A fair dynamical game over networks

A model of dynamical network game is presented that provides a fair environment for the participants without assuming any trusted parties. A game is regarded as identical discrete-time dynamical systems running individually on each participant's computer. They are driven by the identical input at each discrete-time clock tick. The participants in the equal condition decide the input at the same time. The identity and the equality are realized by the lock-step synchronization well-established on the basis of cryptographic commitment and digital signature. A new technique that works for chaotic systems is proposed to spoil attacks by intentional delay and robot players. This technique is based on the notion of fair random noise generated out of a part of the input to be injected to the other part of the input. An example implementation of pinball is reported.