simple stochastic games risk taking in strategic contexts
play

Simple Stochastic Games: Risk Taking in Strategic Contexts Ryan O. - PowerPoint PPT Presentation

Jan 15, 2023 •491 likes •915 views

Simple Stochastic Games: Risk Taking in Strategic Contexts Ryan O. Murphy Chair of Decision Theory and Behavioral Game Theory ETH Zrich Latsis Symposium September 12, 2012 www.dbgt.ethz.ch rmurphy@ethz.ch Michel Barnier, the EUs

  1. Simple Stochastic Games: Risk Taking in Strategic Contexts Ryan O. Murphy Chair of Decision Theory and Behavioral Game Theory ETH Zürich Latsis Symposium September 12, 2012 www.dbgt.ethz.ch rmurphy@ethz.ch

  2. Michel Barnier, the EU’s financial services chief, has proposed that bank investors should have set maximum ratios on the size of their bonuses compared with their fixed pay. Bonuses that are a “large” multiple of fixed pay “are likely to encourage excessive risk taking and undermine confidence in the financial sector generally,” according to the plans. Aug 31, 2012

  3. Contexts • Decision Theory • Certainty One decision maker . • Risk • Uncertainty • Game Theory- Strategic More than one decision maker . Knight, 1921; Luce and Raiffa, 1957.

  4. Decision making Decision theory (Certainty, Risk, Uncertainty) • Risk- Single DM and risky prospects (well defined- • option set, probability space, and payoffs) Typically very simple gambles are used to measure • people’s preferences for risk

  5. Risky decision making • Purview of Decision Theory • Static risky decision • A: a sure gain of 240 • B: a 25% chance to gain 1000 (75% chance of nothing) A very basic static risky choice Common tool in EUT, Prospect theory

  6. Risky decision making • Purview of Decision Theory • Static risky decision EV Behavioral tendency to prefer • A: a sure gain of 240 240 the sure thing; risk aversion • B: a 25% chance to gain 1000 (75% chance of nothing) 250 A very basic static risky choice Common tool in EUT, Prospect theory

  7. Risky decision making ^ dynamic • Good draws are worth 1 • Bad draws result in bankruptcy and the termination of the task • Draws are made with replacement • The DM may make one draw at a time 90% good • The choice for the DM is when to 10% bad stop making draws A very basic dynamic risky choice

  8. Dynamic risky decision making • Devil’s Task (Slovic, 1966) • Iowa Card Task (Bechara et al., 1994) • Balloon Analog Risk Task- BART (Lejuez et al., 2002) • Columbia Card Task (Figner et al., 2009) Other simple dynamic risky and uncertain multi-stage decision tasks See Edwards (1962)

  9. Dynamic risky decision making • Devil’s Task (Slovic, 1966) • Iowa Card Task (Bechara et al., 1994) • Balloon Analog Risk Task- BART (Lejuez et al., 2002) • Columbia Card Task (Figner et al., 2009) Other simple dynamic risky and uncertain multi-stage decision tasks See Edwards (1962)

  10. Dynamic risky decision making • Devil’s Task (Slovic, 1966) • Iowa Card Task (Bechara et al., 1994) • Balloon Analog Risk Task- BART (Lejuez et al., 2002) • Columbia Card Task (Figner et al., 2009) Other simple dynamic risky and uncertain multi-stage decision tasks See Edwards (1962)

  11. Dynamic risky decision making • Devil’s Task (Slovic, 1966) • Iowa Card Task (Bechara et al., 1994) • Balloon Analog Risk Task- BART (Lejuez et al., 2002) • Columbia Card Task (Figner et al., 2009) Other simple dynamic risky and uncertain multi-stage decision tasks See Edwards (1962)

  12. Dynamic risky decision making • Devil’s Task (Slovic, 1966) • Iowa Card Task (Bechara et al., 1994) • Balloon Analog Risk Task- BART (Lejuez et al., 2002) • Columbia Card Task (Figner et al., 2009) Dynamic, well defined payoffs and risks, constant risk level Other simple dynamic risky and uncertain multi-stage decision tasks See Edwards (1962)

