Managing competiiition for (public) resources: Decision‐making & some congestion‐cost‐cutting approaches
Papers co-authored by I. Stavrakakis may be downloaded from htt p:// cgi .di .uoa.gr/ ~i st avrak/ publi ca tions. htm l
Τμήμα Πληρ. & Τηλεπ. – ΕΚΠΑ : ΠΜΣ523 Προηγμένες Δικτυακές Τεχνολογίες – 2015
Wireless Medium Access Competition “equivalent”
Basics of wireless communication networking
ALOHA (ethernet, etc)
o A (common) resource (channel) o Distributed non‐communicating users (competitors) o Aware of resource / random need for it o Collisions / competition costs
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 2 Rich information about inexpensive city‐wide resources
Resource availability becomes known to potential users Can go for them, instead of trying more SNOWexpensive workshop, alternatives March
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 3
Access point association:
Cheap but best‐effort (public) WLAN vs. More reliable fee‐based wireless access point
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 4 Route selection:
Slower (public) toll‐free road Vs Faster toll road
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 5
Parking spot selection:
Cheap but scarce (public) on‐street parking vs. Expensive but abundant parking lots
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 6 Richer information easier/better decisions?
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 7
Richer information easier decisions?
A free spot over there !!!
. Go for it!
. Opps! Go for another one
. Opps! Try another one
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 8 Better if I was not told anything!!!
E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Opportunistically‐assisted parking service discovery: now it helps, now it does not”, Pervasive and Mobile Computing (PMC), Vol. 8, Iss. 2, April 2012. ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Opportunistically‐assisted parking service discovery: now it helps, now it does not”, Pervasive and Mobile Computing (PMC), Vol. 8, Iss. 2, April 2012.
2 different strategies for localizing and occupying parking spots.
A) Non-assisted parking search (NAPS) • Random sequential search • End of search: the first vacant parking spot • parking search time parking search area
B) Opportunistically-assisted parking search (OAPS) • Inter-vehicle & vehicle-parking spot communication • Parking spots equipped with sensors • Vehicles equipped with wireless interfaces (e.g. 802.11x) adequate storage, processing capability • No global common knowledge
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Opportunistically‐assisted parking service discovery: now it helps, now it does not”, Pervasive and Mobile Computing (PMC), Vol. 8, Iss. 2, April 2012. Simulation Environment
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Opportunistically‐assisted parking service discovery: now it helps, now it does not”, Pervasive and Mobile Computing (PMC), Vol. 8, Iss. 2, April 2012. Methodology
NAPS: random search OAPS: temporal & spatial filtering of storage
NAPS, OAPS: The radius of the search area grows progressively as parking search time increases.
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Opportunistically‐assisted parking service discovery: now it helps, now it does not”, Pervasive and Mobile Computing (PMC), Vol. 8, Iss. 2, April 2012. Performance Metrics Once the driver enters the initial parking search area…
1) Parking search time, Tps
2) Parking search route length, Rps
3) Destination-parking spot distance, Dp
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Opportunistically‐assisted parking service discovery: now it helps, now it does not”, Pervasive and Mobile Computing (PMC), Vol. 8, Iss. 2, April 2012. Simu la tion resu lts
-- Does the opportunistic sy stem assisted p arking discovery alway s help ?? --
We compare the parking search approaches under two scenarios:
a) uniformly distributed destinations
b) concentrated destinations within a particular (hotspot) road.
information dissemination → synchronizes movement patterns → intensifies competition OAPS worse than NAPS
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Richer information easier decisions?
A free spot over there !!!
???
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 15
Richer information easier decisions?
A free spot over there !!!
Think wiser !
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 16 Overview of this talk PART I : Decision‐making in Distributed, Uncoordinated, Resource‐limited ,Competitive Environments
With some cost if trying but failing to find a resource (spot)
17 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Major Question posed:
to compete or not to compete? that is the question
18 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 1. Uncoordinated resource selection
19 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Decision making: Parking spot selection
(to compete for the cheap on‐street parking resource or not?)
– N drivers : autonomous selfish decision‐makers – 2 types of parking resources (non‐divisible goods) • First type : R “cheap” on‐street parking spots – cost : non‐decreasing function of demand o (congestion impact – competition dynamics) – demand exceeds supply, competition emerges • Second type : “infinite” expensive spots in parking lots – cost : fixed, insensitive to demand (non‐rivalrous)
20 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες The full rationality vs. bounded rationality question
• Efficiency of resource sharing under different assumptions about the way the agents make their decisions?
‒ Perfect vs. imperfect information/knowledge ‒ Full or limited computational capacity to assess the impact of choices ‒ Cognitive biases
• Furthermore: ‒ How to model bounded rationality and assess its impact?
