Optimization Seminar
Thursday, December 8, 2016 · 10:30 AM - 12 PM
In-Person
·
Mathematics/Psychology : 401
Title: Solving linear games with cone programs
Speaker: Michael Orlitzky
Abstract:
In a two-person zero-sum matrix game, two players play a fixed (finite) set of “moves,” and a winner is determined based on those moves. Afterwards, a payout is made (by convention) from the second player to the first. A strategy is an assignment of probabilities to the moves, and it is known that (on average) there are optimal strategies for both players. Recently, Gowda and Ravindran extended this concept to any symmetric cone, instead of just the nonnegative orthant from which the probabilities are chosen in the classical case. In fact, their work can be extended even further to asymmetric proper cones without much collateral damage. Dantzig showed in 1951 that classical matrix games can be solved through linear programming. We demonstrate that a general game over a proper cone can be solved by cone programming, and present a Python library that does so.
Speaker: Michael Orlitzky
Abstract:
In a two-person zero-sum matrix game, two players play a fixed (finite) set of “moves,” and a winner is determined based on those moves. Afterwards, a payout is made (by convention) from the second player to the first. A strategy is an assignment of probabilities to the moves, and it is known that (on average) there are optimal strategies for both players. Recently, Gowda and Ravindran extended this concept to any symmetric cone, instead of just the nonnegative orthant from which the probabilities are chosen in the classical case. In fact, their work can be extended even further to asymmetric proper cones without much collateral damage. Dantzig showed in 1951 that classical matrix games can be solved through linear programming. We demonstrate that a general game over a proper cone can be solved by cone programming, and present a Python library that does so.