We study Bayesian automated mechanism design in unstructured dynamic environments, where a principal repeatedly interacts with an agent, and takes actions based on the strategic agent's report of the current state of the world. Both the principal and the agent can have arbitrary and potentially different valuations for the actions taken, possibly also depending on the actual state of the world. Moreover, at any time, the state of the world may evolve arbitrarily depending on the action taken by the principal. The goal is to compute an optimal mechanism which maximizes the principal's utility in the face of the self-interested strategic agent.We give an efficient algorithm for computing optimal mechanisms, with or without payments, under different individual-rationality constraints, when the time horizon is constant. Our algorithm is based on a sophisticated linear program formulation, which can be customized in various ways to accommodate richer constraints. For environments with large time horizons, we show that the principal's optimal utility is hard to approximate within a certain constant factor, complementing our algorithmic result. These results paint a relatively complete picture for automated dynamic mechanism design in unstructured environments. We further consider a special case of the problem where the agent is myopic, and give a refined efficient algorithm whose time complexity scales linearly in the time horizon. In the full version of the paper, we show that memoryless mechanisms, which are without loss of generality optimal in Markov decision processes without strategic behavior, do not provide a good solution for our problem, in terms of both optimality and computational tractability. Moreover, we present experimental results where our algorithms are applied to synthetic dynamic environments with different characteristics, which not only serve as a proof of concept for our algorithms, but also exhibit intriguing phenomena in dynamic mechanism design.
Hanrui Zhang (Duke University)
Vincent Conitzer (Duke University)
Vincent Conitzer is the Kimberly J. Jenkins University Professor of New Technologies and Professor of Computer Science, Professor of Economics, and Professor of Philosophy at Duke University. He received Ph.D. (2006) and M.S. (2003) degrees in Computer Science from Carnegie Mellon University, and an A.B. (2001) degree in Applied Mathematics from Harvard University. Conitzer works on artificial intelligence (AI). Much of his work has focused on AI and game theory, for example designing algorithms for the optimal strategic placement of defensive resources. More recently, he has started to work on AI and ethics: how should we determine the objectives that AI systems pursue, when these objectives have complex effects on various stakeholders? Conitzer has received the Social Choice and Welfare Prize, a Presidential Early Career Award for Scientists and Engineers (PECASE), the IJCAI Computers and Thought Award, an NSF CAREER award, the inaugural Victor Lesser dissertation award, an honorable mention for the ACM dissertation award, and several awards for papers and service at the AAAI and AAMAS conferences. He has also been named a Guggenheim Fellow, a Sloan Fellow, a Kavli Fellow, a Bass Fellow, an ACM Fellow, a AAAI Fellow, and one of AI's Ten to Watch. He has served as program and/or general chair of the AAAI, AAMAS, AIES, COMSOC, and EC conferences. Conitzer and Preston McAfee were the founding Editors-in-Chief of the ACM Transactions on Economics and Computation (TEAC).
More from the Same Authors
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