21 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Formulation: The parking spot selection game unbounded / bounded rationality wrt amount of information/g/knowledge
Drivers = strategic players
Perfect information about pricing and amount of resources available
Regarding the parking demand:
Complete knowledge of the Stra teg ic game (A) parking demand Methodology Equilib ri um stttates Probabilistic knowledge Bayesian game (B) Optimal outcomes Comparison via Price of Anarchy
Strictly incomplete knowledge Pre Bayesian game (pB) E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Leveraging information in parking assistance systems”, IEEE Transactions on Vehicular Technology, 62, 4309–4317, 2013.
22 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες The (strategic) parking spot selection game
•N drivers / players N {1, ... , N}, N > 1
• R pppublic spots + Infinite ppprivate spots RR osp R pl,,||,|| R = || R osp1, || R pl N
• Action set: {on-street-parking – osp (public), parking lot – pl (private) }
• Action of player i : αi
• Actions of all players except player i: α-i
• Action profile α=(αi , α-i) 2**N of them
• Action meta-profile α(m): any profile with m players competing N+1 meta-profiles
23 Cost of private spot whenΠΜΣ k>S523 : Προηγμένεςcompete: ∆ικτυακές Τεχνολογίες
The (strategic) parking spot selection game
Cost functions:
• cosp,s : cost of osp (on-street parking - public spot)
• cpl: cost of pp(pl (parking lot - pp)rivate) is fixed = β cosp, s
• cost of competing for public, failing and then using private:
cosp,f = γ cosp,s > β cosp,s
• δ = γ - β , overhead cost / congestion penalty
24 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες The (strategic) parking spot selection game Actio n meta -pporofil e α(m): m p laye rs co mpete, N +1 meta -pporofil es
(Action profile α=(αi , α-i) 2**N)
Cost of player choosing a public ( osp) / private ( pl) spot when k>R compete:
wkosp() min(1,/) Rkc osp,, s 1 min(1,/) Rkc osp s
wpl()k c pl
Cost functions for R=50 and cosp,s =1vate spot 25 whenΠΜΣ 523 k>S : Προηγμένες compete: ∆ικτυακές Τεχνολογίες
The (strategic) parking spot selection game
Expected cost for player i under action profile α=(αi , α-i) Cost of private spot when k>S compete:
. Nash Equilibrium state: a situation in which no player can decrease its cost (increase its utility) b y ch angi ng hi s strategy unil aterall y
Every symmetric game with two strategies has an equilibrium in pure strategies . Cheng, S.G. et al.: Notes on the equilibria in symmetric games, Proc. 6hWkhOGThiAdDiiThiA6th Workshop On Game Theoretic And Decision Theoretic Agents (collocated with IEEE AAMAS). New York, USA (2004) 26 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Derivation of pure equilibrium states/strategies
. The action profile α=(αi , α-i) is a pure Nash equilibrium if for all iϵN
. How to find EQ: Identify the conditions on the number of competing agents that break the equilibrium definition and reverse them. A driver is motivated to change his action in the following circumstances
(*)
(()**)
27 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Derivation of pure equilibrium states/strategies
Lemma: a player is motivated to change his action αi in following cases
Hint: for (b), require that (*) holds and for the second bullet require that (**) holds
and get the condition on Nosp(α)
28 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Pure equilibrium strategies
• The strategic parking spot selection game has the following
29 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Efficiency of pure equilibrium states/strategies Metric*: The Price of Anarchy ( PoA ≥ 1) = [ social cost under EQ state ] / [ optimal social cost ] Social cost under action profile α:
Use under a* : if N ≤ N0 use Nosp(α*) = N ; if N ≥ N0 use Nosp(α*)=
Optimal social cost: (exactly R players compete –no fail and all osp used)
Price of Anarchy
, PoA ≤ 1 / [1-R/N]
*E. Koutsoupias, C. H. Papadimitriou, “Worst-case equilibria”, Computer Science Review, vol. 3, no. 2, 2009 30 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Efficiency of pure equilibrium states/strategies
PiPrice of AAhnarchy
31 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Efficiency of pure equilibrium states/strategies
# drivers, N Social cost in EQ, Ceq Optimal social cost, Copt R(1) N compete cNRNR[min( , ) max(0, )] cNosp, s[min(,)(1)] NR osp, s R(1) R(γ-1)/δ cNosp, s R competing drivers compete
PoA>1 : due to competition and paying the (lack-of-coordination) cruising cost
Pricing (β) and failure cost/ overhead (δ) shaping guidelines
βδPoA 1 Ceq When PoA 1? ()NR R ↑β 0 Copt R ()NR R ↓β 0 R
R(1) ↓δ 1 R 32 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες The (strategic) mixed‐action selection game
PilPractical strategi ifes for real systems / a mi idixed action p = (posp , ppl)
Expected cost for player choosing osp or pl, respectively, when all N -1play1 play according to the mixed-action p ost of private spot when k>S compete:
Expected cost for symmetric profile (all play according to the mixed-action p) CtfitCost of private spot th when k>S compet e:
33 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
The (strategic) mixed‐action selection game
