InflGame documentation

Date: December 03, 2025

The InflGame package lets you model influencer games via adaptive dynamics (gradient ascent along the reward function) and MARL (multi agent reinforcement learning.) Through these methods players maximize their reward. In symmetric games this leds to a symmetric Nash under certian circumstances.

Influencer Games

The main focus of this package is to provide a framework to studying the dynamics of spatial influence in a multi-player resource competition game. The package takes two paths to study influence games

1. Adaptive dynamics (gradient ascent of the reward vectors)

   • By following the gradient of the rewards available to a player they can move toward a maxima value for their return

2. Multi Agent Reinforcement learning

   • Q-learning: Independent Q-learning

   • Deep reinforcement learning from [RAYRL](https://docs.ray.io/en/latest/rllib/index.html)

The project is based on the work of Mark Lovett, Feng Fu at Dartmouth Mathematics with insights from Alex McAvoy at UNC .

• Original paper with theoretical results will published in early 2026.

An influence game’s form

The payoff for player \(i\) ( \(u_i(\mathbf{x})\) ) of an influence game over a resource distribution \(B=\{B(b)|b\in \mathbb B\}\) is the expected return of resources for a player. Given a discrete resource distribution \(u_i\) has the following form

\[u_i(\mathbf{x})=\sum_{b\in \mathbb{B}} B(b)G_{i}(x_i,x_{-i},b).\]

For a continuous resource distribution the game has the following form

\[u_i(\mathbf{x})=\int_{\mathbb{B}} B(b)G_{i}(x_i,x_{-i},b)db.\]

Where \(G_{i}(x_i,x_{-i},b)\) is the probability of influence and is the ratio of a players influence over a resource point to the sum of all influence on that point. The probability of influence is defined as

\[G_i(x_i,x_{-i},b)= \frac{f_{i}(x_i,b)}{\sum_{j\in I} f_{j}(x_j,b)},\]

where \(f_{i}(x_i,b)\) is the \(i\) th players influence over a resource point \(b\) .

Why study influencer games?

There are many games in society that take the form of a influence game with spatial influence playing a major role. To list a few:

1. Voter dynamics: The competition for votes or influence over the masses in politics is an example where politicians are players who must optimize their expected return of votes to win elections. politicians can optimize their voter turn by changing their ideological point of view or that of their campaign at least or by changing the reach of their influence to reach un-touched voter populations who choose an “abstaining” candidate.

2. Fishing and net choice: Fisherman try to optimize their haul via choosing optimal finishing territories aka their influence over fish populations or by changing their strategies to harvest their territory more efficiently (effectively changing their reach)

3. Marketing and content generation: Influencer and marketers compete for limited consumer view time by choosing content topics in the form of a zero sum influence game

4. Market maker competition: Market makers compete for resources in the form of volumes of trades, which creates a zero sum influence game.

5. And many more

The influence game package allows scholars to use a code frame work to study these games and understand how their influence kernels impact the existence and stability of symmetric Nash.

The influence game package allows scholars to use a code frame work to study these games and understand how their influence kernels impact the existence and stability of symmetric Nash.

Indices

• Module Index