Game Theory- synthesized introduction cont

Last time, I wrote about terms and basic concepts in game theory. This time, I will focus on the assumption and mathematical terms to formulate a game theory problem.

Since game theory is a study of strategy and decision making, the basic assumption in game theory is that every participant (i.e. agent) is rational. Basically, there is no emotion, no irrational behavior, or any human error when making decision. In my opinion, this makes game theory incomplete, because humans are well-known for irrational behavior. Therefore, when one uses game theory, he or she must use it within certain context for pragmatic purpose.

After the rational assumption for decision making, every participant is assigned a function called utility function. The utility function is an economist’s term, which indicates a person’s overall happiness and well-being. In engineering term, the utility function is equivalent to a cost function. Since game theory models the strategic interaction among participants, the goal of game theory is to find a strategy to maximize your utility function and minimize your enemy’s function.

Since the inter-dependence of players is critical in game theory, according to Geckil et al. [1], game theory exhibits a social science corollary to fundamental principles in physics: every action has a reaction. Therefore, there are two ways to model these actions: sequential and simultaneous.

Sequential action: think of it as a chess game. Every player is aware of each other’s action in previous turns. In addition, every player knows that his or her own action will affect the outcome of the game.

Simultaneous: think of it as a rock-paper-scissor, poker, or any game that participants are not aware of each other’s move in previous turns. Though they do not aware of each other in previous turns, they aware of each other during the game. For example, poker players are aware of their opponent’s hands during the game if they do not fold.

To be continued.

 

 

Bibliography:

1. Geckil, Ilhan K., and Patrick L. Anderson. Applied game theory and strategic behavior. CRC Press, 2009.

Game theory-synthesize introduction

There has been a lot of blogs about game theory. The most prominent one is https://agtb.wordpress.com/. This blog is written by professors and experts in the field of game theory. If one wants to see the application of game theory, he or she should check out this blog http://mindyourdecisions.com/blog/category/game-theory/.  In my case, I want to blog about game theory in a simple manner with a little math. I will try to give some codes in python for different game theory algorithm as well.

Game theory is the field to study strategy and decision when two or more individual interact with each other. Game theory is a combination of mathematics (i.e. optimization), statistics, and computer science. Game theory has been applied in business (i.e. management, marketing, strategy consulting), public policy, biology, politics, and dating. Game theory has been in mainstream media through the movie: The beautiful mind.

Before I go any further, I want to give some key concepts in game theory. These key concepts are from the book Applied game theory and strategic behavior.

1. Tree form of a game: this describes the rules of the game. It describes how players move, information that players possess, probabilities affecting the game, and the payoff from each player.
2. Strategy or strategic behavior/actions: this is the player’s actions, tactics, and strategies. In my opinion, strategy is different from tactics. Strategy is a high-level thinking of move, while tactics is the maneuver based on strategy. Most game theory stops at strategy in my knowledge (i.e. I can be wrong).
3. Matrix form: this matrix provides values that demonstrate the outcomes and payoffs for each player. Most game theory works formulate into the matrix form. This forms help players make appropriate decisions, and let them realize that no outcome is an isolated decision.
4. Mixed or randomized strategy: This strategy allows players to choose strategies from a set of different strategies instead of one single strategy. For example, when one play poker, the mixed strategy player can choose to bet, fold, or call based upon his or her hand, the showing cards, and guesses for opponents’ hands with different probability values.
5. Individual rationality: That is the assumption in game theory that everyone is rational. In my opinion, this assumption is quite stupid, because humans are well-known for being irrational. This has led to behavior finance field, which studies humans’ behavior and their decision in finance. The behavior finance has challenged the rationality assumption. However, in this framework of game theory, individual rationality assumption suggests that one can act in certain direction to maximize his or her gains. This action can be modeled as an utility function (i.e. cost function in engineering term).
6. Perfect and imperfect information game: as the name says. Examples for each of them are Go, Backgammon, chess, etc. for perfect information, and poker, blackjack, investment for imperfect information.
7. Mini-max theorem: this is the key formulation in game theory. Min-max means that I want to maximize my gain while minimize others.

To be continued….

Literature Review in Text Mining

I have done some work on text mining and I will blog some literature review on the subject.