. EiExistence of fMid Mixed-action N as h Equ ilibri um: Every symmetric game with more than two players and increasing cost functions (of the number of players) has a unique mixed-action equilibrium . Ashlagi, I., Monderer, D., Tennenholtz, M.: Resource selection games with unknown number of players. In: Proc. AAMAS ’06. Hakodate, Japan (2006)
. The Mixed-action Nash Equilibrium state: The strategic parking spot selection game has a unique mixed-action NE
Sketch of proof: Set the requirement to be fulfilled by the profiles at EQ:
34 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Equilibrium states/strategies (pure / mixed‐action strategies)
# drivers, N#competing drivers . Pure NE for public parking space R(1) N R(1) R(1)
# drivers, N Probability of competing for public parking space R(1) 1 . SiidSymmetric mixed-actiNEion NE R(1) R(1) N
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
Decision‐making under knowledge constraints (a type of bounded rationality)
. The Bayesian model: probabilistic information – Drivers know a) probability for a driver to be active (interested in parking) b) t ot al numb er of d ri vers
. The pre Bayesian model: strictly incomplete information – Drivers know their total number (upper bound on competitors)
36 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες A Bayesian parking spot selection game
37 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες
A Bayesian parking spot selection game
Equilib ri a:
Derivation approach
Equilibria:
38 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Equilibrium states under Bayesian Game
. Symmetric mixed‐action Bayesian Nash equilibria
AtiActivati on (ti)(symmetric) probability, pact Probability of competing R(1) < 1 N R(1) R(1) min ,1 N Npact
ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 39
Equilibrium states under strict uncertainty
Knowledge of an upper bound on demand, N
For the pre-Bayesian parking spot selection game it holds that Symmetric mixed-action safety-level equilibrium (playing to min worst cost) ↕ Symmetric mixed-action equilibrium of the strategic game with N players
40 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Less‐is‐more phenomena under strictly incomplete knowledge of parking demand
. Social cost increases with the probability of competing . Probability of competing (in EQ states), decreases with N
. If N is maximum number of drivers and K( (provided the average number of drivers that compete for public space is still over R) 41 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες EQ strategies for Strategic, Bayesian and pre‐Bayesian Resource Selection Game 42 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Decisions under limited computational capacity (a type of bounded rationality) . Departure from classical expected utility theory framework . Inputs from: —Behavioral Economics —Cognitive Psychology E. Kokolaki, M. Karaliopoulos, I Stavrakakis, "On the human‐driven decision‐making process in competitive environments", Internet Science Conference, April 10‐11, 2013, Brussels 43 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Decisions under Expected Utility Theory framework . Strategic agents acting with perfect information, without behavioral biases, aiming at maximizing own welfare – quantified by the expected gain/cost of their actions . Expected Utility Theory (EUT) framework – Expected utility of a lottery equals the sum of the utilities of the lottery outcomes, U(xi) times their probabilities of the outcomes, p(xi) EU p( xi )U xi , xi : choice / alternativ e. xi . Nash equilibrium – captures best response in terms of expected utility maximization 44 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Deviations from full rationality . (Cumul ati ve) P rospect Th eory maintains most of the concepts/assumptions of EUT manipulating both utility measures and probabilities to account for biases against risk . Alternative equilibrium concepts (Quantal Response Equilib ri um, R osenth al equilib ri um) – Use probabilistic choice models to capture any unobserved and omitted elements, estimation/computational errors, individual’s mood, perceptual variiiations or cogni iibitive biases – In line with the fact that individuals are more likely to make better choices than worse choices, but do not necessarily make the very best choice . Heuristics – ftfast and df frugal reasoni ng sol lti/diiutions / decisions – emphasis on cognitive processes underlying decisions 45 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Prospect theory motivation (1) In several choice problems, individuals’ preferences systematically violate EUT Allais’ paradox (indication that people assess utilities and probabilities of outcomes differently from what full rationality/ EUT predicts => contradictions under EUT formulation) PfPercentage of responses EUTprospectB > EUTprospectA u(2400)>.33u(2500)+.66u(2400) .34u(2400) > .33u(2500) EUTprospectC > EUTprospectD .34u(2400) < .33u(2500) ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 46 Prospect theory motivation (2) Four-fold pattern of risk attitude: (aga in, vi ol ati on of ETU f ramework) – High probabilities: risk aversion for gains & risk seeking for losses – Low