Games with few players 
Gergely Lakatos1, Benedek Nagy2
1 University of Debrecen
e-mail: gergo_gent@freemail.hu
2 Department of Computer Science, University of Debrecen
e-mail: nbenedek@inf.unideb.hu
Abstract
In this paper we investigate the multiplayer games with few participants. In these games we have less participants as the usual in n-player games. For this reason we use a variation of the methods which are used for the 2-player zero-sum strategic games. Some definitions are given analogously and in some cases more definitions are needed because loosing the special case of 2 persons. The game-trees are built with the so-called expected outcome-vectors. The situation – comparing to the 2-player games – looks more like the non-zero-sum games, because more values are needed to calculate the “optimal” strategy.  
Assuming at least 3 players in a game it is not guaranteed that any of the players has a non-loosing strategy. In this paper we present some methods (based on the well-known minimax algorithm) for evaluation of the games. Methods to help for making decisions for the players are also shown both with partial and full evaluation of the game-tree. The question of “rational strategy” is interesting in these games, as for example at the prisoner’s dilemma.

Categories and Subject Descriptors: I.2.1 [Artificial Intelligence]: Applications and Expert Systems - games; G.2.2 [Discrete Mathematics]: Graph Theory - trees
Key Words and Phrases: game theory, artificial intelligence, multiplayer game trees
References
[1] R. D. Luce and H. Raiffa: Games and decisions, Dower, 1989. 
[2] S. J. Russel and P. Norvig: Artificial Intelligence. A Modern Approach. Panem/Prentice Hall, 2000.
[3] M. J. Osborne and A. Rubinstein: A course in game theory, MIT, 1994.

Postal addresses
Gergely Lakatos					Benedek Nagy
University of Debrecen				Department of Computer Science
Hungary						Institute of Informatics
			University of Debrecen
		H-4010 Debrecen, PO Box 12
						Hungary