Existence of Risk Strategy Equilibrium in Games Having No Pure Strategy Nash Equilibrium

Two key properties defining an intelligent agent are reactive and pro-active. Before designing an intelligent agent for any multi-agent system, we need to first understand how agents should behave and interact in that particular application, which can be done by modelling the application as a game. To analyze these games and to understand how decision-makers interact, we can use a collection of analytical tools known as Game Theory. Risk strategies is a new kind of game-theoretic strategy. Simulations in previous work have shown that agents using risk strategies axe reactive as well as pro-active and thus have better performance than agents using other models or strategies in various applications. However, research on risk strategies has been focusing on formalization, application, and games having pure strategy Nash equilibrium. In this paper, we analyze a game having no pure strategy Nash equilibrium. We find that risk strategy equilibrium may exist even the game does not have pure strategy Nash equilibrium. We then summarize general conditions for the existence of risk strategy equilibrium. Simulation shows that agents using risk strategies also have better performance than agents using other existing strategies in a game having no pure strategy Nash equilibrium.