Current study aims to analyse the Russian-Ukrainian conflict and related economic and political sanctions in the framework of game theory, debate the possible outcomes and to suggest the measures, which could contribute to the successful solution of the conflict. “The chicken dilemma” and “the dollar auction game” have been selected among various models for deeper analyse as matching the starting criteria and possible rational options for conflict endgame. The criteria of success and predicted success scenarios are seen different, but as the authors see it, in theory both Russia and the EU could be motivated to “pull back”. However, their willingness not to “lose the game” is determined in real terms by the “breaking points” that both parties to the conflict would like to avoid.