Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 1 Information, Control and Games Shi-Chung Chang EE-II 245, Tel: ext Office Hours: Mon/Wed 1:00-2:00 pm or by appointment Yi-Nung Yang (03 ) ext. 5205,

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 2 HISTORIC PERSPECTIVE Games people play ~ Can be traced back to xxx BC, in fact, since the beginning of mankind Can see animals playing ~ Dogs, cats, dogs and cats, even squirrels Using mathematics to model games started in 1920 and 1930 and established a field in 1944, and can be related to several other fields One DMMany DMs StaticMathematical programming Static game theory DynamicOptimal control theory Dynamic or differential games

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 3 Von Neumann and Morgenstern’s games in extensive form –A game evolves according to a tree structure (e.g., chess) –At every node a decision is made –Dynamic and informational aspects are captured Gradually, the dynamic and informational aspects are suppressed, and the study are concentrated on the strategic aspect ~ Games in normal form, e.g., Prisoner’s dilemma:

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 4 –Two suspects who jointly committed a crime got caught, and are separately interrogated by a district attorney –Each suspect has two options: Confessing what they did, or not confessing SGD.How to model the problem? What are the possible outcomes? Suspect 1\Suspect 2Do not confessConfess Do not confess(-1, -1)(-10, 2) Confess(2, -10)(-5, -5) Q. If you were one of the suspects, are you going to confess? Why or why not? Any insights to share?

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 5 –(Don’t confess, Don’t confess) is the best, however, cannot prevent unilateral deviations –(Confess, Confess) is an “equilibrium” point ~ No incentive for unilateral deviations –This trick is often used by district attorneys or others in similar occasions Q.How would the values be changed if Mafia is involved? Suspect 1\Suspect 2Do not confessConfess Do not confess(-1, -1)(-10, -100) Confess(-100, -10)(-100, -100) –(Don’t confess, Don’t confess) is the only rational choice –Now you know why Mafia has to be brutal to betrayers

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 6 Research focuses are on –Non-cooperative games: Everyone for himself/herself –Cooperative games: Let the pie grow larger by working together, and develop a fair way to cut it –Bargaining: Cooperation with a sense of threat ~ If you don’t do this, I will... Rich in solution concept, however, deficient in methods and algorithms to obtain practically implementable solutions ~ The dynamic and informational aspects have been suppressed On the other hand, there is a separate development on differential games:

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 7 Example: Pursuit-Evasion Games –Plane A is pursuing plane B ~ Wants to get as close as possible –Plane B is trying to get away as far as possible SGD. How to describe this situation mathematically? How to solve it? Practical implications? dx p /dt = f p (x p, u p ), with x p (t 0 ) given dx e /dt = f e (x e, u e ), with x e (t 0 ) given J(u p, u e )  ||x p (t f ) - x e (t f )|| 2, where t f is the terminal time Pursuer: min u p J(u p, u e ) Evader: max u e J(u p, u e )

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 8 Comments: –The problem is similar to an optimal control problem, but much more difficult ~ Differential game –Would require sophisticated mathematics to solve it ~ Shall address it under simplifying assumptions –Complications: Changing the role of the two planes, e.g., in a dig fight, the pursuer suddenly becomes the evader –Have values in aircraft combat, anti-missile defense, and fighter/missile design (parameter tradeoff) One DMMany DMs StaticMathematical programming Static game theory DynamicOptimal control theory Dynamic or differential games

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 9 Mathematical programming: Single DM static optimization with many efficient algorithms –Simplex method, Kuhn-Tucker conditions in the 1950s –The Lagrangian duality and convex analysis in the 1970s –Nonlinear Programming + Discrete Optimization Control and estimation: Single DM dynamic optimization with informational aspects explicitly considered –Optimal control Bellman’s Dynamic programming 1957 and Pontryagin’s Maximum principle 1962 –Estimation and Filtering ~ Kalman filtering 1960 –Optimal Control and Stochastic Control (or Estimation and Detection)

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 10 Decision-making is no longer straightforward when multiple DMs are involved –The problems are important and challenging –Very often problems have to be much simplified to be solvable ~ Solutions may have little practical value Time seems ripe to put these methods together to solve practical problems Successful applications have been found in –District attorney’s daily life –Computer chess and other strategy-oriented games –Pricing strategies for airlines and automakers Putting Together

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 11 –Tradeoff of parameters in fighter design –Missile maneuvering upon interception –Robust system design ~ playing against nature. The game theoretical approach for H  control Potential new applications –Deregulation of the telecommunication markets –E-commerce –Coordination of distributed design and manufacturing activities –Command and control in military operations –Enforcing/encouraging cooperation among users for packet forwarding in multi-hop wireless networks –Many many more

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 12 Course Overview To provide a good understanding about “basic” game theory including dynamic games with perfect information To study multi-person decision-making with imperfect information To examine a higher level issue on the design of markets or systems considering the behaviors of participants To study the applications of the above, including the telecommunication industry, supply chains, etc. To design and play some of the “games”

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 13 The uniqueness of the course: –Treating of the subjects from both economic and control theoretic view points –The use of online games including simple ones such as Rock, scissors, paper, Prisoner’s dilemma tournament, and more complicated market games developed through research projects –The practical context of games in engineering systems –The opportunity for students to work together on collaborative term projects of interest to you

Lecture 1, 09/21/05Information, Control and Game, Fall 05, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 14 Syllabus 94syllabus_v0922.doc 94syllabus_v0922.doc