Tableau-based decision procedures for logics of strategic ability in   multi-agent systems
  We develop an incremental tableau-based decision procedures for the   Alternating-time temporal logic ATL and some of its variants.   While running within the theoretically established complexity upper bound, we claim that our tableau is practically more efficient in the average case than other decision procedures for ATL known so far. Besides, the ease of its adaptation to variants of ATL demonstrates the flexibility of the proposed procedure. 
Valentin Goranko and Dmitry Shkatov