Minimally Farsighted Unstable Networks

We propose the notion of minimal instability to determine the networks that are more likely to emerge in the long run when agents are farsighted. A network is minimally farsighted unstable if there is no other network which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare networks by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating networks. We next compare networks in terms of their absorbtiveness by comparing both their sets of farsighted defeating networks (i.e. in terms of their stability) and their sets of farsighted defeated networks (i.e. in terms of their reachability). A network is maximally farsighted absorbing if there is no other network which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable networks and maximally farsighted absorbing networks, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.