Group-dynamics

Group dynamics can be understood as complex from an interpersonal relationships point of view because it involves:

relationships between two people
relationships between a person and a group
relationships between groups
Group-dynamic games are usually designed for the specific purpose of furthering personal development, character building, and teamwork via a Group-dynamic milieu. The group leader may sometimes also be the game leader, or between peers, the leadership and game-rules can change.
Some games require large spaces, special objects and tools, quietness or many before-game and after-game needs. When aged, frail or disabled people ("special needs") are involved, existing games may need modification to be used.
The use of group dynamic activities has a history of application in conflict resolution, anger management and team building and many other areas such as drug rehabilitation and drama therapy.
Types of group-dynamic games

Dancing (some types)
Dramaturgy (sociology)
Group problem solving activities (or initiative tasks)
Ice-breaker games
Large group games
Leadership-games
Psycho-drama
Role-playing games
Team building games
Trust-building games
Win-win games (= 'cooperative games', 'new games')
Group problem solving activities
There are a number of exercises that propose a problem that the group must solve. Some of these simply benefit from the diversity of perspectives and background knowledge inherent in groups to find the answer more quickly (Trivia, Wuzzles) while another approach is to give each individual some information and the collective information is needed to solve the problem or challenge.
These can be simple or truly elegant situations. Many, like ZinObelisk, can be found for free on various websites and in books designed for use by trainers. Some of these free programs come with adequate support instructions while others are less complete. Many are readily adaptable to different situations and desired outcomes.
Some companies market ready-to-play board games that are good for large groups. An example is Performance Management Company, which sells games like "The Search for The Lost Dutchman's Gold Mine." These types of programs often give teams resources, provides a structured environment for problem solving, and rewards collaboration (rather than competition). You can expect that these for-sale products will be bundled with instructor's guides, templates for play and other facilitation and instructional resources.
Many of these team building kinds of events are available. A good place to search is under the general keywords of "teambuilding exercises"
Tips for running group-dynamic games

Get a book or go a website on this subject written by a professional.
Make sure you have basic knowledge on leadership, teamwork, group dynamics and psychology. Some specific knowledge of specialist areas such as neuro-linguistic programming and transactional analysis is useful, but not necessary.
If intense work is desired, then more background knowledge and experience is required to effectively perform activities
Know your limits
Create a comfortable physical space and a relaxed atmosphere
Participants should wear comfortable clothing
Ensure a minimum of disturbances during sessions (no visitors during sessions etc)
Treat the event holistically: care for body, mind and spirit
Be aware that we learn best (experience things most intensely) when seeing, hearing and touching is involved at the same time (audio, visual, kinesthetic aspects)
Start with ice-breaker games
Then introduce trust-building games
Then tackle group problem solving activities (or initiative tasks)
Use an experiential learning model (e.g., do-review-plan), which includes debriefing and feedback
Use time-outs to clarify problems
Enjoy and have fun, but understand the serious sides of the exercises as well
Always include everyone in a fair and equal way.
There are many books and websites which help explain how to set up groups (fun groups or self-help groups) and which tell which games are safe to play without a professional (psychologist, etc) being at hand.