Towards Decision Support in Reciprocation

TL;DR

This paper introduces a simple, analyzable model of reciprocal interactions over time, predicting how such interactions stabilize and evolve in networks, aiding decision-making in repeated social exchanges.

Contribution

The paper proposes a novel, formal model of reciprocation that predicts the evolution and stabilization of interactions in networks, with analytical results for specific cases and simulations for others.

Findings

Interactions converge to specific limits under certain attitudes.

In networks with all inertia-based agents, actions become equal.

The model can predict interaction development and inform decision-making.

Abstract

People often interact repeatedly: with relatives, through file sharing, in politics, etc. Many such interactions are reciprocal: reacting to the actions of the other. In order to facilitate decisions regarding reciprocal interactions, we analyze the development of reciprocation over time. To this end, we propose a model for such interactions that is simple enough to enable formal analysis, but is sufficient to predict how such interactions will evolve. Inspired by existing models of international interactions and arguments between spouses, we suggest a model with two reciprocating attitudes where an agent's action is a weighted combination of the others' last actions (reacting) and either i) her innate kindness, or ii) her own last action (inertia). We analyze a network of repeatedly interacting agents, each having one of these attitudes, and prove that their actions converge to specific limits. Convergence means that the interaction stabilizes, and the limits indicate the behavior after the stabilization. For two agents, we describe the interaction process and find the limit values. For a general connected network, we find these limit values if all the agents employ the second attitude, and show that the agents' actions then all become equal. In the other cases, we study the limit values using simulations. We discuss how these results predict the development of the interaction and can be used to help agents decide on their behavior.