Electric power systems are undergoing a major transformation as they integrate intermittent renewable energy sources, and batteries to smooth out variations in renewable energy production. As privately-owned batteries grow from their role as marginal "price-takers" to significant players in the market, a natural question arises: How do batteries operate in electricity markets, and how does the strategic behavior of decentralized batteries distort decisions compared to centralized batteries? We propose an analytically tractable model that captures salient features of the highly complex electricity market. We derive in closed form the resulting battery behavior and generation cost in three operating regimes: (i) no battery, (ii) centralized battery, and (ii) decentralized profit-maximizing battery. We establish that a decentralized battery distorts its discharge decisions in three ways. First, there is quantity withholding, i.e., discharging less than centrally optimal. Second, there is a shift in participation from day-ahead to real-time, i.e., postponing some of its discharge from day-ahead to real-time. Third, there is reduction in real-time responsiveness, or discharging less in response to smoothing real-time demand than centrally optimal. We also quantify the impact of the battery market power on total system cost via the Price of Anarchy metric, and prove that it is always between 9/8 and 4/3. That is, incentive misalignment always exists, but it is bounded even in the worst case. We calibrate our model to real data from Los Angeles and Houston. Lastly, we show that competition is very effective at reducing distortions, but many market power mitigation mechanisms backfire, and lead to higher total cost. The work provides stakeholders with a framework to understand and detect market power from batteries. It also shows that the potential loss from battery market power is relatively small compared to the cost reduction achievable from having enough battery capacity in the system. Therefore, independent system operators in rapidly changing markets might want to prioritize market entry of batteries and only shift to market power mitigation once the market is more mature.

A seller wants to sell an indivisible item to n buyers. The buyer valuations are drawn i.i.d. from a distribution, but the seller does not know this distribution; the seller only knows the support [a, b]. To be robust against the lack of knowledge of the environment and buyers' behavior, the seller optimizes over dominant strategy incentive compatible (DSIC) mechanisms, and measures the worst-case performance relative to an oracle with complete knowledge of buyers' valuations. Our analysis encompasses both the regret and the approximation ratio objectives.

Classical Bayesian mechanism design relies on the common prior assumption, but the common prior is often not available in practice. We study the design of prior-independent mechanisms that relax this assumption: the seller is selling an indivisible item to n buyers such that the buyers' valuations are drawn from a joint distribution that is unknown to both the buyers and the seller; buyers do not need to form beliefs about competitors, and the seller assumes the distribution is adversarially chosen from a specified class. We measure performance through the worst-caseregret, or the difference between the expected revenue achievable with perfect knowledge of buyers' valuations and the actual mechanism revenue.

Social services often face the challenge of congestion due to their limited capacity relative to their demand. The congestion partly stems from the inclusionary intent of such services: a toll-free road is available to everyone, even those able to afford alternative tolled ones. A broad range of low- and middle-income households are eligible to apply for public housing. How can a social service provider reduce congestion and thus the efficiency loss associated with service delay? In this context, the two controls commonly used for managing congestion, pricing and centralized admission control, are inapplicable due to fairness and implementation considerations. However, the service provider may have control over the information about the system state that it shares with the users. Local traffic managers and public housing authorities have accurate information about the level of congestion for their corresponding services. As such, the service provider can leverage this informational advantage to persuade some of those with lower needs to forgo the service and reduce congestion in the system. In this paper, we study how effective such an informational lever is.

The DeGroot model of naive social learning assumes that agents only communicate scalar opinions. In practice, agents communicate not only their opinions, but their confidence in such opinions. We propose a model that captures this aspect of communication by incorporating signal informativeness into the naive social learning scenario. Our proposed model captures aspects of both Bayesian and naive learning. Agents in our model combine their neighbors' beliefs using Bayes' rule, but the agents naively assume that their neighbors' beliefs are independent. Depending on the initial beliefs, agents in our model may not reach a consensus, but we show that the agents will reach a consensus under mild continuity and boundedness assumptions on initial beliefs. This eventual consensus can be explicitly computed in terms of each agent's centrality and signal informativeness, allowing joint effects to be precisely understood. We apply our theory to adoption of new technology. In contrast to Banerjee et al. [2018], we show that information about a new technology can be seeded initially in a tightly clustered group without information loss, but only if agents can expressively communicate their beliefs.