Two-player trick-taking games on bipartite tournaments.

We consider a two-person game played on a bipartite tournament with equal size parts. The game is modeled after trick-taking card games like bridge or euchre. The two players, South and North, each receive one of the parts as their hand, and the arcs from a vertex in one hand beat the corresponding vertices in the other hand. The game is played over rounds called tricks where the number of tricks is equal to the number of vertices in each player’s hand. At the beginning of the game, one player is designated as the leader, and they play the first vertex of the first trick after which the other player, the follower, plays one of their vertices. Whichever player’s vertex beats the other vertex wins the trick and becomes the leader for next trick. The goal of the game is to win as many tricks as possible. On account of the changing leads, deducing an optimal strategy is difficult. In this paper we derive some bounds for the scores achieved on different tournaments and compare these to some of the corresponding bounds derived for a game where the tournament has no directed cycles.