THE SYMMETRICAL RENDEZVOUS-EVASION GAME

E. J. Anderson and R. R. Weber, J. Appl. Probab., 28 (1990), pp. 839-8 51, considered the problem of two rendezvousers, R-1, R-2, randomly pl aced among n indistinguishable locations, who seek to meet in least ex pected time, using the same mixed strategy. We retain their dynamics b ut modify the rendezvousers' aim to meeting each other before either e ncounters an enemy searcher S. We solve this zero-sum game in minimal space (3 locations) and time (2 steps after placement), and find that optimal play requires that the rendezvous team use a mixture over beha vioral strategies. While such complicated strategies are known to be n ecessary in principal for team games (the theory of Isbell and Alpern) , we believe this is the first naturally occuring game where such a so lution is derived. (An earlier paper by Lim solved a similar game in w hich R-1 and R-2 were allowed to use different strategies and joint ra ndomization.).