Public Goods on Networks : Statics, Welfare & Mechanisms
Abstract: This thesis studies a network game of heterogeneous and asymmetric public goods. Players allocate their wealth between private and public goods, benefiting from the public goods provisioned by their out-neighbors on the network graph. Utilities are given by a Cobb-Douglas function to capture substitutability and decreasing marginal returns. I prove that the game is well-behaved under a condition relating a simple network characteristic – the spectral radius – to the preferences of the players. Under this assumption, the best response dynamic is guaranteed to converge, and the equilibrium strategy is unique. Equilibrium public good contributions are then linear in the wealth of others contributors. Next, the game is studied through a normative lens. I show that equilibrium outcomes, as a rule, are inefficient with regards to important welfare metrics. Three mechanisms on the game are formalized, drawing on the economic literature of public goods: taxes & subsidies, enforceable contracts, and redistribution. For each mechanism, the scope of attainable welfare improvements is characterized and design considerations discussed.
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