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. Shenoy (1980) 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 Rubinstein (1980). 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 (1980) and it is always non-empty for simple committee games with linear preferences. Other attractive properties are also proved. 1. Introduction Our game model is the one considered by Shenoy [1], committee game that generalizes the voting model introduced by von Neumann and Morgenstern [2] under the name of simple game. A committee game consists in any finite group of persons who have to pick one option from the finite given set of outcomes through a voting rule by which the committee arrives at a decision. The rule is designed such that the decision of the committee will consist of a unique outcome. Any player is allowed to suggest any alternative for consideration by the committee and players get their payoffs only when the committee has made a decision. In such a social choice context, the question generally asked is how a player should behave or should vote when solicited to join a coalition in order to decide over a status quo. Another relevant issue is to determine what could be a suitable choice of a given player if he is given the opportunity to introduce a motion. The core is a solution concept in which any player is recommended to vote for against whenever he strictly prefers to (i.e., ) ( is the player utility function; instead of considering utilities vectors one could consider that each member of the committee has a preference relation which is a weak order on the set of all outcomes, thus yielding a preference profile) if is opposed to . Furthermore, a committee member should propose an outcome if it is the (or one of his) best element in the core. An outcome belongs to the core if it is undominated, that is, there does not exist another outcome , a coalition powerful on and all members of which are strictly better off at than at .
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