Abstract
We consider systems where agents in a society choose actions from their strategy sets and incur a cost. This cost depends not only on their own choices, but also on those of other agents in the society. Guided by their own interests, agents at equilibrium decide on strategies to minimise their individual cost given the actions of everyone else. But a central planner can do better and select for each agent an action such that the sum of costs in the society is minimised. The gap between this minimum and the cost of the worst equilibrium is known as the Price of Anarchy (PoA). Since its introduction by Koutsoupias and Papadimitriou (1999), PoA has stood as the gold standard for system efficiency. Taken literally, PoA is a measure of the inefficiency accruing to “anarchic” decentralisation. However, in many systems, mechanisms exist to induce optimal equilibria, where the society incurs costs equal to those it would incur under the governance of the central planner. This is a “designed” decentralisation, where a mechanism has modified the incentives and behaviour of the agents. In that case, PoA is simply 1. The present thesis investigates the ties between efficiency, regret and inequality in decentralised systems. We exhibit four connected questions to conduct this investigation: 1. When optimal equilibria exist but inefficiency arises from the complexity of reaching these equilibria, can a centralised authority help agents coordinate? 2. When agents follow no-regret learning dynamics and reaching a Nash equilibrium is hard, can we guarantee efficiency bounds of the limit states? 3. In a large, real system such as the Singapore transportation network, what are data-driven proxies for the theoretically defined notions of regret and PoA? Is the latter as pessimistic in real life as its theoretical bounds predict? 4. When agents are endowed with initial wealth, how do mechanisms inducing optimal equilibria modify the distribution of wealth?