Cooperation in Groups: a Game-Theoretic Investigation of Behaviour, Mechanisms, and Dynamics

What makes people cooperate? How can one design mechanisms in order to incentivize players to contribute to public goods? These are the kinds of fundamental questions that are exemplified by analysis of the free-rider problem: The problem arises from the fact that, while an entire population benefits from the presence of a public good produced at some cost by cooperative individuals, free-riders (defectors) can benefit from the public good even when not producing any of it. Using the tools of Game Theory, Mechanism Design and Experimental Economics, one can identify and understand the underlying conflicting forces leading to such free-riders problems in human interactions. This understanding can then be used to design suitable mechanisms to avoid ``tragedies of the commons", i.e. convergence to socially sub-optimal outcomes. In this dissertation, I focus on Public Goods games, and in particular on understanding under which conditions the public good is successfully provided and sustained through voluntary contributions, when players interact in groups. I not only focus on how cooperation can emerge as a result of incentive mechanisms and/or behavioural regularities, but I also study the implications of said mechanisms in terms of the total welfare of the players. The aim is to assess how robust positive predictions obtained for Voluntary Contribution Games are, when transferred to more general models which are closer to real-world social dilemmas situations. I extend the Voluntary Contribution Game in several ways: by considering different strategy spaces and public good provision efficacies, by adding noise, and, crucially, by accounting for heterogeneity among players. Using a mixture of analytical, experimental and computational tools, I show that highly-efficient equilibria are enabled by so called ``grouping'' mechanisms but that they also often cease to exist when heterogeneity is taken into account. I identify under which conditions high cooperation can be achieved and determine what is the optimal mechanism in terms of social welfare, as a function of a social planner's preference. Finally, I also investigate mechanisms based on reputations expressed by ``scores", and show that the positive results obtained in pairwise interactions do not necessary apply to multiplayer prisoner’s dilemmas, regardless of how much information is provided about the past behaviour of the interacting partners