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As part of the game theory student seminar our team played the Split-Steal game in class.
Two players with two actions each, Split or Steal. The treasure was comically 2 gingerbread cookies!
Essentially a form of Hawk-Dove game. Hawk: aggressive (escalates conflict) i.e. Steals , Dove: non-aggressive (backs down from escalation) so naturally Splits.
Different strategies / roles
Final Part of the game:
More parts of the seminar
This game can also be seen as a Bayesian game. Information about characteristics or types of the other players (i.e. payoffs) is incomplete in such games. Nature assigns a random variable to each player which could take values of types for each player and associating probabilities (or a probability density function with those types). At least one player is unsure of the type and the payoffs of another player. Players have initial beliefs about the type of each player and can update their beliefs according to Bayes' Rule as play takes place in the game. The belief a player holds about another player's type might change on the basis of the actions they have played.
In a Bayesian game setting there are three meaningful notions of expected utility: ex post, ex interim and ex ante.
Analysis of the Game:
My group's project in Humanoid Robotics course (14/15). We used Chabot robot to be controlled over a network (based on a TCP client-server connection), using a Kinect. Therefore, this system could be use to control the robot on-line from another different place. As can be seen in the video, the robot is able to follow all the arm-movements and also recognizes our hands in order to open or close his clamps.
In the course Humanoid Robotics, my group used genetic algorithms to let a Bioloid robot evolve a walking behaviour. The training phase (evolution) took place in the simulation environment V-REP. The robot is controlled by a CPG (central pattern generator) which was optimized using a genetic algorithm.
An often confusing aspect of reading the payoff matrix in a game theory setting (at-least for new comers or those delving into the subject after a hiatus) is the confusion between the row players and column players. A more intuitive method maybe to keep track of the process of propensity of movement of player's states (as per moving in the direction of higher utility) using some sort of color coding to see the direction in which they move. The following figure tries to capture the same - and observe the point where the arrows meet is the location of Nash Equilibrium. I know it may seem too formal an approach to bring in a design aspect (colors and arrows), but then game theory itself is a formalism of something most people would say is common sense, intuition so a bit more formalism wont harm - let me know if this becomes more intuitive:
Generic background: As is evident a rational agent has clear preferences (i.e. states that he likes) and always chooses to perform the action with the optimal expected outcome for itself from among all feasible actions. A utility function (in the form of the above payoff matrix) is used to map out real world choices to quantitative numbers. These numbers can be seen to be levels of happiness of the agent in those corresponding states.
Intuitively, a Nash equilibrium is a stable strategy profile: no agent would want to change his strategy if he knew what strategies the other agents were following. Nash equilibria can be strict and weak, depending on whether or not every agent’s strategy constitutes a unique best response to the other agents’ strategies.
Student seminars from the 2014-2015 class - Complex Systems Seminars
Siamak Esmi Erkani
Selvin Cephus Jayakumar
Björn Persson Mattson
Marcus Schmidt Birgersson
Helga Kristín Ólafsdóttir
Toby St. Clere Smithe
Featuring the details of thesis projects being conducted by CAS students currently or next spring!
ONGOING THESIS PROJECTS
Using situation based predictive risk estimation for subject and surrounding traffic to ensure safe maneuvering of long combination vehicles (LCVs) in highway driving scenarios.
"When driving long-combination vehicles (trucks so long and heavy that they need a special permit to be driven on roads), it is important that the driver handles the vehicle as safely as possible. This master thesis will explore methods for estimating the risks for the subject vehicle and surrounding traffic which allow safe maneuvering. This will be used both for alerting the driver of dangerous situations and autonomous driving. The work includes adaptive systems and risk analysis, and will be performed at Volvo Group Trucks Technology."
Bjorn Persson Mattsson
Multi-level evaluation of autonomous vehicles using agent-based transport simulation for the case of Singapore
Based on an existing large-scale agent-based simulation of Singapore (MATSIM) the impacts of autonomously driving vehicles are examined. The focus of investigation lies on the emerging choice behaviour of customers in the multi-modal public transport scenario. Different pricing scenarios and service schemes are simulated to compare the acceptance and usability of the new technology.
January until June 2016 @ ETH Singapore Center Future Cities Laboratory (FCL) - www.futurecities.ethz.ch
Presentation: mid-July 2016
Real-time optimization of traffic situation maneuvers for long combination vehicles (LCVs)
An approach to improve traffic safety and to further increase transport efficiency of LCVs is to utilize automated driving functionalities including propulsion, braking and steering. This master thesis will propose an optimization scheme which allows real-time actuation generation for highway maneuvers of LCVs. The work includes adaptive systems and programming and optimization, and will be performed at Volvo Group Trucks Technology.
Here are some tips from our director on doing thesis project. A summary of information about the master thesis:
- Start early (i.e. now), looking for a project: talk to teachers, look for posters, search the web. I will also forward occasional project proposals.
- The project should be CAS (or physics) related, interpreted in a wide sense. The most most important thing is that it has a solid scientific or engineering perspective.
- You need an examiner at Chalmers. You need a supervisor at Chalmers or elsewhere, such as in a company. (Examiner and supervisor may be the same person for a local Chalmers project.)
- Typically the project should be registered at the department where the examiner is active.
- Before you start, you need to have the registration form signed by the MPA, and the examiner. There should be a short project plan which is what I need to see to approve it as a CAS thesis.
- Don’t forget to fill in the work card once you start on the project (which implies attending other thesis presentations, etc.)
- More information is found at the Studentportal Examensarbete
If you have questions or need help, you very welcome to contact the Director.
From Prof. Bernhard Mehlig
I'd like to advertise that there are opportunities for MSc projects in Dynamical Systems in our group. We analyse the dynamics of particles in turbulent flows with dynamical-systems methods, analytically, by computer simulations, and experimentally.
This question has important applications in cloud physics (droplet dynamics in turbulent clouds and rain initiation), astrophysics (planet formation), biology (plankton dynamics), and industry (fiber suspensions).
Recently we received a grant from the Knut and Alice Wallenberg foundation (https://www.wallenberg.com/kaw/forskning/beviljade-anslag/projektanslag-2014) that will allow us to employ one or two PhD students on this subject from July 2015.
Information meeting for new CAS students 2015, Monday August 31st, 10.15-11.15, room FL71, Origo (Physics) building, Chalmers Johanneberg.
The meeting is intended for both Chalmers and Gothenburg University students. There will be a brief introduction to the program and an opportunity to meet many of the teachers.
Mats Granath, Director of CAS
This presentation by CAS student Carl Retzner was voted by the students to be one of the two best student presentations of the Complex Systems Seminars 2013-2014. The presentation is on Game Theory.
This presentation by student Angelica Andersson was voted by the students to be one of the two best student presentations of the Complex Systems Seminars 2013-2014. The presentation is on complexity perspectives on Social Norms.