Modeling Multi-Agent Interactions through State Transitions in Games of Deterrence

Michel Rudnianski and Hélène Bestougeff

When considering assistance in the frame of task achievement, multi-agent interaction can be defined as a set of "request / commitment" pairs. One key problem is then preventing congestion, that is, to avoid a steady state of the system such that communication flow drops under a predefined level. In [Bestougeff and Rudnianski 1988a, 1988b], we have introduced an interaction model for a multi-agent system based on a two-player game of deterrence together with a control algorithm derived from the game Boolean solution set. The approach was based on a step by step analysis. The general case led, for a large number of agents, to numerous equilibria. Fuzzyfying the solution set [Rudnianski and Bestougeff 1997, 2000], enabled an ordering on this set and improvement of the decision procedure. In order to refine strategies selection, we shall now analyze which state transitions lead to congestion. We present in section 1, the main definitions and properties of games of deterrence and graphs of deterrence, then in section 2, agent interactions modeling using two player games of deterrence and analysis of congestion control analysis.

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