By Chanden Sen
Strategically Speaking There is a student at my school who plays games, all by himself, in his spare time on his mobile hand-held device, PlayStation 2 I believe. He also has a huge album of game cards. In order to get him interested in the serious side of games – pardon the oxymoron – I googled “game theory” and came up with an interesting Wikipedia article, which I read and subsequently printed and gave to my student, Ryan. I also came to know that Professor Nash, who features in the movie, A Beautiful Mind, won the Nobel Prize for his work on game theory. Another famous professor in the field is Avinash Dixit, of Princeton University, who has co-authored the fascinating book, “The Art of Strategy,” which promises to bring the reader and practitioner success in business and life. Briefly, game theory deals with the myriad of strategic interactions that we have to deal with every day. It may help you negotiate with your child about when to go to bed, or to decide how your firm should react to a rival’s price-cutting measures, or even with yourself in sticking to a New Year’s Resolution. As the blurb on the book says, you can either muddle through these interactions and hope for good luck, or you can become better at recognizing, even anticipating, strategic situations and knowing how to respond. I must hurriedly add that game theory is not by any means competition only. In fact, Dr. Dixit has written another book called “Co-opetition” which addresses the important field of cooperation, mixed with competition. In many simple games, players have perfect knowledge of the other player or players’ objectives, but that is not necessarily the case in games people play in business, politics, and social interactions. Motives in such games are complex combinations of selfishness and altruism, concern for justice and fairness, short run and long run considerations and so on. I checked out “The Art of Strategy” from the library and also viewed the 42 min video clip on YouTube. Dr. Dixit gives a very entertaining lecture in the latter, using clips from movies to illustrate game-theoretic points. Your strategic thinking depends on how well you can put yourself in the other person’s shoes. Should cave dwellers Barney and Fred, from The Flintstones, go rabbit hunting on their own, or stag hunting together? Should Clint Eastwood and Lee van Cleef, in the film The Good, the Bad and the Ugly, draw first…and whom should they aim at in the three-party gun duel? Should the penalty shooter in a game of soccer kick to the left or to the right in order to score a goal? The book answers all these questions and more. The children’s game, Rock Paper Scissors points out the strategic advantage of being unpredictable. This is technically called a mixed strategy. Other technical terms are minimax strategy, payoffs, Nash equilibrium, and squaring the circle. The game table or payoff table, invented by Thomas Schelling, portrays possible combinations in a spreadsheet like table with rows and columns. Although Schelling developed many of the most important concepts of game theory—-focal point, credibility, commitment, threats and promises, he himself modestly wrote that he should be best remembered as the inventor of the staggered payoff table. Saathee.com
The payoff table, if properly filled in after some simple calculations, yields a dominant strategy for each player, in which he gets max payoff irrespective of what his opponent does. But who is your opponent? Humorously enough, it could be you! Your night-self, for example, seeking to have a productive day tomorrow, sets the alarm clock optimistically at 5 am. Your morning-self, on the other hand, drowsily reaches for the snooze button when the alarm rings. Read Dr. Dixit’s intriguing exposition of how the night-self can win—-say by putting the alarm clock out of reach of the morning-self on a bookshelf far away. This is called a commitment. Game theory has been used in the Cold War in brinkmanship, and at auctions, biddings, and contests. It can be used to study and impact voting, bargaining and the giving of incentives. The case studies range from Ali Baba to America’s Cup, and the lessons learned can help you outmaneuver rivals, find avenues for cooperation, and become more successful in all your pursuits. And if you want to be fair to your adversaries, share your knowledge with them! Jean Piaget’s Magnificent Obsession The famous Swiss psychologist, Jean Piaget (1896-1980) is a giant in the field of developmental psychology. We owe to him the present field of children’s cognitive development. It was Piaget, along with William James and John Dewey, who envisioned children as active, constructive thinkers. In my career as a teacher, I have found intense satisfaction in helping children think through things and make sense of the world around them. Piaget observed his own three children – indeed, he was a genius when it came to observing children. He came up with terms like schemas, preoperational stage, formal operational stage, etc, and gave meaning to these terms. Technically, Piaget is considered to be a cognitive constructivist. From birth to two years of age, infants are considered, in Piaget’s theory, to be in the sensori motor stage. The infant constructs an understanding of the world by coordinating sensory experiences with physical actions. An infant progresses from instinctive, reflexive actions at birth to the beginning of symbolic thought towards the end of the stage. Similarly, Piaget has divided the rest of childhood, from two years through early adulthood, into three more stages: the preoperational stage, concrete operational stage, and formal operational stage. Renowned educationist, Dr. John Santrock, advises teachers to ask children to justify their answers when they draw conclusions, especially when they are preoperational thinkers. Similarly, concrete operational thinkers should be encouraged to discover concepts and principles, by asking them relevant questions about what is being studied to help them focus on some aspect of their learning. For the adolescents considered to be formal operational thinkers, Dr. Santrock suggests that the teachers encourage students to create hierarchical outlines when asking them to write papers. Piaget’s theories have been challenged in a number of areas: estimates of children’s competence at different development continued on page 70
Chandan Sen Contact: chandansen33@hotmail.com
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April 2011