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UID:event-73@tuemeche.nl
DTSTAMP:20261007T234651Z
DTSTART;TZID=Europe/Amsterdam:20270216T133000
DTEND;TZID=Europe/Amsterdam:20270216T150000
SUMMARY:Evolutionary Equilibria in Mean Field Games: Theory and Applicati
 ons to Token Economies
DESCRIPTION:Speaker: Leonardo Pedroso Duarte\nHost: Mauro Salazar\n\nMode
 rn societies increasingly rely on shared infrastructures such as transpor
 tation networks\, energy systems\, cloud platforms\, communication channe
 ls\, and other resources whose value depends on how many users access the
 m at the same time. When users act selfishly\, the resulting allocation i
 s often inefficient from a societal perspective. Classical mechanism-desi
 gn solutions address this problem through monetary prices or tolls. Yet m
 oney can compromise fairness\, because access then depends on wealth. Fai
 rness is especially delicate when users belong to different classes with 
 different needs or constraints\, since a desirable allocation may intenti
 onally favor those who are worse off. An appealing alternative is to use 
 non-tradable tokens that users earn and spend when accessing resources. S
 uch token economies can promote turn-taking. Users alternate between more
  and less favorable outcomes\, allowing efficiency and fairness to be rec
 onciled over time. This thesis develops the theoretical and design founda
 tions for such token-based mechanisms in dynamic resource allocation prob
 lems.\n\nThe choices to be priced are not necessarily isolated resources\
 ; they are combinations of resources that many agents use repeatedly over
  time. For example\, a traveler may choose a path consisting of several r
 oad links\, and the travel time of that path depends on the congestion of
  each link. The design problem is therefore to determine token tolls for 
 combinations of resources so that the collective behavior induced by indi
 vidual choices leads to fair and efficient long-run outcomes. To address 
 this problem\, this thesis models token economies as continuous-time stoc
 hastic dynamic games with finitely many boundedly rational agents. Each a
 gent has an individual state\, namely the number of tokens in their walle
 t\, and repeatedly chooses actions from the set of resource combinations 
 available to satisfy their needs. These decisions are made according to p
 olicies\, which map individual states to actions. They affect the agents'
  future states and shape the aggregate congestion experienced by the popu
 lation.\n\nBecause real users cannot be expected to know the full game\, 
 compute equilibria\, or behave as perfectly rational optimizers\, the the
 sis adopts an evolutionary-game-theoretic perspective. Evolutionary model
 s replace strong rationality assumptions by simple myopic revision protoc
 ols: rules by which agents occasionally revise their policies based on cu
 rrently perceived payoffs. This is a natural level of behavioral detail f
 or large populations. Crucially\, the relevant question is not only which
  outcomes are equilibria\, but also whether such outcomes can emerge and 
 persist under plausible behavioral dynamics.\n\nThe first part of the the
 sis develops a new evolutionary theory for continuous-time finite-state s
 tochastic dynamic games of many players. A mean-field approximation is in
 troduced and shown to approximate the finite-population game with strong 
 guarantees as the population grows. This approximation makes it possible 
 to study the joint state-policy distribution of the population through a 
 deterministic ordinary differential equation induced by simple evolutiona
 ry revision rules. The thesis shows that standard equilibrium concepts fo
 r this class of games lack an evolutionary interpretation\, because they 
 do not allow individual heterogeneity in the policies used by the players
 . To overcome this limitation\, a new solution concept is introduced: the
  mixed stationary Nash equilibrium. It admits an evolutionary interpretat
 ion and exists under mild conditions. Moreover\, for broad classes of mea
 ningful revision protocols\, mixed stationary Nash equilibria coincide wi
 th the rest points of the proposed mean-field evolutionary dynamics. The 
 thesis then studies their evolutionary stability\, establishing condition
 s under which population trajectories approach (or remain close to) the s
 et of mixed stationary Nash equilibria. This gives equilibrium a design-r
 elevant meaning: if a game is constructed so that a desired population st
 ate is a mixed stationary Nash equilibrium\, the theory provides tools to
  show that this state can emerge and persist against strategic deviations
 .\n\nThe second part of the thesis applies this theory to the design of t
 oken economies for fair and efficient dynamic resource allocation in cong
 estion games. Three performance objectives are considered. Intra-class fa
 irness requires users with the same needs to experience the same long-run
  average reward\, independently of individual factors such as wealth. Int
 er-class fairness concerns how rewards are distributed across different u
 ser classes\, for instance to favor classes that are worse off. Efficienc
 y aims to maximize the societal utility of the resources\, such as the av
 erage reward of the whole population or environmental performance. The de
 sign problem is then formulated as the choice of token tolls that guarant
 ee intra-class fairness while optimizing a prescribed trade-off between i
 nter-class fairness and efficiency. The thesis shows that intra-class fai
 rness holds for any choice of tolls\, establishes existence and essential
  uniqueness of the mean-field equilibrium resource flows\, and shows conv
 ergence of the token economy to a neighborhood of equilibrium from any in
 itial condition. Finally\, it derives closed-form integer tolls that indu
 ce an equilibrium at the desired optimal trade-off between fairness and e
 fficiency.\n\nAltogether\, this thesis bridges mechanism design\, evoluti
 onary game theory\, and control engineering to provide a principled frame
 work for dynamic resource allocation without money. Its main contribution
  is twofold: it develops a new evolutionary equilibrium theory for contin
 uous-time finite-state dynamic games\, and it uses this theory to design 
 token economies whose long-run behavior is fair\, efficient\, and can eme
 rge robustly under boundedly rational behavior.\n\nMore info: https://www
 .tue.nl/en/research/researchers/leonardo-pedroso-duarte
LOCATION:Atlas 0.710
URL:https://tuemeche.nl/peoplepages/event.php?id=73
CATEGORIES:PhD Defense
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