Characterizing distribution rules for cost sharing games

In noncooperative cost sharing games, individually strategic agents choose resources based on how the welfare (cost or revenue) generated at each resource (which depends on the set of agents that choose the resource) is distributed. The focus is on finding distribution rules that lead to stable allocations, which is formalized by the concept of Nash equilibrium, e.g., Shapley value (budget-balanced) and marginal contribution (not budget-balanced) rules.

Recent work that seeks to characterize the space of all such rules shows that the only budget-balanced distribution rules that guarantee equilibrium existence in all welfare sharing games are generalized weighted Shapley values (GWSVs), by exhibiting a specific 'worst-case' welfare function which requires that GWSV rules be used. Our work provides an exact characterization of the space of distribution rules (not necessarily budget-balanced) for any specific local welfare functions remains, for a general class of scalable and separable games with well-known applications, e.g., facility location, routing, network formation, and coverage games.

We show that all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to GWSV rules on some 'ground' welfare functions. Therefore, it is neither the existence of some worst-case welfare function, nor the restriction of budget-balance, which limits the design to GWSVs. Also, in order to guarantee equilibrium existence, it is necessary to work within the class of potential games, since GWSVs result in (weighted) potential games.

We also provide an alternative characterization—all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to generalized weighted marginal contribution (GWMC) rules on some 'ground' welfare functions. This result is due to a deeper fundamental connection between Shapley values and marginal contributions that our proofs expose—they are equivalent given a transformation connecting their ground welfare functions. (This connection leads to novel closed-form expressions for the GWSV potential function.) Since GWMCs are more tractable than GWSVs, a designer can tradeoff budget-balance with computational tractability in deciding which rule to implement.

Death or taxes? The political economy of sanitation expenditure in nineteenth-century Britain

This thesis consists of three papers studying the relationship between democratic reform, expenditure on sanitation public goods and mortality in Britain in the second half of the nineteenth century. During this period decisions over spending on critical public goods such as water supply and sewer systems were made by locally elected town councils, leading to extensive variation in the level of spending across the country. This dissertation uses new historical data to examine the political factors determining that variation, and the consequences for mortality rates.

The first substantive chapter describes the spread of government sanitation expenditure, and analyzes the factors that determined towns' willingness to invest. The results show the importance of towns' financial constraints, both in terms of the available tax base and access to borrowing, in limiting the level of expenditure. This suggests that greater involvement by Westminster could have been very effective in expediting sanitary investment. There is little evidence, however, that democratic reform was an important driver of greater expenditure.

Chapter 3 analyzes the effect of extending voting rights to the poor on government public goods spending. A simple model predicts that the rich and the poor will desire lower levels of public goods expenditure than the middle class, and so extensions of the right to vote to the poor will be associated with lower spending. This prediction is tested using plausibly exogenous variation in the extent of the franchise. The results strongly support the theoretical prediction: expenditure increased following relatively small extensions of the franchise, but fell once more than approximately 50% of the adult male population held the right to vote.

Chapter 4 tests whether the sanitary expenditure was effective in combating the high mortality rates following the Industrial Revolution. The results show that increases in urban expenditure on sanitation-water supply, sewer systems and streets-was extremely effective in reducing mortality from cholera and diarrhea.