Research

Groups and flocks can also be formed temporally, such as the flocks of birds during spring migration. During the migration, they form flocks that provide protection, reduce individual predation risk, and increase navigation accuracy by pooling information; some birds such as the Canada geese and white pelicans form V-shaped flocks during migration to increase their energy. Upon arrival at a breeding ground, these birds compete with each other for territory to increase their reproductive success. 

These sequential models capture the trade-off between cooperation (benefit of flocking, e.g. increased foraging efficiency, reduced predation risk, higher energy efficiency, and more accurate navigation) and competition for better territories at the breeding grounds.

Agents with different strengths, such as skills, experience, and health conditions, compete with each other for better resources. At the same time, they form groups to lower individual costs when being part of a group affords benefits such as protection against predation risk, energy efficiency, and resource pooling. Specifically, agents determine an arrival time and form groups by arriving simultaneously. We examine in detail the 2-agent and 3-agent games, demonstrating that under natural assumptions, there always exists a pure strategy Subgame Perfect Equilibrium (SPE) through backward induction. We further characterize a number of properties of SPEs and derive conditions for various grouping behaviors, including two special cases:(1) a grand group (simultaneous arrivals of all agents; only cooperation and no competition) and (2) no group (only competition and no cooperation). In addition, We also study a more relaxed definition of grouping, whereby agents whose arrival times fall within a small window are considered to be of the same group and enjoy the same group benefits. Compared to the strict grouping definition, this more relaxed definition gives rise to a greater diversity of SPEs.

One of the key tradeoffs in the formation of spatial groups is between adding more resources to a group (resource pooling) vs. making it less cohesive (spatial cohesion). For example, when a club broadens its interests, it can add more members, but at the cost of less thematic cohesion. When a gang expands its territory, it can add more members (who add the ability to offer protection to others), but at the cost of less spatial cohesion, which makes it harder to coordinate actions. Similarly, when a strategic alliance comprises more countries, it can draw on more strength, but will suffer in less geographic cohesion.

To study what group structures can merge under such settings, we introduce simultaneous games in which the group members’ utilities capture a trade-off between the combined resources of the group and the geographical dispersion. 

Each agent is endowed with a certain amount of resources and has a spatial location. Agents then team up in disjoint groups so as to be in groups of high collective strength. This strength could be group identity, reputation, or protection, and is equally shared by all group members. The group's access to resources, obtained from its members, is traded off against the geographic dispersion of the group: spread-out groups are more costly to maintain. We seek to understand the stability and structure of such partitions. We adopt and define two types of equilibria: Individually Stable Equilibrium (ISE) and Strong Individually Stable Equilibrium (SISE). We show that under natural assumptions on the group utility functions, SISE always exists and thus ISE exists; and that any sequence of improving moves by a subset of agents from the same group converges to an SISE. 

We further derive spatial properties of the equilibria: we find that all other structures are possible except mutually-encroaching structures in any equilibrium under our original model, while all are possible in any equilibrium under the more general model. To get a better visualization of the encroachment relationship among different groups, we also apply graph theory to map the equilibrium to directed graphs. In particular, in the orginal group utility setting, we showed that each SISE, or ISE under certain conditions, can be represented by a DAG, and conversely, that under mild conditions on the utility functions, every DAG can arise as an ISE of a suitably defined instance of the group formation game.

We then apply our model to understand the spatial and territorial relationships among a set of well-established criminal gang groups in Los Angeles using a real-world dataset. We further extended our model with the study of the contractual version of ISE and SISE.

Research shows that through repeated interactions with automation, human operators are able to learn how reliable the automation is and update their trust in automation. The goal of the present study is to investigate if this learning and inference process approximately follows the principle of Bayesian probabilistic inference. First, we applied Bayesian inference to estimate human operators’ perceived system reliability and found high correlations between the Bayesian estimates and the perceived reliability for the majority of the participants. We then correlated the Bayesian estimates with human operators’ reported trust and found moderate correlations for a large portion of the participants. Our results suggest that human operators’ learning and inference process for automation reliability can be approximated by Bayesian inference.