Jun Kobayashi

In this paper, I show that persons reach unanimous opinions even when they have different initial opinions and different social influences in social influence networks. Friedkin and Johnsen introduced a model of social influence networks, and identified conditions for initially diverse opinions to converge. However, they did not examine conditions of "unanimous" convergence. Hence, I provide sufficient conditions of such unanimous consensus by focusing on three typical but conflicting social influences: the equal influence, the influence of the lowest opinion, and no influence. I show that unanimous opinions occur even when persons have antagonistic social influences such as the equal influence and the influence of the lowest opinion. I also demonstrate that the most cooperative type is the equal influence, but the most central type is the no influence.

     This note extends the concept of evolutionarily stable strategy from symmetric two-player random matching games to games with more than two players. First, I extend the definition of evolutionarily stable strategy. Second, I show, as the necessary and sufficient condition of the definition, the procedure to check whether a strategy is evolutionarily stable or not.

     This article argues that, during repeated unanimous consensus makings, evaluating strategies that assign a whole weight to a specific individual are evolutionarily stable. Evaluating strategies represent ways of evaluating alternatives with respect to others' utilities. I derive the following three conclusions: first, when a consensus is reached by two individuals, the maximin strategy evolves rather than the utilitarian strategy or the selfish strategy. Second, this result is robust for consensuses comprising two or more individuals. Finally, in general, concerns for a specific individual evolve.

     The article shows that various types of mutual concerns yield a unanimous evaluation function after infinitely repeated evaluation formations. Harsanyi stated that the unanimous utilitarian principle yields a unanimous evaluation function. The question arises: Do various types of concerns yield unanimity? The model assumes that each individual's evaluation functiion is formed repeatedly through convex linear combinatioin of all individuals' utility values in the previous time period. (1) It is concluded that mutual concerns yield a unanimous limiting evaluatiion function for any alternative whatever initial utility functions are and whatever evaluating principles are. (2) It is also obtained that some individuals' concerns for the same one combined with the rest individuals' concerns for all yield unanimity. It is derived from these conclusions that the maximin principle and the selfish principle have the same characteristic, and that the utilitarian principle and the maximin principle coexist.