on f: func+on that incorporates the risk of adding future passengers –  Route Planner: g: func+on that incorporates the risk of losing future passengers = (1 , 2 , … , , , ) = $ 0, < + ,, ≥ = $ , < + , − ( ), ≥ = % ' + ) ≠ − ( )

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 Processes Set of Services Design Time Run Time

En+ty Hierarchies •  En++es can form hierarchies (of en++es):
–  For example: people and systems par+cipate in a department en+ty, which in turn may par+cipate in a division en+ty, which in turn may par+cipate in a corpora+on en+ty. •  U+lity of higher-‐level en+ty could be deﬁned as the sum of the u+li+es of the en++es one level below (and so on recursively), •  But, op+mal u+lity of a higher-‐level en+ty is NOT necessarily the sum of the op+mal values of the u+li+es of the immediate lower-‐level en++es. •  … a number of interes+ng research ques+ons… 13/01/2015 nikolau @ tsl.gr 38

Role of u+lity in Evolu+on •  U+lity func+on
with incorrect (or par+ally correct) parameters –  may result in wrong selec+on of ensembles –  e.g., use of incorrect travel dura+on etc. Execu+on Context EvoKnowledge Monitor U+lity Evolve U+lity func+on selects the proposed solu+on with highest u+lity taking into account goal, context and user preferences (measured u&lity) 1 Ensemble with high u+lity is executed 2 Parameters of u+lity func+on are adjusted according to past execu+ons and the calculated u+lity and monitored u+lity in a given context 3 U+lity Func+ons

Specializa+on tree Goal ……... specializa+on ……… ……...
specializa+on ……… Ensemble N U+lity Func+ons ……... specializa+on ………

Example Goal: Reach a des+na+on Car sharing
Non-‐Public Transporta+on Public Transporta+on Rent car U1 (t,c) U2 (t,c,r,d) t: travel +me c: cost r: reliability d: walking distance

Example (in Collabora+on with IPVS) t: travel
+me c: cost r: reliability d: walking distance Goal: Reach a des+na+on Non-‐Public Transporta+on Public Transporta+on Train Flexibus U1 (t,c) U2 (t,c, r,d)

Coopera+ve Games •  In coopera&ve game theory, interest is
on outcomes of coali+ons of players rather than ac+ons of individual players –  focus in coopera+on games is on coali+ons that will be formed and on the sharing of value or cost incurred among members of the coali+on. •  Cost alloca&on problem in which players perform a joint task and allocate its cost among them •  Why use coopera+ve games –  Helpful tool if performance of an intelligent system and its en++es can be improved when several players cooperate •  Dynamic coopera+ve game (??) •  Implementa+on issues: –  get informa+on on game parameters and data from EvoKnowledge (?), –  test game and obtain results in ALLOW Ensembles plauorm, …. 13/01/2015 nikolau @ tsl.gr 43

The General Idea of an Algorithm for Coopera+ve
Games •  Game (, ) •  Specify set ={1,…,} of poten+al users involved (=||). •  Specify cost func+on : 2↑ →ℝ of a route, where () is the joint cost of the route used by the set ⊆ of users ((∅)=0). •  A required property for : •  Subaddi+ve 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 ((↓1 ∪↓2 )≤(↓1 )+(↓2 ), ↓1 ,↓2  ⊂). •  In a subaddi+ve game: ()≤∑↑▒({}) . If this condi+on holds with strict inequality then the game is called essen&al (each player gains from coopera+on). •  If subaddi+vity property does not hold, coali+ons other than the grand coali+on might be possible. •  Cost should reﬂect: –  Services required by the operator, Infrastructure costs, Payments, … 13/01/2015 nikolau @ tsl.gr 44

Algorithm (cont.) •  Allocate () among the users
in . •  Specify an alloca+on rule :()=(↓1 ,…,↓ ) .. ∑↑▒↓  =() (such as Shapley value for fairness or core for stability). •  is an imputa&on of game (,) if the following hold: –  ∑↑▒↓  =() (1) feasibility of the grand coali+on (costs are reimbursed) and –  Pareto eﬃciency: ↓ ≤({}) ∀ (2) no player pays a higher price in the grand coali+on than he would do independently 13/01/2015 nikolau @ tsl.gr 45

The ALLOW ENSEMBLES project •  The Strategic Ensemble Concept •  The FlexiBus Scenario •  Game Theory: Non-‐coopera+ve and coopera+ve games •  Future Work -‐ Publica&ons 13/01/2015 nikolau @ tsl.gr 46

Future Work •  In the case of one route
–  Permit ac+ons such as adding pick-‐up points in order to serve new passenger requests or removing pick-‐up points in case of cancela+ons –  Perform nego+a+ons with current passengers when a new request arrives •  Consider mul+ple 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 publica+ons •  “A Game Theore+c Approach
for Managing Mul+-‐Modal Urban Mobility Systems”, Vasilios Andrikopoulos, Marina Bitsaki, Antonio Bucchiarone, San+ago Gómez Sáez, Dimka Karastoyanova, Frank Leymann, Christos Nikolaou, Marco Pistore, 2th Interna+onal Conference on the Human Side of Service Engineering Human Factors and Ergonomics, 2014/7/19, Kraków, Poland: CRC Press/Taylor & Francis •  "U+lity-‐based Decision Making in Collec+ve Adap+ve Systems.“, Proceedings of the 4th Interna+onal Conference on Cloud Compu+ng and Services Science (CLOSER’14), Andrikopoulos Vasilios, Marina Bitsaki, San+ago Gómez Sáez, Dimka Karastoyanova, Christos Nikolaou, and Alina Psycharaki. (2014). •  “Towards Modelling and Execu+on of Collec+ve Adap+ve Systems”. A. V. Andrikopoulos, A. Bucchiarone, S. Gomez Saez, D. Karastoyanova, and C. Antares Mezzina. 9th Interna+onal Workshop on Engineering Service-‐ Oriented Applica+ons (WESOA 2013), In conjunc+on with ICSOC 2013, December 2nd 2013, Berlin, Germany. 13/01/2015 nikolau @ tsl.gr 48

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

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

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