# Investigate the Emergence of Subgraphs over time as an Indicator of Strategic Behavior on Gitcoin Grants
###### tags: `Research`

*Contributors: Marc Minnee*

This is a research question for the TE-gitcoin course, leveraging the gitcoin cadCAD model.

For more background information on this course, join the [Discord group](https://discord.gg/Cvjznmqy).

## Intro

**One of the issues of the way Gitcoin Grants rounds are organized is the threat of collusion**.

We can imagine that colluders will optimize their tactics and strategies for maximizing their objective of maximizing funding outcomes, while organic actors will have a more random structure due to the diversity and heterogenity of tactics and choice functions.

For the Gitcoin Grants case, this means that any subgraph structures that emerge over time during a grants Round might show strategic behavior resembling some form of collusion. We should be able to show disctinctions between obvious colluding and organic behavior in a time-based fashion.

In this research plan, we explore the above idea by using Subgraphs as a proxy for those network structures.

We then examine the type of connections (edges) being formed among the stakeholders (nodes) while transacting during the grants Round and look at the 'weights' of the connections in these subgraphs, expressing the staked amount and the alleged correlation between stakeholders over time.
**we call this the 'emergent strategic behavior'.**

As a working question, **we hypothesize that contributor behavior will change over time and certain patterns emerge during a round and in between rounds:**
- **Cluster of contributors 'kicking off the party'** representing behavior early on in the round in order to influence the community on staking accordingly
- **Cluster of contributors 'HODLing to the max'**, mostly staking in the end phase of the round, looking at 'how the wind blows' or exercising some kind of sentiment
- **Cluster of contributors 'forming alliances'**, showing strategic behavior in order to get the max out of their stake - obfuscating colluding behavior.

*An example of emergent behavior in the cadCAD model, bipartite graphs at timesteps 10, 50 and 100.


## Definitions

D0: The full contribution graph $G$, for each vertex is either a grant (whose nodes constitute the set $\mathcal{G}$) or a contributor (constituing the set $\mathcal{C}$). All edges go from a vertex of type contributor to a vertex of type grant.

---

D1: $Subgraph(g)= \{n \in \mathcal{G} \; \forall \; d(g, n) \leq 3 \}$
- $n$: node (grant or contributor)
- $g$: grant
- $d(u, v)$: Degree distance between nodes $u$ and $v$

---

D2: The weights $w$ in a subgraph expresses the staking amounts $S$ on the edge $e$ of the contributors to the grants.

$WeightedSubgraph(g)= \{n \in \mathcal{G}, w \in \mathcal{S} \; \forall \; d(g, n) \leq 3 \}$
- $n$: node (grant or contributor)
- $g$: grant
- $w$: weights
- $d(u, v)$: Degree distance between nodes $u$ and $v$

---

D3: The association $a$ in a subgraph expresses the relationship $R$ of one contributor to the other by looking at mirroring staking behavior, like '*tit-for-tat*' or overlapping staking

---

D4: The metric of interest is the change in time of the weights and the associations between contributors staking on grant $g$.

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## Hypothesis

H1: Contributor behavior will change over rounds and round time, forming 3 types of contributors: first movers, HODLers and alliance seekers
- the type 'alliance seekers' is susceptible to 'colluders' mode and should be investigated further using other data sources and AI-tooling.

## Methodology

The execution of this research plan will be done partly through course working sessions, which will have live streams and sessions with course participants.

We will use the Rounds 6, 7 and 8+ dataset and matching algorithm.

We'll perform a Exploratory Data Analysis over the metrics, seeking to characterize the aforementioned clusters as well as exploring emergent properties that may arise.

## Applications

If hypothesis is confirmed:

- Big cluster of alliance seekers may signal strong colluding behavior,
- Actionability of policies on mitigating unwanted behavior: improve staking incentives opposite of emerging behavior by adjusting the QF-pairwise algoritm or implementing new AI-powered algoritms

Else:

- Formulate an alternative for H1
- Formulate an alternative for D2

Note that these applications are not exhaustive.

## Next Steps

- Gathering data on rounds 6 to 8+
- Plotting subgraphs with several network algoritms
- Include the time factor and emerging effects
- Use community detection subgraphs and rewiring to investigate typical behaviors
- Use AI to look for patterns in behavior comprising rounds 6, 7 and 8+