Interpersonal trust is a one-sided social dilemma. Building on the binary trust game, we ask how trust and trustworthiness can evolve in a population where partners are matched randomly and agents sometimes act as trustors and sometimes as trustees. Trustors have the option to costly check a trustee's last action and to condition their behavior on the signal they receive. We show that the resulting population game admits two components of Nash equilibria. Nevertheless, the long-run outcome of an evolutionary social learning process modeled by the best response dynamics is unique. Even if unconditional distrust initially abounds, the trustors' checking option leads trustees to build a reputation for trustworthiness by honoring trust. This invites free-riders among the trustors who save the costs of checking and trust blindly, until it does no longer pay for trustees to behave in a trustworthy manner. This results in cyclical convergence to a mixed equilibrium with behavioral heterogeneity where suspicious checking and blind trusting coexist while unconditional distrust vanishes. (author's abstract) / Series: Department of Economics Working Paper Series

In this technical note we use insights from the theory of projective geometry to provide novel and non-algebraic proofs of convergence of continuous-time fictitious play for a class of games. As a corollary we obtain a kind of equilibrium selection result, whereby continuous-time fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4x4 zero-sum games.

Deux situations de comportement égoïste des agents dans les réseaux de communication sont considérées dans le cadre de la théorie des jeux.La première situation concerne les réseaux de communication utilisant un routage décentralisé basé sur des agents autonomes. Nous étudions les propriétés de convergence des dynamiques de meilleures réponses dans un jeu de routage sur des liens parallèles. Le jeu implique un nombre fini d'agents, chacun décidant comment son trafic est routé sur les liens de manière à minimiser son propre coût. Nous proposons l'utilisation du rayon spectral généralisé des matrices Jacobiennes de l'opérateur de meilleure réponse pour démontrer la convergence.La seconde situation apparaît dans les réseaux tolérants aux délais dont l'objectif est de permettre la communication dans des environnements où la connectivité n'est qu'intermittente et où les délais de communication peuvent être très longs. Nous proposons tout d'abord un mécanisme d'incitation basé sur une récompense pour convaincre les noeuds mobiles de relayer les messages, et analysons l'influence de l'information donnée par la source (nombre de copies du message, âge de ces copies) aux relais sur le prix à payer pour transmettre le message. Nous considérons ensuite un modèle dans lequel la source propose une récompense fixe. Les noeuds mobiles peuvent alors décider d'accepter ou non le message, et s'ils l'acceptent, peuvent ensuite à tout moment décider de l'abandonner. Nous modélisons l'interaction entre les noeuds mobiles sous la forme d'un jeu stochastique partiellement observable et analysons les politiques optimales pour les relais. / This thesis focuses on the issues related to the selfish behavior of the agents in the communication networks. We are particularly interested in two situations in which these issues arise and we address game-theoretical framework to study them.The first situation relates to communication networks using a distributed routing based on autonomous agents. Compared to a centralized routing, this type of routing offers significant advantages in terms of scalability, ease of deployment or robustness to failures and environmental disturbances. We investigate the convergence properties of the sequential best-response dynamics in a routing game over parallel links. The game involves a finite number of routing agents each of which decides how much flow to route on each of the links with the objective of minimizing its own costs. For some particular cases (e.g., two players), the convergence of the best-response dynamics can be proved by showing that this game has a potential function. For other cases, a potential function has remained elusive. We propose the use of non-linear spectral radius of the Jacobian of the best-response dynamics as an alternative approach to proving its convergence.The second situation occurs in Delay Tolerant Networks (DTNs) that have been the subject of intensive research over the past decade. DTN has an idea to support communication in environments where connectivity is intermittent and where communication delays can be very long. We focus on game-theoretic models for DTNs. First, we propose an incentive mechanism to persuade selfish mobile nodes to participate in relaying messages, and investigate the influence of the information given by the source (number of existing copies of the message, age of these copies) to the relays on the rewards proposed. For static information polices, that is the same type of information given to all the relays, it is shown that the expected reward paid by the source is independent of the policy. However, the source can reduce the reward by dynamically adapting the type of information based on the meeting times with the relays. For the particular cases, we give some structural results of the optimal adaptive policy. Next, we consider the model where the source proposes a fixed reward. The mobile relays can decide to accept or not the packet and then to drop the packet in the future. This game can be modelled as a partially-observable stochastic game. For two relays, we have shown that the optimal policies for the relays relates to the threshold type.

Pourquoi faire un effort pour la communauté sans rien recevoir en retour? C’est habituellement par conviction ou pour répondre à une norme sociale. En s’intéressant au problème du recyclage, nous définissons un modèle de comportement qui intègre ces deux facteurs. Nous déterminons sous quelles conditions un individu décide d’agir bénévolement, puis nous étudions comment ce comportement se propage dans la population. Cela nous permet de déduire comment un gouvernement doit pondérer ses efforts entre la publicité et la consigne pour tendre vers un taux de recyclage parfait au coût minimal. Nous prouvons aussi que dans certaines circonstances, il est préférable de ne pas encourager la participation au bien public. En effet, à mesure que plus de gens y participent, des tensions sociales émergent entre ceux qui font un effort et ceux qui n’en font pas. Celles-ci peuvent être assez fortes pour contrebalancer les bénéfices attendus du bien public / The commons need not be a tragedy: impact of peer-pressure and opinions Why do people help the community without getting anything in return? Usually, they either hold the firm belief they should do so or they want to follow a social norm. The behavioural model of this paper takes those two factors into account and applies them to recycling issues. It shows under which condition people act selflessly and how this behaviour spreads across the population. This paper then determines how governments must balance advertising and packaging refunding in order to increase recycling rate at minimal cost. It also proves that under certain circumstances it is preferable not to start transition toward cooperation. Indeed, as people progressively start cooperating, the population becomes divided between followers and opponents to this new attitude. As long as this heterogeneity remains, peer-pressure causes a cost that may outweigh the expected benefits of cooperation.