We join the goals of two giant and related fields of research in group decision-making that have historically had little contact: fair division, and efficient mechanism design with monetary payments. To do this we adopt the standard mechanism design paradigm where utility is assumed to be quasilinear and thus transferable across agents. We generalize the traditional binary criteria of envy-freeness, proportionality, and efficiency (welfare) to measures of degree that range between 0 and 1. We demonstrate that in the canonical fair division settings under any allocatively-efficient mechanism the worst-case welfare rate is 0 and disproportionality rate is 1; in other words, the worst-case results are as bad as possible. This strongly motivates an average-case analysis. We then set as the goal identification of a mechanism that achieves high welfare, low envy, and low disproportionality in expectation across a spectrum of fair division settings. We establish that the VCG mechanism is not a satisfactory candidate, but the redistribution mechanism of [Bailey, 1997; Cavallo, 2006] is.

Consider a multi-agent system in a dynamic and uncertain environment. Each agent's local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent's MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multi-agent variant of the multi-armed bandit problem is obtained as a special case.

A principal seeks production of a good within a limited time-frame with a hard deadline, after which any good procured has no value. There is inherent uncertainty in the production process, which in light of the deadline may warrant simultaneous production of multiple goods by multiple producers despite there being no marginal value for extra goods beyond the maximum quality good produced. This motivates a crowdsourcing model of procurement. We address efficient execution of such procurement from a social planner's perspective, taking account of and optimally balancing the value to the principal with the costs to producers (modeled as effort expenditure) while, crucially, contending with self-interest on the part of all players. A solution to this problem involves both an algorithmic aspect that determines an optimal effort level for each producer given the principal's value, and also an incentive mechanism that achieves equilibrium implementation of the socially optimal policy despite the principal privately observing his value, producers privately observing their skill levels and effort expenditure, and all acting only to maximize their own individual welfare. In contrast to popular "winner take all" contests, the efficient mechanism we propose involves a payment to every producer that expends non-zero effort in the efficient policy.

Much of AI is concerned with the design of intelligent agents. As we extend the ideas of mechanism design from economic theory, the mechanisms (or rules) become algorithmic and many new challenges surface. Starting with a short background on mechanism design theory, the aim of this paper is to provide a nontechnical exposition of recent results on dynamic incentive mechanisms, which provide rules for the coordination of agents in sequential decision problems. The framework of dynamic mechanism design embraces coordinated decision-making both in the context of uncertainty about the world external to an agent and also in regard to the dynamics of agent preferences.

Much of AI is concerned with the design of intelligent agents. A complementary challenge is to understand how to design “rules of encounter” by which to promote simple, robust and beneficial interactions between multiple intelligent agents. This is a natural development, as AI is increasingly used for automated decision making in real-world settings. As we extend the ideas of mechanism design from economic theory, the mechanisms (or rules) become algorithmic and many new challenges surface. Starting with a short background on mechanism design theory, the aim of this paper is to provide a nontechnical exposition of recent results on dynamic incentive mechanisms, which provide rules for the coordination of agents in sequential decision problems. The framework of dynamic mechanism design embraces coordinated decision-making both in the context of uncertainty about the world external to an agent and also in regard to the dynamics of agent preferences. In addition to tracing some recent developments, we point to ongoing research challenges.