Compromise solutions based on bankruptcy In this paper we introduce a new family of compromise solutions for the class of compromise admissible games.These solutions extend bankruptcy rules.In particular, we show that the compromise extension of the runtothebank rule coincides with the barycentre of the core cover and characterise this rule by consistency.We also provide a characterisation of the TALfamily of rules. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Using Combinatorial Solutions and Atomic Weights to Play Competitive AI Clobber. Clobber is a twoplayer abstractstrategy game with no element of random chance. Introduced by game theorists Michael H. Albert, J. P. Grossman and Richard Nowakowski in 2001, it has subsequently been extensively studied for its combinatorial properties. Since 2005, it has been a major event in the Computer Olympiad.Although the concept of endgame tables has been introduced for Clobber and a use case suggested, usage of such has been scant in the Computer Olympiad or in the further development of other areas of Combinatorial Game Theory. We remedy this gap in this paper and demonstrate how to implement and use combinatorial solutions and atomic weights in an endgame table to perfect the play of Clobber by AI.We find that with the proper leveraging of endgame tables, it is possible to play perfectly on many Clobber positions of up to 70 pieces (on a 10x10 opening position) within time limits of most tournaments, and the solutions of Clobber on some significantly sized boards are likely reachable in the near future.