The Prisoners Dilemma

It is worth talking about game theory, for a moment; if anything just to clear up any misconception let us take a look brief look game theory.  Game theory has actually very little to do with Gamification or game design in fact, it is about mathematical modeling that is used to predict outcomes “on the actions of more than one agent, as well as perhaps on other facts about the world. Game Theory is the study of what rational agents do in such situations.”(Weatherson, 2011).  Myerson (1991) defines game theory as the “study of strategic decision making. More formally, it is “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.”

One of the most famous models that is often used is what is commonly referred to as the prisoners dilemma.  As you can see from the matrix below we have two men, both have been apprehended by the police.  If both remain silent (game theory calls this cooperation), they will only receive a one year jail sentence each.  Both are offered a chance to confess and send the other player to jail for 20 years (game theory calls this defection from a cooperative relationship).  If both players cooperate they would receive the best outcome, however, both are thinking that if they turn on each other, they may not do jail time and therefore will defect and confess to the crime.

PD Matrix

Fig, 1: The Prisoners Dilemma shown as a martix

Theorists tell us that the criminals will always confess as they will only act in their own self-interest, therefore leading them to both go to jail for 5 years.

This is the prisoner’s dilemma. Game theorists have determined that confessing is always the answer for both parties in this case. The reason for this is that each party must assume that the other will act with only self-interest in mind.   By listing the preferences of the choices we can predict what the criminals will do.

  1. 20 year term
  2. 5 year term
  3. 1 Year Term
  4. Get out of Jail free

PD Preferences

Fig, 2: The Preference Matrix of the Prisoners Dilemma

Looking at Player 1’s preferences in the first column we can see that the 5 year term is preferable over a 20 year term if he does not confess (2 is great than 1).  In Column 2 we can see that see that not going to jail is better than going to jail for 1 year, therefore, the best strategy is to confess no matter what his partner this does is called the dominant action. The prisoner’s dilemma is the simplest of the game theory models, as we add more variables and players the mathematics become much more complicated.

References:

Myerson, R. B. (1991). ‘Game Theory: Analysis of Conflict, Harvard University Press, p. 1. Chapter-preview links, pp.vii – xi

Weatherson, B. (2011) ‘Lecture notes on game theory.’ [Online]. Available at: http://brian.weatherson.org/StA-GameTheoryNotes.pdf (Accessed: October 17, 2013)

Balancing Safety and Challenge (and Critical Thinking)

This weeks post from my Adult Education Course at the University of Victoria

 

While I can’t speak to the challenges of facilitating in a classroom as I have yet to have that experience.  However in terms of informal education I spent almost 20 years as a Chef.  When teaching apprentices and cooks as a chef, there is still balancing the need to provide a safe learning environment for everyone as well as ensure that the staff was up to the various challenges ahead as they learn new skills.

 The notion of safety as stated in our study notes comes basically in two forms, first the physical environment.  As a teacher/facilitator we must ensure that the physical environment is safe for each student.  Whether the environment is a classroom or a kitchen, students need to feel safe and secure.   UVIC (2013) course notes state “Taking care to ensure a comfortable physical learning environment sends a message to participants that we genuinely care about their needs.” As a chef, the responsibility is high to ensure the learner whether it is a first time cook or an experienced apprentice to ensure that the physical surroundings were safe so that learners feel comfortable without worry to whether or not they would be harmed by sharp objects or heavy kitchen equipment. 

But it is more than that it is making sure they have the proper equipment regardless of whether it is a knife to cut food in the kitchen or a workspace in the classroom.  Taking away the fear or concern of the physical space is one step towards ensuring the comfort and safety of the students.  The next step of course as stated in the UVIC(2013) course notes that the second part of safety is the emotional and social environment. 

A good example is this week’s assignment of safety, for Assignment one, Colleen in the forums posted that our assignments do not have to be posted.  Since some of our assignments are personal not everyone may have the comfort level to share with the class.  This agrees with the University of Wisconsin’s (n.d.) that states “The teacher may state that s/he will not call on students individually to participate, and students have the right to not participate.” 

In adult learning there may be the potential to have a wider variety of diversity in the classroom.  Not only is there potential for cultural diversity, but also gender, age, education and experience all come to play in a group setting.  The University of Wisconsin (n.d.) states “All learning and change involves some degree of culture shock to the degree that they challenge our basic perspectives.”  What this suggests to me is that when we put a group of people into a setting where they will be challenged facilitators may have to deal with a wide array of emotional reactions of their learners. 

Wlodkowski  (2005) states that establishing participation guidelines is important in adult learning, since as facilitators part of our role as a guide is to ensure the emotional and social stability of the group, by opening up and discussing with what they can expect from me as a teacher in the class room is important.  But also, understanding what the students expect from me as well as what students expect from each other.  Much like we do at teams in the work place understanding and developing group norms is important.  Mutual respect for each other as a person, that each person’s voice is important, and that each person adds value to the classroom in some way, in a way we are creating a sub-culture in the classroom with our own beliefs, symbols, behaviors, stories, etc..

It took me awhile to see the connection between a safe environment and critical thinking.  There are a number of different definitions of critical thinking.   The one I like the best is from Scriven and Paul (n.d.) that states Critical thinking is that mode of thinking – about any subject, content, or problem – in which the thinker improves the quality of his or her thinking by skillfully taking charge of the structures inherent in thinking and imposing intellectual standards upon them.” Fostering critical thinking in Adult Education is very important, often we think with our emotions and our experience, but critical thinking goes beyond that. 

In the safe classroom critical thinking is important in formulating responses to other students.  Critical thinking in my opinion is really meta-thinking, what I mean by that is that we think about thinking, before we respond to someone’s thought, we think from all angles.  We have to look at it logically and try to remove our prejudices and biases in order to formulate a response or action.  In the classroom with a high level of diversity we need to encourage students to see all sides of the argument and be able to respond in an intelligent logical manner, as opposed to an emotional manner.  If we respond with our heart rather than our brains, we may make other students feel uncomfortable, your prejudices or biases could also hurt another person’s feelings. 

Safety then in the classroom encompasses three elements, the physical, and the social/emotional side.  Related to the social/emotional side is also being able to critically think as well.  Without critical thinking skills, I do not think any education will affect social issues of the day, if that is what adult education is trying to achieve.

 

References:

Duncan, J. (n.d.) ‘Critical thinking’[Online]. Available at: http://ctl.utsc.utoronto.ca/twc/sites/default/files/CriticalThinking.pdf (Accessed: October 7, 2013)

Scriven, M. and Paul, R. (n.d.) ‘Defining Critical Thinking’ [Online]. Available at: (Accessed: http://www.criticalthinking.org/pages/defining-critical-thinking/410)

UVIC(2013) ‘Module 4: Safe and challenging adult learning spaces’ [Online course notes] Available at: http://distance.moodle.uvcs.uvic.ca/mod/page/view.php?id=67492 (Accessed: October 6, 2013) Note: Available to students only

University of Wisconsin (n.d.) ‘Creating a safe and engaging classroom climate’ [Online]. Available at: http://www.uww.edu/learn/diversity/safeclassroom.php  (Accessed: October 6, 2013)

Wlodkowski, R. (2005) ‘Motivational Strategies’[Online]. Available at: http://userpages.umbc.edu/~koconne1/605TheAdultLearner/strategies.htm (Accessed: October 6, 2013)