Abstract
We introduce the concept of a horizon-K farsighted set to study the influence of the degree of farsightedness on network stability. The concept generalizes existing concepts where all players are either fully myopic or fully farsighted. A set of networks G_{K} is a horizon-K farsighted set if three conditions are satisfied. First, external deviations should be horizon-K deterred. Second, from any network outside of G_{K} there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in G_{K}. Third, there is no proper subset of G_{K} satisfying the first two conditions. We show that a horizon-K farsighted set always exists and that the horizon-1 farsighted set G_{1} is always unique. For generic allocation rules, the set G_{1} always contains a horizon-K farsighted set for any K. We provide easy to verify conditions for a set of networks to be a horizon-K farsighted set, and we consider the efficiency of networks in horizon-K farsighted sets. We discuss the effects of players with different horizons in an example of criminal networks.
Highlights
Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy and how they vote
We introduce the concept of a horizon-K farsighted set to study the influence of the degree of farsightedness on network stability
From any network outside of G K there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in G K
Summary
Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy and how they vote. The decision to initiate a change to the network is based on rules that weigh improving paths that might follow their change, but which are not necessarily improving paths for the players who made the initial change Using computer simulations they show that, in the co-author model of Jackson and Wolinsky (1996), limited farsighted players can overcome the tension between stability and efficiency only if the number of players is small. Their concept is a refinement of the set of pairwise stable networks.
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