Optimal Relative Performance Criteria in Mean Field Contribution Games

to appear in Mathematics of Operations Research

37 Pages Posted: 8 Feb 2021 Last revised: 14 Nov 2022

See all articles by Zhou Zhou

Zhou Zhou

The University of Sydney

Date Written: December 4, 2020

Abstract

We consider mean-field contribution games, where players in a team chooses some effort level at each time period, and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the expected reward of her own share subject to her cost of effort. To reduce free-rider issue, we propose some relative performance criteria (RPC), based on which the reward is redistributed to each player. We are interested in those RPCs which implement the optimal solution for the corresponding centralized problem, and we call such RPC an optimal one. That is, the expected payoff of each player under the equilibrium associated with an optimal RPC is as large as the value induced by the corresponding problem where players completely cooperate.

We first analyze a one-period model with homogeneous players, and obtain natural RPCs of different forms. Then we generalize these results to a multi-period model in discrete time. Next, we investigate a two-layer mean-field game: The top-layer is an inter-team game (team-wise competition) in which the reward of a team is impacted by the relative achievement of the team with respect to other teams; the bottom layer is an intra-team contribution game where an RPC is implemented for reward redistribution among team members. We establish the existence of equilibria for the two-layer game and characterize the intra-team optimal RPC. Finally, we extend the (one-layer) results of optimal RPCs to the continuous-time setup as well as to the case with heterogenous players.

Keywords: optimal relative performance criteria, mean field contribution games, free rider issue, centralized control, two-layer mean field game

JEL Classification: C73, C02

Suggested Citation

Zhou, Zhou, Optimal Relative Performance Criteria in Mean Field Contribution Games (December 4, 2020). to appear in Mathematics of Operations Research, Available at SSRN: https://ssrn.com/abstract=3742584 or http://dx.doi.org/10.2139/ssrn.3742584

Zhou Zhou (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
108
Abstract Views
433
Rank
453,810
PlumX Metrics