probabilities: risk seeking for gains & risk aversion for losses ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 47 Prospect theory formulation • Defines prospects (Kahneman & Tversky, 1979): Prospect : (xpxp1122 , ; , ;...; xpnn , ) • Desirability of a prospect is quantified through generalization of the utilityyggg functions and their weighting through weiggghting functions p i • Decision maker is still a utility maximizer ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 48 The Prospect Theory (PT) model (Kahneman & Tversky, 1979) Diminishing sensitivity : . impact of a chance diminishes with distance from Reference Point (a gain from reference 50 to 100 is less valuable than from 0 to 50) (people are more sensitive to extreme outcomes and less in intermediate ones) Loss aversion: . the curve is steeper for losses than for gains (a high loss hurts more than a high pleasure) ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 49 The Cumulative PT (CPT) model (Tversky & Kahneman, 1992) Pt(Prospect : (x1122,px ; , p ;...; xnn , p ) CPT fixes some (experimentally observed) inconsistencies of PT Mo difies the pro ba bility wei ghti ng f uncti ons . PT : transforms probabilities of separate outcomes . CPT: transforms probabilities of {an outcome or anyygthing better (or worse ) than that} Desirability of a prospect is qqggguantified through generalizing: A. Outcome probabilities {pi} via decision weights {w(pi)} (diminishing sensitivity: more sensitive around 0 and 1, and less in the middle) A. Outcome values {xi} via utility functions {U(xi )} ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 50 The Cumulative PT (CPT) model (Tversky & Kahneman, 1992) Desirability of a prospect is quantified through generalizing: A. Outcome probabilities {pi} via decision weights {w(pi)} B. Outcome values {xi} via utility functions {U(xi )} The values that best fit the experimental results of Kahneman & Tversky are:{ ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 51 Applying CPT to Resource Selection Problem tltti/two alternatives/prospect s: l (limit ed resource, osp) and u (liitd(unlimited resource, pl) CPT value for prospects l and, u respectively: With the cost of selecting prospect l when k others do the same given by The values that best fit the experimental results and the probabilities pk for this are Binomial (N, pl^CPT). are ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 52 Equilibrium concepts over Cumulative Prospect Thy . Nash Equilibrium state: no player can increase his/her utility (expected utility value) by changing his/her strategy unilaterally – Mixed-action profiles: • EU value of strategy 1 = EU value of strategy 2 . CPT Equilibrium state: no player can increase his/her utility (cumulative prospect value) by changing his/her strategy unilaterally – Mixed-action profiles: • CPT value of prospect 1 = CPT value of prospect 2 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 53 Applying CPT to Resource Selection Problem • N= 150 players -2 prospect 1 - public parking • R=50 resources prospect 2 - private parking -4 alue NE OPT(min social cost) • Cost of limited, low‐cost -6 resource : 1€ • Cost of unlimited, high‐cost e weightedv -8 resource : 5€ -10 • Cost of failing the competition Cumulativ for limited resource): 3€ -12 0 0.2 0.4 0.6 0.8 1 Probability of competing CPT eq: 0.79 NE: 0.78 OPT: 0.33 . CPT equilibrium condition : – CPT value of prospect 1 = CPT value of prospect 2 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 54 Alternative decision‐making models: motivation . OnOwn‐pay off effects in generalized matching pennies game . ()(NE) theory prescriptions : no NE in pure strategies, one in mixed strategies X = 1 : EQ strategy for both players : Pcol(H)=Pcol(T)=Prow(H)=Prow(T)=0. 5 X > 1 : EQ strategy for row player remains same (Prow(H)=Prow(T)=0.5) EQ strategy for column player changes (Pcol(H) 55 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Alternative decision‐making models: motivation Own-payoff e ffec ts i n generalized mat chi ng penni es game . (NE) theory prescriptions : no NE in pure strategies, one in mixed strategies (see nex t slid e) X = 1 : EQ strategy for both players : Pcol(H)=Pcol(T)=Prow(H)=Prow(T)=0.5 X > 1 : EQQgypy strategy for row player remains same (Prow(()H)=Prow(()T)=0.5 ) EQ strategy for column player changes (Pcol(T) < Pcol(H ) But, experiment suggests that Prow(H) increases with payoff X! This questions the usage of NASH EQ to predict people’s behavior/decisions Consider alternative EQ definitions 56 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Mixed‐action Nash EQ for the generalized matching pennies game …in the mixed‐strategy equilibrium the expected utilities of the two strategies are equal… Column player (under EQ, set them equal to get: Prow(H)=Prow(T)=0.5) Exp_column(action=H)=prob_row(H)*0+prob_row(T)*1 Exp_column (action=T)=prob_row(H)*1+prob_row(T)*0 Row player(under EQ, set them equal to get: X*Pcol(T)=Pcol(H)) Exp_row(action=H)=prob_column(H)*X+prob_column(T)*0 Exp_row(action=T)=prob_column(H)*0+prob_column(T)*1 57 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Some results . N agents compete for R=50 resources that cost 1 unit . They have