[Paper Review] Conventions and Coalitions in Repeated Games

S. Nageeb Ali, Ce Liu|arXiv (Cornell University)|Jun 1, 2019

Game Theory and Applications33 references4 citations

TL;DR

This paper develops a theory of repeated games with coalitional behavior, where players and coalitions can deviate but lack commitment. With perfect monitoring, all feasible and strictly individually rational payoffs can be supported via history-dependent conventions; however, secret side-payments lead to coalitional minmax outcomes, potentially restricting supportable payoffs to the core of the stage game.

ABSTRACT

We develop a theory of repeated interaction for coalitional behavior. We consider stage games where both individuals and coalitions may deviate. However, coalition members cannot commit to long-run behavior, and anticipate that today's actions influence tomorrow's behavior. We evaluate the degree to which history-dependence can deter coalitional deviations. If monitoring is perfect, every feasible and strictly individually rational payoff can be supported by history-dependent conventions. By contrast, if players can make secret side-payments to each other, every coalition achieves a coalitional minmax value, potentially reducing the set of supportable payoffs to the core of the stage game.

Motivation & Objective

• To model repeated interactions where both individuals and coalitions can deviate, without commitment to long-run strategies.
• To examine how history-dependent behavior can deter coalitional deviations in repeated games.
• To investigate the impact of monitoring accuracy and side-payment mechanisms on the set of supportable payoffs.
• To determine whether and how coalitional behavior alters the set of equilibrium outcomes compared to individual behavior.
• To compare the role of perfect monitoring versus secret side-payments in sustaining cooperative outcomes.

Proposed method

• Model stage games allowing deviations by both individuals and coalitions, with no commitment to long-run strategies.
• Use history-dependent conventions to sustain cooperation, where future play depends on past actions.
• Analyze the set of supportable payoffs under perfect monitoring, showing all feasible and strictly individually rational outcomes are achievable.
• Introduce secret side-payments between coalition members to model unobservable transfers.
• Define the coalitional minmax value as the worst payoff a coalition can enforce against the rest, under side-payment constraints.
• Compare the set of supportable payoffs under perfect monitoring versus side-payment environments, showing the core of the stage game becomes the limiting set.

Experimental results

Research questions

• RQ1 Can history-dependent conventions sustain all feasible and strictly individually rational payoffs in repeated games with coalitional deviations?
• RQ2 How does the presence of secret side-payments affect the set of supportable payoffs in repeated games?
• RQ3 What is the role of perfect monitoring in enabling cooperation when coalitions can deviate?
• RQ4 How does the coalitional minmax value constrain the set of achievable outcomes when side-payments are allowed?
• RQ5 In what way does the core of the stage game emerge as the limiting set of supportable payoffs under secret side-payments?

Key findings

• With perfect monitoring, every feasible and strictly individually rational payoff vector can be supported by history-dependent conventions.
• When players can make secret side-payments, every coalition achieves its coalitional minmax value, limiting the set of supportable payoffs.
• The introduction of secret side-payments reduces the set of supportable payoffs to the core of the stage game.
• Coalitional deviations are deterred by history-dependent strategies only when monitoring is perfect and side-payments are not possible.
• The core of the stage game becomes the minimal set of supportable payoffs when side-payments are allowed, due to the enforcement of coalitional minmax values.
• Perfect monitoring enables a broader set of equilibrium outcomes than when secret side-payments are present.