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Computing and Approximating Equilibria : How… …and What’s the Point?. Yevgeniy Vorobeychik Sandia National Laboratories. Who am I?. Ph.D. CS, University of Michigan, advised by Michael Wellman approximating/estimating equilibria in simulation-based games; computational mechanism design

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computing and approximating equilibria how and what s the point

Computing and Approximating Equilibria: How… …and What’s the Point?

Yevgeniy Vorobeychik

Sandia National Laboratories

who am i
Who am I?
  • Ph.D. CS, University of Michigan, advised by Michael Wellman
    • approximating/estimating equilibria in simulation-based games; computational mechanism design
  • Postdoc, University of Pennsylvania, advised by Michael Kearns
    • behavioral experiments on social networks (e.g., networked battle-of-the-sexes, network formation, etc)
  • Currently: Sandia National Labs
    • game theoretic analysis of complex systems
is computing a nash equilibrium hard
Is Computing a Nash equilibrium Hard?
  • PPAD complete – seems pretty hard
  • Leveraging graphical structure helps
    • AGGs (action-graph games), graphical games, etc
    • still hard…
  • Custom solvers for special cases:
    • e.g., Stackelberg games for security
  • Simple search methods
    • often really good: most games in GAMUT have equilibria with very small support size (most have a pure strategy Nash equilibrium)
what about giant games
What about GIANT games?
  • Infinite strategy spaces? Bayesian games? Dynamic games?
  • Yikes!
  • Heuristics seem to work really well at approximating Nash equilibria
    • Variations on iterative best response (TABU best response, keeping track of game theoretic regret, etc)
    • min-regret-first heuristic (explore deviations from lowest-regret profiles)
  • Noisy payoff function evaluations?
    • Take lots of samples
    • compute the next best sample (previous work based on KL divergence of before/after probability distributions of minimum regret profiles)
    • EVI (expected value of information)-based heuristic
great we can solve games now what
Great, we can solve games. Now what?
  • Stackelberg games for security:
    • Compute optimal protection decisions against an intelligent adversary
    • Implemented by airports, federal air marshal
  • Solve other, or more complex,security related games…
great we can solve games now what1
Great, we can solve games. Now what?
  • Mechanism design:
    • can make policy decisions, solving game induced by a policy choice to “predict” strategic outcomes
    • example:
      • government can make or subsidize infrastructure investments in the electric grid
      • can determine the development of grid network; goal: facilitate development of renewable sources (e.g., wind)
      • decisions about building wind farms and generating electricity are based on grid development; done by an imperfectly competitive market
great we can solve games now what2
Great, we can solve games. Now what?
  • Computational “characterizations”
    • map out a “strategic landscape” for a complex game theoretic model
    • example A: what happens in a keyword auction (appropriately stylized) when market conditions change (e.g., increased/decreased number of competitors; increased/decreased number of search engines; changing ranking/pricing rules)
    • qualitative AND quantitative illustrations
      • multi-unit auctions example: know that bid under value; underbidding increases with quanitity; can we quantify this in specific settings?
    • somewhat related to “mechanism design”, but not entirely
beyond nash equilibria
Beyond Nash Equilibria
  • We want a predictive model of behavior
    • humans
    • or computers
  • Try to use data from multiple sources (game models, actual behavior) to predict behavior in future settings
  • Consider principled models of non-financial motivations; maybe alternative representations of preferences (prospect theory, goals-plans)
    • people care about a variety of things ($$, social capital, fairness, etc)