as second option an unlimited resource set that costs 4 units . Penalty cost of 16 units for those who fail the competition – Small deviation from the full rationality framework –Risk‐prone behavior under high penalty cost 58 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Deviations from full rationality Alternative decision-making models . Use probabilistic choice models to capture any unobserved and omitted elements, estimation/computational errors , individual ’s mood, perceptual variations or cognitive biases Quantal Response equilibrium, Rosenthal equilibrium 59 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Quantal response equilibrium (McKelvey & Palfrey, 1995) . “Individuals are more likely to select better choices than worse choices, but do not necessarily succeed in selecting the very best choice.” . Due to noise/disturbances in their anticipation of exact choices ’ payoffs . Introduce some randomness in the decision-making process to capture people’s inabilit y t o pl ay al ways th e st rat egy th at maxi mi zes th e expect ed utilit y . “Choices are made with probabilities that are monotone in their expected payoffs” . Logit QRE => disturbances follow the extreme value distribution eEU (r1 ) p(r`1 ) eEU (r1 ) eEU (r2 ) [0, ∞ ] : rationality control parameter : full rationality (Nash EQ) p(r1 ) 1 pr2 60 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Quantal response equilibrium for Resource Selection Problem , t : full rationality (Nash , t 0 : irrationality (random choice) EQ)1 1 0.8 0.8 r player i r player player i o r 0.6 0.6 0.4 0.4 of competing fo ty of competing f Player i y 0.2 Player i NE 0.2 NE Probabili OPT(min social cost) Probabilit OPT(min social cost) 0 0 0.2 0.4 0.6 0.8 1 0 0 0.2 0.4 0.6 0.8 1 Probability of competing for players -i Probability of competing for players -i QRE: 0.77 NE: 0.78 OPT: 0.33 QRE: 0.55 NE: 0.78 OPT: 0.33 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 61 Rosenthal equilibrium (Rosenthal, 1989) “The difference in probabilities with which two actions are played equals a parameter t multiplied by the difference of the corresponding expected costs” p(r`1 ) pr2 tEU r`1 EU r2 p(r1 ) 1 pr2 t [0,∞] : rationality control parameter t ∞ : full rationality 62 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Rosenthal equilibrium for Resource Selection Problem t ∞ : full rationality (NE) t 0 : no rationality (random choice) RE: 0.77 NE: 0.78 OPT: 0.33 RE: 0.55 NE: 0.78 OPT: 0.33 1 1 er i yer i yer y 080.8 a 080.8 0.6 0.6 ompeting for pla ompeting for pl c 040.4 c 040.4 Player i Player i 0.2 NE 0.2 OPT(min social cost) NE Probability of Probability of OPT(min social cost) 0 0 0.2 0.4 0.6 0.8 1 0 Probability of competing for players -i 0 0.2 0.4 0.6 0.8 1 Probability of competing for players -i ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 63 Some results . N agents compete for R=50 resources that cost 1 unit . They have as second option an unlimited resource set that costs 3 units . PlPenalty cost o f1ifhf 1 unit for those wh hfilho fail the competi iition . t = λ= 020.2 . t= λ in [0.1,100] . N = 180 64 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Some results under low/medium demand the inaccuracies in computing the best action as modeled in these equilibrium concepts decrease the competing probability and hence, the per-user cost in these cases is drawn to near-optimal levels. ΠΜΣ 523 : Προηγμένες ∆ικτυακές 65 Τεχνολογίες Deviations from full rationality •Heuristic reasoning – satisficing instead of maximization of expected utilities (Simon 1955) 66 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Heuristic strategy for the resource selection problem Satisficing: itdfinstead of computi ti/ng/compari ng expect tded cost tittits. it estimates the probability to hit an empty public spot and plays according to this. Confidence heuristic rule: “risk competing for resource r1 according to the probability of winning one of the R resources” – Under the belief that other players think the same way . Fixed-point equation R1 p(r1 ) Pr(#competitors R) Bin( j, N 1; p(r1 )) j0 67 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Heuristic strategy for the resource selection problem . Confidence heuris tic: “ris k fo r pub li c parkin g space accord ing to the probability of winning public parking space” R1 pospPr(# competitors R ) Bin ( j ; N 1, p osp ) j0 1 r i e 0.8 0.6 peting for play peting m 0.4 Player i 0.2 NE robability of co robability P OPT(mi n soci al cost) 0 0 0.2 0.4 0.6 0.8 1 Probability of competing for players -i HE 0.34, NE 0.78, OPT 0330.33 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 68 Some results . It implicitly seeks to avoid tragedy of commons effects . It is shown to yield near‐optimal results 69 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Conclusions for the models of bounded rationality • Formulation of the parking spot selection application drawing on models from behavioral economics and cognitive psychology: • (Cumulative) Prospect Theory : – The decision maker is still a utility maximizer – The desirability of outcomes is expressed through the transformed probabilities of them – Small deviation from the full rationality