Intelligent Interaction Modelling: Game Theory

Game theory is a mathematical tool for supporting decision making in a multiple players situation where one player’s utility will be determined not only by his own decision, but also by other players’ decisions. An illustrative example of this situation is the Rock/Scissors/Paper game (“RSP” game). In an RSP game, whether a player wins or loses depends on both what he plays and what his opponent plays. This is a well-known game between mostly children with very simple rules. Two ‘players’ hold their right hands out simultaneously at an agree signal to represent a rock (closed fist), a piece of paper (open palm), or a pair of scissors (first and second fingers held apart). If the two symbols are the same, it’s a draw. Otherwise rock blunts scissors, paper wraps rock, and scissors cut paper, so the respective winners for these three outcomes are rock, paper and scissors. The RSP game is what is called a ‘two-player zero-sum non-cooperative’ game. There are obviously many other types of game and the field of game theory is very powerful to provide (mathematical) insights into strategic decision-making.

[1]  Genserik Reniers,et al.  A Game-Theoretical Model to Improve Process Plant Protection from Terrorist Attacks. , 2016, Risk analysis : an official publication of the Society for Risk Analysis.

[2]  M. Friedman.  Essays in Positive Economics , 1954 .

[3]  S. Skaperdas.  Contest success functions , 1996 .

[4]  Zhilong Chen,et al.  Using game theory to optimize allocation of defensive resources to protect multiple chemical facilities in a city against terrorist attacks , 2016 .

[5]  Martin J. Osborne,et al.  An Introduction to Game Theory , 2003 .

[6]  Bin Chen,et al.  Integrating the API SRA methodology and game theory for improving chemical plant protection , 2018 .

[7]  C. E. Lemke,et al.  Equilibrium Points of Bimatrix Games , 1964 .

[8]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[9]  Jesus Rios,et al.  Adversarial Risk Analysis for Counterterrorism Modeling , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[10]  Xiaotie Deng,et al.  Settling the Complexity of Two-Player Nash Equilibrium , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[11]  A. Kelly.  Decision Making Using Game Theory: An Introduction for Managers , 2003 .

[12]  B. Stengel,et al.  Leadership with commitment to mixed strategies , 2004 .

[13]  Milind Tambe,et al.  Security and Game Theory - Algorithms, Deployed Systems, Lessons Learned , 2011 .

[14]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Seth D. Guikema,et al.  Game Theory Models of Intelligent Actors in Reliability Analysis: An Overview of the State of the Art , 2009 .

[16]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[17]  Jun Zhuang,et al.  Robust Allocation of a Defensive Budget Considering an Attacker's Private Information , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[18]  Sarit Kraus,et al.  Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition , 2010, Artif. Intell..