Multi-agent Optimal Control Problems and Variational Inequality Based Reformulations

George Leitmann (), Stefan Pickl () and Zhengyu Wang ()
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George Leitmann: University of California, Berkeley
Stefan Pickl: Universität der Bundeswehr München
Zhengyu Wang: Nanjing University

A chapter in Dynamic Games in Economics, 2014, pp 205-217 from Springer

Abstract: Abstract The multi-agent optimal control problem involves a decision process with multiple agents, where each agent solves an optimal control problem with the individual cost functional and strategy set, and the cost functional is dependent on all the other agents’ state and/or control variables. Here the “agent” can be understood as a true decision maker, or as an abstract optimization criterion. The strategy sets, along with admissible control set, are often described by a system of parameterized ordinary differential/difference equations (the state dynamic) or partial differential equations, and in realistic settings they may be dependent on the rivals’s variables due to, for example, certain constraints from the common resources. This chapter describes the multi-agent optimal control problem, and studies the reformulation of a system of differential equations constrained by parameterized variational inequalities, along with some initial and/or boundary conditions. This reformulation presents differential equations, variational inequalities, and equilibrium conditions in a systematic way, and is advantageous since it can be treated as a system of differential algebraic equations, for which abundant theory and algorithms are available.

Keywords: Variational Inequality; Optimal Control Problem; Differential Algebraic Equation; Quasi Variational Inequality; Nash Equilibrium Problem (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-642-54248-0_10

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DOI: 10.1007/978-3-642-54248-0_10

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