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Software Agents in Economic Environments

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					         CARAT 2002/2003
 Software Agents in Economic
 Environments
Robert S. Gazzale
Ph.D. Candidate, Department of Economics

Jeffrey MacKie Mason
Professor, Dept. of Economics & School of Information


                 April 9, 2003
Funding: Past & Present

           Many thanks to:

                CARAT
                NSF
                IBM


April 9, 2003         CARAT: Gazzale & MacKie Mason
Collaborators
       Chris Brooks
          Computer Science, University of San Francisco
       Yan Chen
          School of Information
       Rajarshi Das
          IBM Institute for Advanced Commerce
       Ed Durfee
          AI Lab, EECS
       Jeff Kephart
          IBM Institute for Advanced Commerce

April 9, 2003       CARAT: Gazzale & MacKie Mason
A Model of Economic Modeling
     Environment                                Outcomes




April 9, 2003   CARAT: Gazzale & MacKie Mason
A Model of Economic Modeling
     Environment                                Outcomes




April 9, 2003   CARAT: Gazzale & MacKie Mason
A Model of Economic Modeling
     Environment                                Outcomes




April 9, 2003   CARAT: Gazzale & MacKie Mason
A Model of Economic
Modeling: Alternative View
     Environment                                Outcome




April 9, 2003   CARAT: Gazzale & MacKie Mason
A Model of Economic Modeling:
Which Mapping?
     Environment                                Outcomes




April 9, 2003   CARAT: Gazzale & MacKie Mason
Equilibrium: The Mapping
from Environment to Outcome
        One Agent Environment
          Optimal action
        Non-cooperative Games
          Nash Equilibrium
                 Given what everybody else is
                 doing, no one agent can change
                 strategy to do better.



April 9, 2003          CARAT: Gazzale & MacKie Mason
John Nash?




April 9, 2003   CARAT: Gazzale & MacKie Mason
Problem: Finding Equilibria
        Is it solvable?
        If so, will agents find it?
          Bounded Rationality (Herbert Simon)
                 Cognition is not free.
                 Satisfice rather than optimize?




April 9, 2003           CARAT: Gazzale & MacKie Mason
Problem: Out of equilibrium
matters!
       Particularly if agents are boundedly
      rational
       Do we get to equilibrium?
       What happens on path to equilibrium?




April 9, 2003   CARAT: Gazzale & MacKie Mason
More Problems with
“Equilibrium”
        Which Equilibrium?
          If there are many equilibria, which is going
           to happen when?




April 9, 2003      CARAT: Gazzale & MacKie Mason
Why Software Agents?
       Useful in alleviating equilibrium issues.
       Cheap.
       Present/Future of software agents in
      real markets
          Particularly where equilibrium not solvable.




April 9, 2003      CARAT: Gazzale & MacKie Mason
Application 1: Convergence to
Equilibrium


                                                Nash
                                                Equilibrium



       Theory: Supermodular (SPM) games
       played by learning agents converge
       to Nash Equilibrium
April 9, 2003   CARAT: Gazzale & MacKie Mason
Application 1: Convergence to
Equilibrium
                Trust me, you don’t need
                to know what this is!
                                                  Nash
                                                  Equilibrium



       Theory: Supermodular (SPM) games
       played by learning agents converge
       to Nash Equilibrium
April 9, 2003     CARAT: Gazzale & MacKie Mason
Application 1: Convergence to
Equilibrium


                                                Nash
                                                Equilibrium




 Theory makes no predictions if NOT
 Supermodular.
April 9, 2003   CARAT: Gazzale & MacKie Mason
Application 1: Convergence to
Equilibrium


                                                Nash
                                                Equilibrium




 Is more supermodular “better”?

April 9, 2003   CARAT: Gazzale & MacKie Mason
Application 1: Convergence to
Equilibrium


                                                Nash
                                                Equilibrium




 Answers to these questions important
 in designing markets!
April 9, 2003   CARAT: Gazzale & MacKie Mason
Convergence to Equilibrium:
Human Experiment
      Methodology
          Design game where parameter controls
           whether or not game is SPM
          Laboratory experiments with human
           subjects playing for real money!




April 9, 2003     CARAT: Gazzale & MacKie Mason
Convergence to Equilibrium:
Human Experiment
      Methodology
          Design game where parameter controls
           whether or not game is SPM
          Laboratory experiments with human
           subjects playing for real money!




April 9, 2003     CARAT: Gazzale & MacKie Mason
Convergence to Equilibrium:
Human Experiment Results
    Problem: Dynamics not complete with
    human subject experiments (60 rounds)




April 9, 2003   CARAT: Gazzale & MacKie Mason
                              Convergence to Equilibrium:
                              Human Experiment Results                                       a20b00
                                                    Efficiency of Outcome:                   a20b18
                                                      Experimental Data                      a20b20
                                                                                             a20b40
                                                                                             a10b20
                              100%


                              90%
Fraction of Maximum Welfare




                              80%


                              70%


                              60%


                              50%


                              40%
                                     0        10      20       30      40          50   60    Round




                              April 9, 2003        CARAT: Gazzale & MacKie Mason
                              Convergence to Equilibrium:
                              Human Experiment Results                                       a20b00
                                                    Efficiency of Outcome:                   a20b18
                                                      Experimental Data                      a20b20
                                                                                             a20b40
                                                                                             a10b20
                              100%


                              90%
Fraction of Maximum Welfare




                              80%


                              70%


                              60%


                              50%
                                                   Will this treatment catch-up?

