A theory of farsightedness in committee games (Q457864)

Summary: We study the committee decision making process using game theory. A committee here refers to any group of people who have to select one option from a given set of alternatives under a specified rule. \textit{P. P. Shenoy} [Manage. Sci. 26, 387--400 (1980; Zbl 0451.90006)] introduced two solution concepts, namely, the one-core and a version of bargaining set for committee games. Shortcomings of these solutions concepts are raised and discussed in this paper. These shortcomings are resolved by introducing two new solutions concepts: the farsighted one-core and the bargaining set revised, inspired by an idea of farsightedness initially defined by \textit{A. Rubinstein} [J. Econ. Theory 23, 150--159 (1980; Zbl 0457.90007)]. It is shown that the farsighted one-core is always non-empty and is better than the one-core. In a well-specified sense, the bargaining set revised is also better than the bargaining set as defined by Shenoy [loc. cit.] and it is always non-empty for simple committee games with linear preferences. Other attractive properties are also proved.