Resolving social dilemmas with minimal reward transfer

TL;DR

The paper addresses multi-agent social dilemmas by introducing reward-transfer mechanisms that align individual incentives with collective welfare. It defines two core metrics, the symmetrical self-interest level $s^*$ and the general self-interest level $g^*$, and provides an algorithm—via a linear program—to compute minimal reward-transfer structures that make the socially optimal outcome dominant. Through analytical and experimental results on graphical multi-player dilemmas, it shows how transfer topology and the number of players affect the ease of achieving cooperation, and demonstrates sparse, efficient transfer patterns in many cases. The work yields a descriptive diagnostic of cooperation difficulty and a prescriptive method for realizing cooperation with minimal reward redistribution, with potential applications in mechanism design and environment modelling.

Abstract

Social dilemmas present a significant challenge in multi-agent cooperation because individuals are incentivised to behave in ways that undermine socially optimal outcomes. Consequently, self-interested agents often avoid collective behaviour. In response, we formalise social dilemmas and introduce a novel metric, the general self-interest level, to quantify the disparity between individual and group rationality in such scenarios. This metric represents the maximum proportion of their individual rewards that agents can retain while ensuring that a social welfare optimum becomes a dominant strategy. Our approach diverges from traditional concepts of altruism, instead focusing on strategic reward redistribution. By transferring rewards among agents in a manner that aligns individual and group incentives, rational agents will maximise collective welfare while pursuing their own interests. We provide an algorithm to compute efficient transfer structures for an arbitrary number of agents, and introduce novel multi-player social dilemma games to illustrate the effectiveness of our method. This work provides both a descriptive tool for analysing social dilemmas and a prescriptive solution for resolving them via efficient reward transfer contracts. Applications include mechanism design, where we can assess the impact on collaborative behaviour of modifications to models of environments.

Figures (2)

• Figure 1: Representations of the graphical dilemmas
• Figure 2: Social welfare of the Functional social dilemma