Essays in learning, optimization and game theory

This thesis studies the interaction of selfish economic agents in three differentsettings. In the first setting, they have to take decisions daily based on information they got in the past, and learn from what happened before how to take good decisions based on feedback they get after taking a decision. Studied are algorithms that guarantee the agents to take good decisions over the long run. In the second setting, traffic network problems are studied. An algorithm is studied that takes into account the commuting paths and desired arrival time of the commuters to give them a recommendation of their departure time and the path they should choose in order to reduce the traffic, and in such a way that the commuters have to follow the recommendations of the algorithm. In the third setting, a setting is studied in which two laboratories receive alternatively a grant to find a cure against a disease with mutations. Each time a laboratory receives a grant, it can invest one technology out of a finite number of them. Under common knowledge on the disease, and assuming that both laboratories are perfectly aware of the technologies used by the other laboratory, the behaviour is studied that both laboratories should have in order to maximize their individual probability to find a cure against the current mutation of the disease.