Planning under uncertainty for multiple agents has flourished with the development of formal models such as multi-agent MDPs and decentralized MDPs. Despite their richness, applicability of these models remains limited due to their computational complexity. We present the class of event-detecting Multi-agent MDPs (eMMDPs), designed to detect multiple mobile targets by a team of sensor agents. We show that eMMDPs are NP-Hard and present a scalable 2-approximation algorithm for solving them using matroid theory and constraint optimization. Its complexity is linear in the state-space and number of agents, quadratic in the horizon, and exponential only in a small parameter that depends on the interaction among the agents. Despite the worst-case approximation ratio of 2, experimental results show that the algorithm produces nearoptimal policies for a range of test problems.

We introduce a framework so that communities can exchange reputation information about agents in environments where agents are migrating between communities. We view the acquisition of the reputation information as a purchase and focus on the design of a payment function to facilitate the payment for information in a way that motivates communities to truthfully report reputation information for agents. We prove that in our proposed framework, honesty is the optimal policy and demonstrate the value of using a payment-function approach for the exchange of reputation information about agents between communities in multiagent environments. Using our payment function, each community is strengthened: it is able to reason more effectively about which agents to accept and can enjoy agents that are motivated to contribute strongly to the benefit of the community.

We develop and test computational methods for guiding collaboration that demonstrate how shared plans can be created in real-world settings, where agents can be expected to have diverse and varying goals, preferences, and availabilities. The methods are motivated and evaluated in the realm of ridesharing, using GPS logs of commuting data. We consider challenges with coordination among self-interested people aimed at minimizing the cost of transportation and the impact of travel on the environment. We present planning, optimization, and payment mechanisms that provide fair and efficient solutions to the rideshare collaboration challenge. We evaluate different VCG-based payment schemes in terms of their computational efficiency, budget balance, incentive compatibility, and strategy proofness. We present the behavior and analyses provided by the ABC ridesharing prototype system. The system learns about destinations and preferences from GPS traces and calendars, and considers time, fuel, environmental, and cognitive costs. We review how ABC generates rideshare plans from hundreds of real-life GPS traces collected from a community of commuters and reflect about the promise of employing the ABC methods to reduce the number of vehicles on the road, thus reducing CO2 emissions and fuel expenditures.

Buoyed by recent successes in the area of distributed constraint optimization problems (DCOPs), this paper addresses challenges faced when applying DCOPs to real-world domains. Three fundamental challenges must be addressed for a class of real-world domains, requiring novel DCOP algorithms. First, agents may not know the payoff matrix and must explore the environment to determine rewards associated with variable settings. Second, agents may need to maximize total accumulated reward rather than instantaneous final reward. Third, limited time horizons disallow exhaustive exploration of the environment. We propose and implement a set of novel algorithms that combine decision-theoretic exploration approaches with DCOP-mandated coordination. In addition to simulation results, we implement these algorithms on robots, deploying DCOPs on a distributed mobile sensor network.

This paper considers the setting wherein a group of agents (e.g., robots) is seeking to obtain a given tangible good, potentially available at different locations in a physical environment. Traveling between locations, as well as acquiring the good at any given location consumes from the resources available to the agents (e.g., battery charge). The availability of the good at any given location, as well as the exact cost of acquiring the good at the location is not fully known in advance, and observed only upon physically arriving at the location. However, a-priori probabilities on the availability and potential cost are provided. Given such as setting, the problem is to find a strategy/plan that maximizes the probability of acquiring the good while minimizing resource consumption. Sample applications include agents in exploration and patrol missions, e.g., rovers on Mars seeking to mine a specific mineral. Although this model captures many real world scenarios, it has not been investigated so far. We focus on the case where locations are aligned along a path, and study several variants of the problem, analyzing the effects of communication and coordination. For the case that agents can communicate, we present a polynomial algorithm that works for any fixed number of agents. For non-communicating agents, we present a polynomial algorithm that is suitable for any number of agents. Finally, we analyze the difference between homogeneous and heterogeneous agents, both with respect to their allotted resources and with respect to their capabilities.