framework • Alternative equilibrium concepts (Quantal Response Equilibrium, Rosenthal equilibrium) – The diidecision maker is a satifiisfizer – Symmetric mixed‐action equilibria as fixed‐point solutions – A degree of freedom quantifies the rationality in the model (convergence to the Nash equilibrium as the free parameter goes to infinity) • Heuristics – The decision maker is a satisfizer – Confidence heuristic: fast and frugal reasoning solution that is shown to yield near‐optimal resultsΠΜΣ within 523 : Προηγμένες the particular ∆ικτυακές application Τεχνολογίες concept 70 Example heuristic for the ppgarking search problem . evidenced in real‐world reasoning settings . Taking into account interactions of individuals’ decisions /strategies (collective behavioral decision making) E. Kokolaki, I. Stavrakakis, “Equilibrium analysis in the parking search game with heuristic strategies”, 2nd Workshop on Vehicular Traffic Management for Smart Cities (VTM), of the 79th IEEE Vehicular Technology Conference (VTC), 18‐21 May 2014, Seoul, Korea. 71 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Background and preliminary concepts .Parking search amounts to a type of sequential search ‒Sequential search problems: •choices must be made between opportunities that arise more‐or‐less one at a time •qualities (e.g., values, costs, utilities) of future opportunities are unpredictable and returning to an opportunity that arose earlier is costly or impossible ↓ Decisions about each opportunity must be made on the spot (e.g., mate search, secretary problem, house selling, parking search problem) ***Empirical evidence shows that decision‐makers respond to the complexity of sequential search problems by acting heuristically*** 72 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες The fixed‐distance heuristic • …ignores all places until the ddiriver reaches a specific distance from the destination and then takes the first vacant one” • …incorporates two fundamental practices in behavioral decision‐making: ‐one‐at‐time processing of pieces of information ‐use of thresholds 73 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Cost functions parking at the kth parking spot while travelling in the approach lane costs ending in the same parking spot while travelling in the return lane entails a higher cost, that is 74 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Symmetric equilibria: strategy of mutant driver minimizing his exp cost = strategy of population • b+d‐2a≥0: (prefer walking than driving) Best response: fully conserva ve a tude → op mal alloca on: no one pays the ``pri ce of anarchh’’y’’ (PoA) (take first empty spot far from destination) • 2(b‐a)+b+d+e<0: (prefer driving than walking) Best response: fully aggressive attitude ‐> optimal allocation: All but one ppyay the extra cost of driving in the return lane (()PoA) • b+d‐2a<0 and 2(b‐a)+d+e ≥ 0: no clear preference over walk/drive and no symmetric EQ 75 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 2. Congestion‐cost‐cutting Approaches In Resource‐ limited Competitive Environments X 76 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 2. Congestion‐cost‐cutting Approaches In Resource‐ limited Competitive Environments X Coordinated resource selection A. Decentralized resource allocation through social applications Resolve competition through ICT 77 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες A. Decentralized resource allocation through social applications User would subscribe to be able to more effectively use public resources in a competitive environment Social apps for parking resources: (Sfpark, Parking Defenders, Parkomotivo) E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Parking assisting applications: effectiveness and side-issues in managing public goods”, 3rd AWARE workshop on Challenggges for Achieving Self-Awareness in Autonomic Systems of the Self-Adaptive and Self-Organizing systems conference (SASO 2013), Sept. 9-13, 2013, Philadelphia ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 78 Some important questions .Are these apps effective and “fair” to their users? –Do they require high user subscription to be effective? –Do they treat equally similar users? –Do they create a wealth (through coordination and congestion cost cutting) that rightfully distribute to their users? Or simply benefit by eliminating competition by non‐users (exclusion)? .Wha t is the itimpact on non‐users? –Are non‐users of these apps suffering substantially (or almost excluded from) accessing public goods? ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 79 3 Driver profiles . Traditional user/driver (non‐users of the application) . App user/driver: – Defender (sharer, fully cooperative) • Announces upcoming freed‐up spot • Waits for selected app user to come • Rates other defender upon parking – Seeker (free rider – not fully cooperative) • Rates defender upon parking ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 80 Effectiveness of the social parking application: low to moderate parking demand (45% , 75%) .Application users experience better performace than traditional drivers .The advantage for Defenders emerges even at low penetration rates . Win – win situations: Non‐users also improve their performance! (the effective competition that non‐users experience is mitigated ) 81 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Effectiveness of the social parking application: Very high parking demand (105%, 145%) At high penetration rates: .Non‐user exclusion trends .Sharer performance ddteter iora tion due to own competition 82 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Effectiveness of the incentive mechanism and some concerns on its fairness •It is effective… • higher success rates are coupled with higher rankings •But not fair… • it discriminates against identical users (=users with similar interests, needs and attitude towards cooperation) • It induces rich‐get‐richer phenomena: winners in the initial competition round earn credits that offer them a competitive edge in the following rounds 83 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Impact of Seekers on the incentive mechanism’s fairness •Seekers tend to restore fairness ↑ Seekers’ por on → ↓ parking spot handovers → ↓ opportuni es for credit‐building/emergence of high rankings 84 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες 2. Congestion‐cost‐cutting Approaches In Resource‐ limited Competitive Environments X CdidCoordinated resource selilection B. Resource allocation through auction‐based systems Resolve competition in the pricing arena 85 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες •E.B. Kokolaki, Centralized M. Karaliopoulos, I. Stavrakakis, resource “Trading public parking allocation space”, IEEE WoWMoM workshopthrough on Smart Vehicles, auction June 16-19, 2014,‐ Syd based systems Eliminate (competition‐induced) cruising cost, by replacing the physical competition for a public parking spot by a competition for the price to be paid Winners will pay a higher price for the public spot ([cpub,s, cpriv]), but Losers will not pay any cruisingEvangelia cost Kokolaki On average, can drivers do better under the auction-based mechanism? E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Trading public parking space”, IEEE WoWMoM workshop on Smart Vehicles , June 16-19, 2014, Sydney, Australia. 86 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες Trading public parking space: auction‐based allocation . N drivers (buyers, bbddidders) . S: spare on‐street public parking spots (non‐divisible, phillhysically identi cal goods) . Public parking operator (auctioneer) –gets informed about the status of public spots –collects requests and drivers’ bids for public spots –determines parking spot allocations, payments –notifies the winners …through sensor networks and wireless communications ΠΜΣ 523 : Προηγμένες ∆ικτυακές 87 Τεχνολογίες 1. Bidding .Drivers: – bid for no more than one of S public spots – seek to maximize their expected profit from bidding (risk‐neutral bidders) –free of budget constraints .Bids: increasing functions of drivers’ valuations of parking spots .Valuations: – Independent and private valuations – i.i.d RVs continuously distributed within [vmin, vmax]= [cpub,s, cpriv] – ‐3 differen t dis tr ibu tions are considere d: 2. Allocation rule: who are awarded parking spots 3. Payment rule: the selling price of each allocated spot ΠΜΣ 523 : Προηγμένες Δικτυακές 88 Τεχνολογίες Multi‐unit auctions with single‐unit demand . Uniform‐price, Vickrey auctions . Discriminatory‐price auctions ΠΜΣ 523 : Προηγμένες ∆ικτυακές 89 Τεχνολογίες Allocation rule in the equilibrium .All auction formats follow the same allocation rule, that is, they assign the spots to the users that –submit the highest bids (standard auctions) –value the public spots most ( efficient auctions) Payment rule in the equilibrium . Uniform‐price, Vickrey auctions (upa): –all parking spots are sold at the same price which is equal to the first losing bid . Discriminatory‐price auctions (dpa): –the winning drivers pay an amount equal to their individual bids ΠΜΣ 523 : Προηγμένες ∆ικτυακές 90 Τεχνολογίες Bidding in the equilibrium . Uniform‐price, Vickrey auctions (upa): –The drivers bid their real valuations (truthful mechanisms) . Discriminatory‐price auctions (dpa): –The drivers bid the expected value of the first losing bid, assuming that theirs was the highest ΠΜΣ 523 : Προηγμένες ∆ικτυακές 91 Τεχνολογίες Trading public parking space: auction‐based allocation Are the 2 bodies better off ? (wrt the uncoordinated approach) 1. Is the public spot operator doing better? (Revenue) 2. Is the average driver doing better? (Aggregate Cost) ΠΜΣ 523 : Προηγμένες ∆ικτυακές 92 Τεχνολογίες Revenue and Aggregate cost in the equilibrium . Auction‐based allocation: –Revenue (i.e., income of the public parking lot operator) –Aggregate cost (of all drivers) ***E{V(N‐S,N)} = expected value of the (N‐S) order statistic of the N competing valuations = first losing bid = expected payment for a single spot . Uncoordinated strategic parking spot selection game: –Revenue (i.e., income of the public parking lot operator) –Aggregate cost (of all drivers) S(() 1) N 0 ΠΜΣ 523 : Προηγμένες ∆ικτυακές 93 Τεχνολογίες Numerical results –On the public operator’s side .The revenue from auctioning exceeds that under the fixed‐cost uncoordinated