Communications in Mathematical Sciences

Volume 17 (2019)

Number 4

Hyperbolic consensus games

Pages: 1005 – 1024



Rinaldo M. Colombo (Istituto Nazionale di Alta Matematica (INdAM) Unit, University of Brescia, Italy)

Mauro Garavello (Department of Mathematics and its Applications, University of Milano Bicocca, Milano, Italy)


We introduce the use of conservation laws in multi-player consensus games. Indeed, a general non-anticipative strategy is proposed within a rigorous analytic framework. By means of numerical integrations, we describe peculiar features of this strategy, such as its effectiveness, the automatic formation of coalitions and the effects of competitions.


hyperbolic consensus game, multi-agent consensus strategies, differential games, instantaneous control

2010 Mathematics Subject Classification

35L65, 91A23, 93B52

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Part of this work was supported by the PRIN 2015 project Hyperbolic Systems of Conservation Laws and Fluid Dynamics: Analysis and Applications and by the GNAMPA 2017 project Conservation Laws: from Theory to Technology. The IBM Power Systems Academic Initiative substantially contributed to the numerical integrations.

Received 20 March 2018

Accepted 23 March 2019

Published 25 October 2019