# On Characterizations of Potential and Ordinal Potential Games

arXiv: https://arxiv.org/abs/2405.06253 · HTML: https://mlsanity.com/paper/2405.06253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2024.

## Built on by (most cited first, 1 of 1)

- [Almost Sure Convergence of Networked Policy Gradient over Time-Varying Networks in Markov Potential Games](https://mlsanity.com/paper/2410.20075/) (2024)

## Abstract (arXiv)

This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with multi-dimensional action spaces, which require differentiable cost functions. Then, we provide a necessary and sufficient conditions for a game to have a potential function by investigating the structure of a potential function in terms of the players' cost differences, as opposed to differentials. This condition provides a systematic way for construction of a potential function, which is applied to network congestion games, as an example. Finally, we provide some sufficient conditions for a game to be ordinal potential and generalized ordinal potential.