parking service proviiision –the same number of drivers park in public space under both practices –drivers pay at least cpub,s in the auction and exactly cpub,s in the uncoordinated game [S=20, cpub,s =1, β=4] The operator always does better under the auction-based mechanism ΠΜΣ 523 : Προηγμένες ∆ικτυακές 94 Τεχνολογίες Numerical results –On the driver’s side 1. the aggr. cost of the drivers parking in public space under the auctioning system exceeds that under the uncoordinated game (left fig.) 2. the aggr. cost of the drivers parking in private space under the auctioning system is lower than that under the parking spot selection game, due to the savings of the “price of anarchy” (right fig.) Drivers do better under the auction-based mechanism if congestion penalty exceeds excess cost from bidding over a minimum cost (cpub,s) Win-Win situation for both the operator and the drivers ΠΜΣ 523 : Προηγμένες ∆ικτυακές 95 Τεχνολογίες Win‐win conditions under high demand .Difference on per‐user costs: .Win‐win situations if Δ>0 .Case NNN00, S(1)/: ALWAYS! ΠΜΣ 523 : Προηγμένες ∆ικτυακές 96 Τεχνολογίες Win‐win conditions under low ‐ medium demand .Case NNN 00, S(1)/ : –Uniformly distributed valuations • Δuincreases with δ: Any increase in δ raises the “price of anarchy” • Δudecreases with β: Any increase in β raises the payments in the auctioning system and hence, reduces the advantage of saving the cruising cost Win-win situations might emerge under proper pricing and failure costs, so that ∆u>0 ΠΜΣ 523 : Προηγμένες ∆ικτυακές 97 Τεχνολογίες Conclusions ΠΜΣ 523 : Προηγμένες ∆ικτυακές 98 Τεχνολογίες PART I : Decision‐making In Distributed, Resource‐limited Competitive Environments .Case study: parking space search in urban environments ‒ DiiDecisions on two differen t sets of parking places .Game‐theoretic formulation of full/bounded rationality (EQ / Social Costs / PoA) .Fully rational decision making > strategic game —Drivers tend to over‐compete for the low‐cost parking space, giving rise to redundant cruising cost —Pricing can alleviate this inefficiency •E. Kokolaki, M. Karaliopoulos, I Stavrakakis, "On the efficiency of information‐ assisted search for ppgarking space: a game‐theoretic approach" , IWSOS'13, Palma de Mallorca, May, 2013. 99 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες .Bounded rational decision making wrt amount of information > (pre)Bayesian game ‒ Less‐is‐more phenomena: more information does not necessarily improve the efficiency of service delivery (i.e., increase social cost) *E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, "Leveraging information in parking assistance systems", IEEE Transactions on Vehicular Technology, vol. 62(9), pp. 4309‐4317, Nov. 2013. .Bounded rationality wrt limited computational cappyacity > ‒ Parking spot selection application drawing on models from behavioral economics and cognitive psychology: •Simple heuristic reasoning ((a) employ heuristic rules: avoids computing/comparing the expected costs of choices but rather estimates the probability to win the competition and plays accordingly, (b) exploit cognitive heuristics) can save price of anarchy and yield near‐optimal results •E. Kokolaki, M. Karaliopoulos, I Stavrakakis, “On human‐driven decision‐making in competitive environments”, Internet Science Conference, Brussels, April, 2013, Best student pppaper award – Special mention. •E. Kokolaki, I. Stavrakakis, Equilibrium analysis in the parking search game with heuristic strategies. IEEE VTC Wrkshp on Vehicular Traffic Mgmnt for Smart Cities, Seoul, May, 2014. 100 ΠΜΣ 523 : Προηγμένες ∆ικτυακές Τεχνολογίες PART II : Coordinated Resource Selection A. Decentralized resource allocation through social applications . ItitdInvestigated effec tiveness / appropriitateness of dis tr ibu te d, socilial public resource (parking) management apps – Effective and mostly non‐exclusive to non‐users Users’ improved performance is mostly due to the increased efficiency they generate in the parking process, rather than excluding traditional users from comppgeting for the resources. – Incentive mechanism is effective But it induces rich‐club phenomena and difficulties to newcomers – Seekers (free‐riders) seems to alleviate those problems *E. Kokolaki, M. Karaliopoulos, and I. Stavrakakis, "Parking Assisting Applications: Effectiveness and Side‐issues in Managing Public Goods", 3rd IEEE SASO workshop on Challenges for Achieving Self‐Awareness in Autonomic Systems, Sept. 2013, Philadelphia, USA ΠΜΣ 523 : Προηγμένες ∆ικτυακές 101 Τεχνολογίες B. Centralized resource allocation through auction‐based systems .Shift competition to price setting level .Eliminate congestion penalties .Considered: –uncoordinated strategic parking spot selection game vs. multi‐units auctions with silingle‐unit dddemand: uniform‐price, Vic krey and discr im ina tory‐price auctions .Guaranteed higher profits for operator .Guaranteed win‐win situations, under high demand, or possible with proper pricing/failure costs, otherwise *E. Kokolaki, M. Karaliopoulos, I. Stavrakakis, “Trading public parking space”, IEEE WoWMoM workshop on Smart Vehicles, Sydney, Australia, June 16‐19, 2014 ΠΜΣ 523 : Προηγμένες ∆ικτυακές 102 Τεχνολογίες