  13. Sequential draw task • Good draws are worth v = 1 • Bad draws result in bankruptcy (i.e. a payoff of 0) and the termination of the task • Draws are made with replacement p w = 0.9 • Probabilities- Well defined and p l = (1- p w ) = 0.1 stable A very basic dynamic risky choice

  14. http://vlab.ethz.ch/seq_draw/

  15. Sequential draw task • What is the normative solution to this task? • At each stage, the DM is choosing between: a sure payoff of their current holdings ( h ) vs. the risky option to marginally increase their holdings by v with p w = 0.9 probability p . p l = (1- p w ) = 0.1 v = 1 A very basic dynamic risky choice

  16. Sequential draw task • What is the normative solution to this task? • At each stage, the DM is choosing between: a sure payoff of their current holdings ( h ) vs. the risky option to marginally increase their holdings by v with p w = 0.9 probability p . p l = (1- p w ) = 0.1 v = 1 h ≤ p w · ( h + v ) h ∗ = p · v 1 − p A very basic dynamic risky choice

  17. 30 25 Optimmal number of draws 20 15 10 5 0.5 0.6 0.7 0.8 0.9 1 p(good draw)

  18. 30 25 Optimmal number of draws p w = 0.95 h * = 19 20 15 p w = 0.9 h * = 9 10 p w = 0.8 h * = 4 5 0.5 0.6 0.7 0.8 0.9 1 p(good draw)

  19. Expected value for a draw policy with p(win)=0.90 EV max = 3.49 4 39% payoff of 9 61% payoff of 0 3.5 3 2.5 EV 2 1.5 1 The task is 0.5 sensitive to individual 0 0 5 10 15 20 25 30 35 40 differences in Draws policy risk aversion

  20. Contexts • Decision Theory • Certainty One decision maker . • Risk • Uncertainty • Game Theory- Strategic More than one decision maker . Knight, 1921; Luce and Raiffa, 1957.

  21. Player 1 Player 2 p w = 0.9 p w = 0.9 p l = (1- p w ) = 0.1 p l = (1- p w ) = 0.1 v = 1 point v = 1 point The players make their draws simultaneously and privately. The player with the most points wins the game and has a payoff of 1. The loser earns nothing. Ties are broken randomly. All of this information is common knowledge. See Shapley (1953) A very simple stochastic game

  22. • What is the normative Player 1 Player 2 solution to this game? • EV max does not help... • If player 1 aims for 9 points, p w = 0.9 p w = 0.9 player 2 can beat him 58% p l = (1- p w ) = 0.1 p l = (1- p w ) = 0.1 v = 1 point v = 1 point of the time by only aiming for 1 point. • Simultaneous and private draws • The most points wins • If player 1 realizes this, he • Ties broken randomly can aim for 2 points and then win 78% of the time • If player 2 realizes this... A very simple stochastic game

  23. Player 2 1 2 3 4 5 6 7 8 9 10 11 12 1 0.50 0.18 0.26 0.33 0.39 0.45 0.50 0.54 0.58 0.62 0.65 0.68 2 0.82 0.50 0.25 0.31 0.37 0.42 0.47 0.52 0.55 0.59 0.62 0.65 3 0.74 0.75 0.50 0.30 0.35 0.41 0.45 0.49 0.53 0.56 0.59 0.62 4 0.67 0.69 0.70 0.50 0.34 0.39 0.43 0.47 0.51 0.54 0.57 0.59 Player 1 5 0.61 0.63 0.65 0.66 0.50 0.37 0.41 0.45 0.49 0.52 0.55 0.57 6 0.55 0.58 0.59 0.61 0.63 0.50 0.40 0.44 0.47 0.50 0.53 0.55 7 0.50 0.53 0.55 0.57 0.59 0.60 0.50 0.42 0.45 0.48 0.51 0.53 8 0.46 0.48 0.51 0.53 0.55 0.56 0.58 0.50 0.44 0.47 0.49 0.51 9 0.42 0.45 0.47 0.49 0.51 0.53 0.55 0.56 0.50 0.45 0.48 0.50 10 0.38 0.41 0.44 0.46 0.48 0.50 0.52 0.53 0.55 0.50 0.46 0.48 11 0.35 0.38 0.41 0.43 0.45 0.47 0.49 0.51 0.52 0.54 0.50 0.47 12 0.32 0.35 0.38 0.41 0.43 0.45 0.47 0.49 0.50 0.52 0.53 0.50 Constant sum game, cells show the p(win) and EV for Player 1 given a strategy profile

