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Multiplayer boycotts in convex games

Robbert Fokkink, Hans de Munnik

TL;DR

The paper extends boycotts in cooperative games from one-on-one to coalitional boycotts in convex (supermodular) cooperative games, formalizing the $A,B$-boycott via $v^{AB}$ and showing that convexity implies $v^{AB} \le v$ for disjoint $A,B$, which makes boycotts impactful. It identifies the Shapley value $\phi$ as the unique efficient payoff that respects boycotts and has balanced impact, with the boycott impact given by $\phi(v)-\phi(v^{AB})$ and a decomposition tied to subgames. The authors derive how different actors are affected: participants see nonnegative impact, invariant players nonpositive, and nonparticipants can even profit, as demonstrated in explicit coalition examples such as triangle networks. They further analyze trade-network implications using block-graph models, showing how boycotts can shelter some players while fragmenting blocks and concentrating losses on key participants; they also acknowledge the computational challenges of extending these analyses to realistic networks.

Abstract

We extend the notion of boycotts in cooperative games from one-on-one boycotts between single players to boycotts between coalitions. We prove that convex games offer a proper setting for studying the impact of boycotts. Boycotts have a heterogeneous effect. Individual players that are targeted by many-on-one boycotts suffer most, while non-participating players may actually benefit from a boycott.

Multiplayer boycotts in convex games

TL;DR

The paper extends boycotts in cooperative games from one-on-one to coalitional boycotts in convex (supermodular) cooperative games, formalizing the -boycott via and showing that convexity implies for disjoint , which makes boycotts impactful. It identifies the Shapley value as the unique efficient payoff that respects boycotts and has balanced impact, with the boycott impact given by and a decomposition tied to subgames. The authors derive how different actors are affected: participants see nonnegative impact, invariant players nonpositive, and nonparticipants can even profit, as demonstrated in explicit coalition examples such as triangle networks. They further analyze trade-network implications using block-graph models, showing how boycotts can shelter some players while fragmenting blocks and concentrating losses on key participants; they also acknowledge the computational challenges of extending these analyses to realistic networks.

Abstract

We extend the notion of boycotts in cooperative games from one-on-one boycotts between single players to boycotts between coalitions. We prove that convex games offer a proper setting for studying the impact of boycotts. Boycotts have a heterogeneous effect. Individual players that are targeted by many-on-one boycotts suffer most, while non-participating players may actually benefit from a boycott.
Paper Structure (3 sections, 5 theorems, 17 equations, 1 table)

This paper contains 3 sections, 5 theorems, 17 equations, 1 table.

Table of Contents

  1. Boycott games
  2. The impact of a boycott
  3. The impact of boycotts on trade blocks

Key Result

Lemma 2

If $A$ and $B$ are disjointly productive, then for all $A'\subset A$ and $B'\subset B$ and $S\subset N\setminus(A\cup B)$

Theorems & Definitions (16)

  • Definition 1: Besner
  • Lemma 2
  • proof
  • Definition 3
  • Definition 4
  • Theorem 5
  • proof
  • Theorem 6
  • proof
  • Definition 7
  • ...and 6 more