A Stackelberg Game Model of Flocking

TL;DR

This paper models a Stackelberg game where two agents decide on arrival times to optimize rewards, exploring cooperation and competition dynamics with a focus on equilibrium analysis.

Contribution

It introduces a relaxed flock formation game allowing close arrival times and analyzes the subgame perfect equilibrium in both continuous and discrete time settings.

Findings

Equilibrium strategies depend on reward and penalty parameters.

Allowing a time window for arrival fosters cooperative behavior.

The model extends previous work by relaxing strict arrival time equality.

Abstract

We study a Stackelberg game to examine how two agents determine to cooperate while competing with each other. Each selects an arrival time to a destination, the earlier one fetching a higher reward. There is, however, an inherent penalty in arriving too early as well as a risk in traveling alone. This gives rise to the possibility of the agents cooperating by traveling together while competing for the reward. In our prior work [1] we studied this problem as a sequential game among a set of $N$ competing agents in continuous time, and defined the formation of a group traveling together as arriving at exactly the same time. In the present study, we relax this definition to allow arrival times within a small window, and study a 2-agent game in both continuous and discrete time, referred to as the flock formation game. We derive and examine the properties of the subgame perfect equilibrium (SPE) of this game.