  We study a simple example of a sequential game illustrating problems
connected with making rational decisions that are universal for social
sciences. The set of chooser's optimal decisions that manifest his preferences
in case of a constant strategy of the adversary (the offering player), is
investigated. It turns out that the order imposed by the player's rational
preferences can be intransitive. The presented quantitative results imply a
revision of the "common sense" opinions stating that preferences showing
intransitivity are paradoxical and undesired.