First, for basic text mining, I mean basic from theory to ground up, I would recommend these books and papers

1. Feldman, Ronen, and James Sanger. The text mining handbook: advanced approaches in analyzing unstructured data. Cambridge University Press, 2007.
2. Hotho, Andreas, Andreas Nürnberger, and Gerhard Paaß. “A Brief Survey of Text Mining.” Ldv Forum. Vol. 20. No. 1. 2005.
3. Hearst, Marti. “What is text mining.” SIMS, UC Berkeley (2003).
4. Manning, Christopher D., Prabhakar Raghavan, and Hinrich Schütze.Introduction to information retrieval. Vol. 1. Cambridge: Cambridge university press, 2008.
5. Manning, Christopher D., and Hinrich Schütze. Foundations of statistical natural language processing. MIT press, 1999.

After being comfortable in the context of text mining, you can try to get your hand dirty. I know python and MATLAB. Therefore, I recommend these books in these two languages only.

1. Banchs, Rafael E. Text Mining with MATLAB®. Springer Science & Business Media, 2012.
2. Bird, Steven, Ewan Klein, and Edward Loper. Natural language processing with Python. ” O’Reilly Media, Inc.”, 2009.
3. Perkins, Jacob. Python 3 Text Processing with NLTK 3 Cookbook. Packt Publishing Ltd, 2014.

From the list above, I read the first two. I think they provide a solid foundation to prototype text mining algorithms with either python or MATLAB.

Afterward, if you want to get deep into the frontier of text mining. You need to have some statistics and machine learning knowledge. From my study, topic modeling is an ongoing area of research of text mining. I have read these papers.

1. Blei, David M. “Probabilistic topic models.” Communications of the ACM 55.4 (2012): 77-84.
2. Mcauliffe, Jon D., and David M. Blei. “Supervised topic models.” Advances in neural information processing systems. 2008.
3. Blei, David M., Andrew Y. Ng, and Michael I. Jordan. “Latent dirichlet allocation.” the Journal of machine Learning research 3 (2003): 993-1022.
4. Shahnaz, Farial, et al. “Document clustering using nonnegative matrix factorization.” Information Processing & Management 42.2 (2006): 373-386.
5. Arora, Sanjeev, Rong Ge, and Ankur Moitra. “Learning topic models–going beyond SVD.” Foundations of Computer Science (FOCS), 2012 IEEE 53rd Annual Symposium on. IEEE, 2012.
6. Jameel, Shoaib, and Wai Lam. “An unsupervised topic segmentation model incorporating word order.” Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval. ACM, 2013.
7. Jameel, Shoaib, Wai Lam, and Lidong Bing. “Supervised topic models with word order structure for document classification and retrieval learning.”Information Retrieval Journal 18.4 (2015): 283-330.
8. Wallach, Hanna Megan. Structured topic models for language. Diss. University of Cambridge, 2008.

There are more in the field. But this is what I have studied so far.

Social Media: Separation or Closeness

Last week, I delivered a speech at my Toastmaster club about social media and relationship.

For the last ten years, there are many social media, such as: Facebook, LinkedIn, Snap-chat, Twitter. Through these social media, we are more connected than ever. For instance, I am able to connect to my old friends from high school and know about their lives despite our geographical and time difference. To be honest, it is great. However, the question brings up: Are we closer or more separated than before? Let examine two facts and determine whether we are closer or more separated with social media.

1. If we are closer, we should be able to get deeper into other’s lives.  With social media, I know about my friends’ lives as long as they update their Facebook’s status or Twitter’s post. Do these posts reflect what is actually going on their lives ? Maybe or maybe not. Let examine the “maybe” situation, because I am an optimist. When someone updates either Facebook’s status or Twitter’s post, there must be some events going on in his or her life. Therefore, a post might give me a glimpse to his or her life. However, it is only a glimpse, not the whole picture. If I want to go further, I am better off calling that individual and ask. There is no way I can make an inference based upon a post. For the “maybe not”, we all know the answer.
2. If we are closer, we will have a discussion not an argument. Social media has attempted to replace the newspaper for the last couple years. For example, Facebook have partnership with some of the news agency, such as CNN, etc. to deliver news to its users. It is a great idea. I got my news from CNN, BBC, etc mostly through Facebook. However, while reading through these news, I have seen intense arguments because of the difference in perspective. We know that we can get away with arguments without anyone holding us accountable. After all, I am just a guy typing on my computer at my apartment. Therefore, we are no longer able to have a discussion. As a result, we are more divided.

After these two facts, I think social media is a great communication tool. If we use it for communication purpose, we can benefit greatly from it. However, we cannot use social medial to bring human closer. In order to be closed to someone, you need to get your hand dirty, such as picking up a phone and call your friend.