Equilibria on a Game with Discrete Variables

TL;DR

This paper explores equilibrium concepts in a game involving discrete variables, specifically focusing on a multi-player lot-sizing problem, highlighting computational challenges and potential strategies in real-world scenarios.

Contribution

It introduces a novel game-theoretic model with discrete variables and analyzes strategies, addressing a gap in equilibrium analysis for such settings.

Findings

Identifies computational difficulties in finding equilibria with discrete variables.

Proposes strategies relevant to real-world multi-player lot-sizing games.

Provides an illustrative example demonstrating the concepts.

Abstract

Equilibrium in Economics has been seldom addressed in a situation where some variables are discrete. This work introduces a problem related to lot-sizing with several players, and analyses some strategies which are likely to be found in real world games. An illustration with a simple example is presented, with concerns about the difficulty of the problem and computation possibilities.