Bicooperative games introduced by Bilbao are generalizations of conventional cooperative games. While in conventional cooperative games each player is allowed to make decisions between two alternatives, i.e., a defender or a defeater, in bicooperative games, he/she is allowed to do among three alternatives, i.e., a defender, a defeater or a fence-sitter. In this paper, we define a one-point solution called a normalized pseudo-Banzhaf value for bicooperative games. It is a normalization of the pseudo-Banzhaf value. The pseudo-Banzhaf value of a player is the expectation of marginal contribution under the assumption that each coalition not containing him/her is equally to arise. An axiomatization of the normalized pseudo-Banzhaf value is obtained.
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