Abstract
This paper presents general solutions for stochastic square duels with continuous interfiring times and various firing strategies such as standby (S), concentrated (C), seperated (I) and random (R) firings. Analysis of these square duels with negative exponential interfiring times and equivalent values of rates of fire and single shot kill probabilities reveal three important facts: i) Strategy (C) is advantageous against the opponent's strategy (S) and the advantage becomes more pronounced for lower values of single shot kill probabilities. ii) Strategy (I) is always better than strategy (C) no matter which of (C) and (I) the opponent uses and its relative advantege increases to a quarter as single shot kill probabilities increase to one but decreases to zero as they go to zero. iii) However, strategy (I) has no advantage over strategy (C) for small values of single shot kill probabilities. In this paper, square duels with strategies (C) and (I) are based on the assumptions that duelists are homogeneous and both duelists of one side fire simultaneously. The problem of relaxing these assumptions and extension of square ($2 \times 2$) duels to more general ($m \times n) duels are now being investigated.