                              40%
                                     0        10      20       30      40          50   60    Round




                              April 9, 2003        CARAT: Gazzale & MacKie Mason
                              Convergence to Equilibrium:
                              Human Experiment Results                                       a20b00
                                                    Efficiency of Outcome:                   a20b18
                                                      Experimental Data                      a20b20
                                                                                             a20b40
                                                                                             a10b20
                              100%


                              90%
                                         Will any of these pull ahead?
Fraction of Maximum Welfare




                              80%


                              70%


                              60%


                              50%
                                                   Will this treatment catch-up?

                              40%
                                     0        10      20       30      40          50   60    Round




                              April 9, 2003        CARAT: Gazzale & MacKie Mason
Software agents to complete
dynamics
        Methodology
          Select various learning models
          Endow agents with these models
          Calibrate models with actual data
          Compare calibrated learning models
          Endow pool of agents with best model and
           let run!



April 9, 2003     CARAT: Gazzale & MacKie Mason
Software agents to complete
dynamics
        Use of computation power
          For each learning model and treatment
                 For each set of parameters (1100 sets)
                      12 agents play in each iteration for 60 rounds
                      1500 iterations of game
          8,910,000,000 “decisions” in <6 hours!
          Select Parameters that most-closely fit
           data.
          For best learning model
                      12 agents each iteration for 1000 rounds
                      1500 iterations of game

April 9, 2003             CARAT: Gazzale & MacKie Mason
                              Simulation Results
                                                          Simulated Results                     a20b00
                                                                                                a20b18
                                                                                                a20b20
                              100%
                                          Pulls ahead for a short while!
                                                                                                a20b40
                                                                                                a10b20

                              95%
Fraction of Maximum Welfare




                              90%


                              85%


                              80%

                                                    “Never” does catch up!
                              75%



                              70%
                                     50       150   250      350     450      550   650   750    Round



                              April 9, 2003         CARAT: Gazzale & MacKie Mason
Application 2: Agents Solving
Difficult Problems
      Many problems without analytical
     solution
      Natural domain for use of computer
     science methods to find optimum
         Many are “hill-climbing” methods
     Economics needs to inform these
     solutions


April 9, 2003     CARAT: Gazzale & MacKie Mason
A not so hard problem for an
agent . . .            No matter
                                                where we start,
                                                rather easy to
                                                get to the
                                                summit!




April 9, 2003   CARAT: Gazzale & MacKie Mason
A more difficult landscape . . .
                                                   Tough to get
                                                 from here



                                                  to here


        Bundle                    Per-article
        Price                     Price


April 9, 2003    CARAT: Gazzale & MacKie Mason
A more difficult landscape . . .
 Made a little easier . . .
                                           Use economic
                                           knowledge to:



                                            reduce the
                                            search space!
         Bundle                    Per-article
         Price                     Price



April 9, 2003     CARAT: Gazzale & MacKie Mason
A more difficult landscape . . .
 Made a little easier . . .
                                           Use economic
                                           knowledge to:



                                             select better
                                             starting values!
         Bundle                    Per-article
         Price                     Price



April 9, 2003     CARAT: Gazzale & MacKie Mason
A more difficult landscape . . .
 Made a little easier . . .
                                          Use economic
                                          knowledge to:




                                 Per-article
         Fee                     Price



April 9, 2003   CARAT: Gazzale & MacKie Mason
A more difficult landscape . . .
 Made a little easier . . .
                                        Use economic
                                        knowledge to:



                                            supply gradient
                                            information!
                                 Per-article
         Fee                     Price



April 9, 2003   CARAT: Gazzale & MacKie Mason
Problem 1: Pricing Problem
       Firm Sells Information Goods
       Consumer demand uncertain
       Many different pricing schedules
      possible
       General rule: Higher profits from
      schedules that are harder to learn.
       What schedule?
          No analytical solution!

April 9, 2003      CARAT: Gazzale & MacKie Mason
The Pricing Problem: Results
         adjusting   Linear      Two-part   Block   Nonlinear




                                                                 Adaptive uses
                                                                knowledge to
                                                                move among
                                                                schedules!




April 9, 2003        CARAT: Gazzale & MacKie Mason
Problem 2: Battle of the
Agents
       Highly complex environment
       Large Search space
       Actions of competitor warp my
      landscape.
       Result: Computer science algorithms,
      without economic knowledge, perform
      quite poorly

April 9, 2003   CARAT: Gazzale & MacKie Mason
Computer algorithm, no
economic knowledge
     4
             4
          x 10           Average Profit per Iteration for Zero know ledge Producer   s
                                                                                                            Equilibrium
   3.5
                                         Equilibrium Profit


     3


   2.5


     2


   1.5


     1


   0.5


     0


   0. 5
                 0.2   0.4      0.6       0.8          1        1.2       1.4        1.6   1.8          2
                                                   Iteratio n                                       4
                                                                                                 x 10


April 9, 2003                      CARAT: Gazzale & MacKie Mason
Computer algorithm, with
economic knowledge
             4                                       36000
      x 10
 4

                                                                              equilibrium profit
3.5
        tremble
                             noise
                                                                                                          }
 3
                                                   noise+adjacency
                                                                                                          }
                                                 number of categories


                                                                                                              Better starting
2.5
                                        gradient

 2
                                                                                                                      values

1.5



 1


                                                                                                              Reduce search
                               zero-know ledge


                                                                                                                      space
0.5



 0

                                                                                                              Gradient info
                 0.2   0.4       0.6      0.8           1       1.2     1.4       1.6        1.8          2
April 9, 2003                          CARAT: Gazzale & MacKie Mason
                                                   Iterations                                         4
                                                                                                   x 10
 That’s all folks!

April 9, 2003   CARAT: Gazzale & MacKie Mason

				
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