This article deals with the allocation of objects where each agent receives a single item. Starting from an initial endowment, the agents can be better off by exchanging their objects. However, not all trades are likely because some participants are unable to communicate. By considering that the agents are embedded in a social network, we propose to study the possible allocations emerging from a sequence of simple swaps between pairs of neighbors in the network. This model raises natural questions regarding (i) the reachability of a given full allocation, (ii) the ability of an agent to obtain a given object, and (iii) the search of Paretoefficient allocations. We investigate the complexity of these problems by providing, according to the structure of the social network, polynomial and NP-complete cases.

We study the fair division problem consisting in allocating one item per agent so as to avoid (or minimize) envy, in a setting where only agents connected in a given social network may experience envy. In a variant of the problem, agents themselves can be located on the network by the central authority. These problems turn out to be difficult even on very simple graph structures, but we identify several tractable cases. We further provide practical algorithms and experimental insights.

This article deals with strategic voting under incomplete information. We propose a descriptive model, inspired by political elections, where the information about the vote intentions of the electorate comes from public opinion polls and a social network, modeled as a graph over the voters. The voters are assumed to be confident in the poll and they update the communicated results with the information they get from their relatives in the social network. We consider an iterative voting model based on this behavior and study the associated “poll-confident” dynamics. In this context, we ask the question of manipulation by the polling institute.