In this paper, we describe an approach to scheduling under uncertainty that achieves scalability through a coupling of deterministic and probabilistic reasoning. Our specific focus is a class of oversubscribed scheduling problems where the goal is to maximize the reward earned by a team of agents in a distributed execution environment.  There is uncertainty in both the duration and  outcomes of executed activities. To ensure scalability, our solution approach takes as its starting point an initial deterministic schedule for the agents, computed using expected duration reasoning. This initial agent schedule is probabilistically analyzed to find likely points of failure, and then selectively strengthened based on this analysis. For each scheduled activity, the probability of failing and the impact that failure would have on the schedule's overall reward are calculated and used to focus schedule strengthening actions. Such actions generally entail fundamental trade-offs; for example, modifications that increase the certainty that a high-reward activity succeeds may decrease the schedule slack available to accommodate uncertainty during execution. We describe a principled approach to handling these trade-offs based on the schedule's "expected reward," using it as a metric to ensure that all schedule modifications are ultimately beneficial. Finally, we present experimental results obtained using a multi-agent simulation environment, which confirm that executing schedules strengthened in this way result in significantly higher rewards than are achieved by executing the corresponding initial schedules.

We study a multi-step hider-seeker game where the hider is moving on a graph and, in each step, the seeker is able to search c subsets of the graph nodes. We model this game as a zero-sum Bayesian game, which can be solved in weakly polynomial time in the players' action spaces. The seeker's action space is exponential in c, and both players' action spaces are exponential in the game horizon. To manage this intractability, we use a column/constraint generation approach for both players. This approach requires an oracle to determine best responses for each player. However, we show that computing a best response for the seeker is NP-hard, even for a single-step game when c is part of the input, and that computing a best response is NP-hard for both players for the multi-step game, even if c = 1. An integer programming formulation of the best response for the hider is practical for moderate horizons, but computing an exact seeker best response is impractical due to the exponential dependence on both c and the horizon. We therefore develop an approximate best response oracle with bounded suboptimality for the seeker. We prove performance bounds on the strategy that results when column/constraint generation with approximate best responses converges, and we measure the performance of our algorithm in simulations. In our experimental results, column/constraint generation converges to near-minimax strategies for both players fairly quickly.

For some well-known games, such as the Traveler's Dilemma or the Centipede Game, traditional game-theoretic solution concepts — most notably Nash equilibrium — predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization,   which exhibits the same qualitative behavior as that observed in experiments in many games of interest, including Traveler's Dilemma, the Centipede Game, Nash bargaining, and Bertrand competition.   As the name suggests, iterated regret minimization involves the iterated deletion of strategies that do not minimize regret.

A significantly complete account of the complexity underlying the computation of relevant solution concepts in compact coalitional games is provided. The starting investigation point is the setting of graph games, about which various long-standing open problems were stated in the literature. The paper gives an answer to most of them, and in addition provides new insights on this setting, by stating a number of complexity results about some relevant generalizations and specializations. The presented results also pave the way towards precisely carving the tractability frontier characterizing computation problems on compact coalitional games.

Computing a Nash equilibrium in multiplayer stochastic games is a notoriously difficult problem. Prior algorithms have been proven to converge in extremely limited settings and have only been tested on small problems. In contrast, we recently presented an algorithm for computing approximate jam/fold equilibrium strategies in a three-player no-limit Texas hold'em tournament — a very large real-world stochastic game of imperfect information. In this paper we show that it is possible for that algorithm to converge to a non-equilibrium strategy profile. However, we develop an ex post procedure that determines exactly how much each player can gain by deviating from his strategy, and confirm that the strategies computed in that earlier paper actually do constitute an epsilon-equilibrium for a very small epsilon (0.5% of the tournament entry fee). Next, we develop several new algorithms for computing a Nash equilibrium in multiplayer stochastic games (with perfect or imperfect information) which can provably never converge to a non-equilibrium. Experiments show that one of these algorithms outperforms the original algorithm on the same poker tournament. In short, we present the first algorithms for provably computing an epsilon-equilibrium of a large stochastic game for small epsilon. Finally, we present an efficient algorithm that minimizes external regret in both the perfect and imperfect information case.