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Multi-agent Optimal Control Problems and Variational Inequality Based Reformulations

In: Dynamic Games in Economics

Author

Listed:
  • George Leitmann

    (University of California, Berkeley)

  • Stefan Pickl

    (Universität der Bundeswehr München)

  • Zhengyu Wang

    (Nanjing University)

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.

Suggested Citation

  • George Leitmann & Stefan Pickl & Zhengyu Wang, 2014. "Multi-agent Optimal Control Problems and Variational Inequality Based Reformulations," Dynamic Modeling and Econometrics in Economics and Finance, in: Josef Haunschmied & Vladimir M. Veliov & Stefan Wrzaczek (ed.), Dynamic Games in Economics, edition 127, pages 205-217, Springer.
    • Handle: RePEc:spr:dymchp:978-3-642-54248-0_10
    DOI: 10.1007/978-3-642-54248-0_10
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