Even the simplest three way games have perplexing strategies. Consider splitting one dollar three ways by majority vote. The obvious strategy is for player A an

Even the simplest three way games have perplexing strategies. Consider splitting one dollar three ways by majority vote. The obvious strategy is for player A and player B to agree to 50-50 and leave out C. Of course, C offers A a better 60-40 split to ditch B. Then B offers A a 70-30 split. Etc.