Studies On Payoff Distribution In Cooperative Games

For a long time, in a cooperative game, how to determine the payoff vectors is a complexissue has been studied by scholars in many fields. The Shapley value appears in1953, as theorigin of power index has solved the problem of non-uniqueness of bargaining solution, and nowit has been widely used in reality. On this basis, with the practical problems become morecomplicated the traditional power indices unable to meet people’s needs. Thus, more and morepower allocation algorithms appear, and the extension of traditional algorithms also endless. Thispaper will continue the thinking of predecessors’ and then do some research and exploration ofspecific algorithms in cooperative games.In this paper, we talk about in simple cooperative games, and make the unit weight ofparticipants as the fundamental staring point, focus on the preference of participants to give twonew power indices from two different view, we call it weighted power index I and weightedpower index II. In the process of calculating the weighted power index I, the probability ofcoalition formation is only determined by the preference of its members, and then computingpower by weight radio. But in weighted power index II, participants’ power is directly obtainedby its maximum unit weight. Thereafter, we provide the axiomatic characteristics of the twoweighted power indices, including dummy, standardization, replacement and mergeable. At last,we present another idea of bargaining solution in cooperative games, and dentally talk about thehomogeneous and inhomogeneous condition in three-people cooperative games.