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Peer Selection with Friends and Enemies

Francis Bloch, Bhaskar Dutta, Marcin Dziubiński

TL;DR

This work addresses designing DSIC, efficient probabilistic mechanisms for peer selection when agents have bilateral friendship/enmity relationships and a binary status $N$ realized by nature. It provides (i) exact DSIC and efficiency constructions when the network is known, via three mechanism templates that exploit impartials, enemies, or friends, under specific intersection conditions; (ii) impossibility results when the network is unknown, followed by two second-best mechanisms (random dictatorship and duples) and a comparative efficiency analysis; and (iii) a sharp characterization under structural balance showing when efficient DSIC mechanisms exist. The results yield a nuanced view of how network structure and information about relationships impact incentive compatibility and allocation efficiency, offering practical guidance for designing fair, non-monetary peer selection rules in networked settings. The findings have potential implications for policy design and resource allocation in settings where social ties influence preferences and outcomes.

Abstract

A planner wants to select one agent out of n agents on the basis of a binary characteristic that is commonly known to all agents but is not observed by the planner. Any pair of agents can either be friends or enemies or impartials of each other. An individual's most preferred outcome is that she be selected. If she is not selected, then she would prefer that a friend be selected, and if neither she herself or a friend is selected, then she would prefer that an impartial agent be selected. Finally, her least preferred outcome is that an enemy be selected. The planner wants to design a dominant strategy incentive compatible mechanism in order to be able choose a desirable agent. We derive sufficient conditions for existence of efficient and DSIC mechanisms when the planner knows the bilateral relationships between agents. We also show that if the planner does not know these relationships, then there is no efficient and DSIC mechanism and we compare the relative efficiency of two ``second-best'' DSIC mechanisms. Finally, we obtain sharp characterization results when the network of friends and enemies satisfies structural balance.

Peer Selection with Friends and Enemies

TL;DR

This work addresses designing DSIC, efficient probabilistic mechanisms for peer selection when agents have bilateral friendship/enmity relationships and a binary status realized by nature. It provides (i) exact DSIC and efficiency constructions when the network is known, via three mechanism templates that exploit impartials, enemies, or friends, under specific intersection conditions; (ii) impossibility results when the network is unknown, followed by two second-best mechanisms (random dictatorship and duples) and a comparative efficiency analysis; and (iii) a sharp characterization under structural balance showing when efficient DSIC mechanisms exist. The results yield a nuanced view of how network structure and information about relationships impact incentive compatibility and allocation efficiency, offering practical guidance for designing fair, non-monetary peer selection rules in networked settings. The findings have potential implications for policy design and resource allocation in settings where social ties influence preferences and outcomes.

Abstract

A planner wants to select one agent out of n agents on the basis of a binary characteristic that is commonly known to all agents but is not observed by the planner. Any pair of agents can either be friends or enemies or impartials of each other. An individual's most preferred outcome is that she be selected. If she is not selected, then she would prefer that a friend be selected, and if neither she herself or a friend is selected, then she would prefer that an impartial agent be selected. Finally, her least preferred outcome is that an enemy be selected. The planner wants to design a dominant strategy incentive compatible mechanism in order to be able choose a desirable agent. We derive sufficient conditions for existence of efficient and DSIC mechanisms when the planner knows the bilateral relationships between agents. We also show that if the planner does not know these relationships, then there is no efficient and DSIC mechanism and we compare the relative efficiency of two ``second-best'' DSIC mechanisms. Finally, we obtain sharp characterization results when the network of friends and enemies satisfies structural balance.

Paper Structure

This paper contains 11 sections, 10 theorems, 42 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Literature
  3. The Model
  4. Known Relationships Networks
  5. Planner knows the sets $I_i$ of each $i$
  6. The planner knows the sets $E_i$ for all agents $i \in V$
  7. The planner knows the sets $F_i$ for all agents $i \in V$
  8. Unknown Relationships Networks
  9. Structural Balance
  10. Planner knows the network
  11. The planner does not know the network

Key Result

Theorem 1

Suppose the planner knows the sets $I_i$ for all $i \in V$. Then, $g^1$ is valid and DSIC. Moreover, if the Intersection Condition I is satisfied, then $g^1$ is efficient.

Figures (1)

  • Figure 1: Two states of the world with $n = 4$ agents. The encircled nodes correspond to the needy agents.

Theorems & Definitions (18)

  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Theorem 3
  • Theorem 4
  • proof
  • Proposition 1
  • Proposition 2
  • ...and 8 more