Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 1 Information, Control and Games Shi-Chung Chang EE-II 245, Tel: Office Hours: Mon 1:00-2:00 pm or by appointment Yi-Nung Yang (03 ) ext. 5205,

Lecture 1, 09/20/07Information, Control and Game, Fall 07, 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 can be related to several other fields One DMMany DMs StaticMathematical programming Static game theory DynamicOptimal control theory Dynamic or differential games

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 3 Example Single-person optimization with two decision variables Two-person optimization with one decision variable each

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 4

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 5

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 6 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 7 Prisoner’s Dilemma –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?

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 8 Matrix form model Q. If you were one of the suspects, are you going to confess? Why or why not? Any insights to share? Suspect 1\Suspect 2Do not confessConfess Do not confess(1, 1)(15, 0) Confess(0, 15)(5, 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?

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 9 –(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(0, 0)(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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 10 Interesting questions –What will each individuals guess about others’ choices? –What action will each person take? –What is the outcome of each of these actions? –Does it make difference if the group interact multiple times? –How do the answer change if each individual is unsure about the characteristics of others in the group? Game Theory: A formal way to consider –The group and players (or Decision-Makers, DMs) –Interactions: a player’s choice directly affects some others –Strategic: an individual accounts for this interdependence in deciding what actions to take –Rational: Each chooses the best action

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 11 Applications You name some? District attorney’s daily job Art auctions and Treasury auctions Voting in the United Nations Sustainable use of natural resources, e.g., forestry & fishery Bankruptcy law R&D efforts by pharmaceutical companies Pricing strategies for airlines and high speed trains Working on a group project

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 12 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 13 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 14 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 15 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 16 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 17

Lecture 1, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 18 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 19 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, 09/20/07Information, Control and Game, Fall 07, Copyright S. C. Chang, Y. N. Yang and P. B. Luh 20 Syllabus 96syllabus_v2.doc 96syllabus_v2.doc