In dynamic mechanism design literature, one critical aspect has been typically ignored-the agents' periodic participation, which they can adapt and plan strategically. We propose a framework for dynamic principal-multiagent problems, augmenting the classic model by incorporating agents' periodic coupled decisions on participation and regular action selections. The principal faces adverse selection and designs a mechanism comprising a task policy profile (defining evolving agent action menus), a coupling policy profile (affecting agent utilities), and an off-switch function profile (assigning rewards or penalties upon agent withdrawal). Firstly, we introduce payoff-flow conservation-a sufficient condition to ensure dynamic incentive compatibility for regular actions. Secondly, we formulate a unique process, persistence transformation, which integrates task policy's implicit functions, enabling a closed-form off-switch function derivation, hence securing sufficient conditions for agents' coupled decisions' incentive compatibility, aligning with the principal's preferences. Thirdly, we go beyond the traditional envelope theorem by presenting a necessary condition for incentive compatibility, leveraging the coupled optimality of principal-desired actions. This approach helps explicitly formulate both the coupling and off-switch functions. Finally, we establish envelope-like conditions exclusively on the task policies, facilitating the application of the first-order approach.

Multi-agent reinforcement learning (MARL) addresses sequential decision-making problems with multiple agents, where each agent optimizes its own objective. In many real-world instances, the agents may not only want to optimize their objectives, but also ensure safe behavior. For example, in traffic routing, each car (agent) aims to reach its destination quickly (objective) while avoiding collisions (safety). Constrained Markov Games (CMGs) are a natural formalism for safe MARL problems, though generally intractable. In this work, we introduce and study Constrained Markov Potential Games (CMPGs), an important class of CMGs. We first show that a Nash policy for CMPGs can be found via constrained optimization. One tempting approach is to solve it by Lagrangian-based primal-dual methods. As we show, in contrast to the single-agent setting, however, CMPGs do not satisfy strong duality, rendering such approaches inapplicable and potentially unsafe. To solve the CMPG problem, we propose our algorithm Coordinate-Ascent for CMPGs (CA-CMPG), which provably converges to a Nash policy in tabular, finite-horizon CMPGs. Furthermore, we provide the first sample complexity bounds for learning Nash policies in unknown CMPGs, and, which under additional assumptions, guarantee safe exploration.

In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal coalition welfare and discuss bidders' incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints.

Every producer chooses as its strategy a supply function returning the quantity S(p) that it is willing to sell at a minimum unit price p. The market clears at the price at which the aggregate demand intersects the total supply and firms are paid the bid prices. We study a game theoretic model of competition among such firms and focus on its equilibria (Supply function equilibrium). The game we consider is a generalization of both models where firms can either set a fixed quantity (Cournot model) or set a fixed price (Bertrand model). Our main result is to prove existence and provide a characterization of (pure strategy) Nash equilibria in the space of K-Lipschitz supply functions.

Multi-agent reinforcement learning (MARL) models multiple agents that interact and learn within a shared environment. This paradigm is applicable to various industrial scenarios such as autonomous driving, quantitative trading, and inventory management. However, applying MARL to these real-world scenarios is impeded by many challenges such as scaling up, complex agent interactions, and non-stationary dynamics. To incentivize the research of MARL on these challenges, we develop MABIM (Multi-Agent Benchmark for Inventory Management) which is a multi-echelon, multi-commodity inventory management simulator that can generate versatile tasks with these different challenging properties. Based on MABIM, we evaluate the performance of classic operations research (OR) methods and popular MARL algorithms on these challenging tasks to highlight their weaknesses and potential.

Developing artificial intelligence approaches to overcome novel, unexpected circumstances is a difficult, unsolved problem. One challenge to advancing the state of the art in novelty accommodation is the availability of testing frameworks for evaluating performance against novel situations. Recent novelty generation approaches in domains such as Science Birds and Monopoly leverage human domain expertise during the search to discover new novelties. Such approaches introduce human guidance before novelty generation occurs and yield novelties that can be directly loaded into a simulated environment. We introduce a new approach to novelty generation that uses abstract models of environments (including simulation domains) that do not require domain-dependent human guidance to generate novelties. A key result is a larger, often infinite space of novelties capable of being generated, with the trade-off being a requirement to involve human guidance to select and filter novelties post generation. We describe our Human-in-the-Loop novelty generation process using our open-source novelty generation library to test baseline agents in two domains: Monopoly and VizDoom. Our results shows the Human-in-the-Loop method enables users to develop, implement, test, and revise novelties within 4 hours for both Monopoly and VizDoom domains.

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve $\widetilde{O}\left(\Delta^{1/4}T^{3/4}\right)$ regret when the degree of nonstationarity, as measured by total variation $\Delta$, is known, and $\widetilde{O}\left(\Delta^{1/5}T^{4/5}\right)$ regret when $\Delta$ is unknown, where $T$ is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

In this paper, we investigate how heterogeneous multi-robot systems with different sensing capabilities can observe a domain with an apriori unknown density function. Common coverage control techniques are targeted towards homogeneous teams of robots and do not consider what happens when the sensing capabilities of the robots are vastly different. This work proposes an extension to Lloyd's algorithm that fuses coverage information from heterogeneous robots with differing sensing capabilities to effectively observe a domain. Namely, we study a bimodal team of robots consisting of aerial and ground agents. In our problem formulation we use aerial robots with coarse domain sensors to approximate the number of ground robots needed within their sensing region to effectively cover it. This information is relayed to ground robots, who perform an extension to the Lloyd's algorithm that balances a locally focused coverage controller with a globally focused distribution controller. The stability of the Lloyd's algorithm extension is proven and its performance is evaluated through simulation and experiments using the Robotarium, a remotely-accessible, multi-robot testbed.

Artificial agents have traditionally been trained to maximize reward, which may incentivize power-seeking and deception, analogous to how next-token prediction in language models (LMs) may incentivize toxicity. So do agents naturally learn to be Machiavellian? And how do we measure these behaviors in general-purpose models such as GPT-4? Towards answering these questions, we introduce MACHIAVELLI, a benchmark of 134 Choose-Your-Own-Adventure games containing over half a million rich, diverse scenarios that center on social decision-making. Scenario labeling is automated with LMs, which are more performant than human annotators. We mathematize dozens of harmful behaviors and use our annotations to evaluate agents' tendencies to be power-seeking, cause disutility, and commit ethical violations. We observe some tension between maximizing reward and behaving ethically. To improve this trade-off, we investigate LM-based methods to steer agents' towards less harmful behaviors. Our results show that agents can both act competently and morally, so concrete progress can currently be made in machine ethics--designing agents that are Pareto improvements in both safety and capabilities.

Communication can impressively improve cooperation in multi-agent reinforcement learning (MARL), especially for partially-observed tasks. However, existing works either broadcast the messages leading to information redundancy, or learn targeted communication by modeling all the other agents as targets, which is not scalable when the number of agents varies. In this work, to tackle the scalability problem of MARL communication for partially-observed tasks, we propose a novel framework Transformer-based Email Mechanism (TEM). The agents adopt local communication to send messages only to the ones that can be observed without modeling all the agents. Inspired by human cooperation with email forwarding, we design message chains to forward information to cooperate with the agents outside the observation range. We introduce Transformer to encode and decode the message chain to choose the next receiver selectively. Empirically, TEM outperforms the baselines on multiple cooperative MARL benchmarks. When the number of agents varies, TEM maintains superior performance without further training.