  24. Player 2 1 2 3 4 5 6 7 8 9 10 11 12 1 0.50 0.18 0.26 0.33 0.39 0.45 0.50 0.54 0.58 0.62 0.65 0.68 2 0.82 0.50 0.25 0.31 0.37 0.42 0.47 0.52 0.55 0.59 0.62 0.65 3 0.74 0.75 0.50 0.30 0.35 0.41 0.45 0.49 0.53 0.56 0.59 0.62 4 0.67 0.69 0.70 0.50 0.34 0.39 0.43 0.47 0.51 0.54 0.57 0.59 Player 1 5 0.61 0.63 0.65 0.66 0.50 0.37 0.41 0.45 0.49 0.52 0.55 0.57 6 0.55 0.58 0.59 0.61 0.63 0.50 0.40 0.44 0.47 0.50 0.53 0.55 7 0.50 0.53 0.55 0.57 0.59 0.60 0.50 0.42 0.45 0.48 0.51 0.53 8 0.46 0.48 0.51 0.53 0.55 0.56 0.58 0.50 0.44 0.47 0.49 0.51 9 0.42 0.45 0.47 0.49 0.51 0.53 0.55 0.56 0.50 0.45 0.48 0.50 10 0.38 0.41 0.44 0.46 0.48 0.50 0.52 0.53 0.55 0.50 0.46 0.48 11 0.35 0.38 0.41 0.43 0.45 0.47 0.49 0.51 0.52 0.54 0.50 0.47 12 0.32 0.35 0.38 0.41 0.43 0.45 0.47 0.49 0.50 0.52 0.53 0.50 Constant sum game, cells show the p(win) and EV for Player 1 given a strategy profile

  25. Player 2 1 2 3 4 5 6 7 8 9 10 11 12 1 0.50 0.18 0.26 0.33 0.39 0.45 0.50 0.54 0.58 0.62 0.65 0.68 2 0.82 0.50 0.25 0.31 0.37 0.42 0.47 0.52 0.55 0.59 0.62 0.65 3 0.74 0.75 0.50 0.30 0.35 0.41 0.45 0.49 0.53 0.56 0.59 0.62 4 0.67 0.69 0.70 0.50 0.34 0.39 0.43 0.47 0.51 0.54 0.57 0.59 Player 1 5 0.61 0.63 0.65 0.66 0.50 0.37 0.41 0.45 0.49 0.52 0.55 0.57 6 0.55 0.58 0.59 0.61 0.63 0.50 0.40 0.44 0.47 0.50 0.53 0.55 7 0.50 0.53 0.55 0.57 0.59 0.60 0.50 0.42 0.45 0.48 0.51 0.53 8 0.46 0.48 0.51 0.53 0.55 0.56 0.58 0.50 0.44 0.47 0.49 0.51 9 0.42 0.45 0.47 0.49 0.51 0.53 0.55 0.56 0.50 0.45 0.48 0.50 10 0.38 0.41 0.44 0.46 0.48 0.50 0.52 0.53 0.55 0.50 0.46 0.48 11 0.35 0.38 0.41 0.43 0.45 0.47 0.49 0.51 0.52 0.54 0.50 0.47 12 0.32 0.35 0.38 0.41 0.43 0.45 0.47 0.49 0.50 0.52 0.53 0.50 Constant sum game, cells show the p(win) and EV for Player 1 given a strategy profile

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Systemic Risk and Stochastic Games with Delay Jean-Pierre Fouque (with Ren e Carmona, Mostafa

Systemic Risk and Stochastic Games with Delay Jean-Pierre Fouque (with Ren e Carmona, Mostafa

Systemic Risk and Stochastic Games with Delay Jean-Pierre Fouque (with Ren e Carmona, Mostafa Mousavi and Li-Hsien Sun) 8th WCMF, University of Washington Seattle, March 24-25, 2017 JP Fouque (UC Santa Barbara) Stochastic Games with Delay

629 views • 49 slides
Stochastic Games Reachability objectives The value (in Formal Verification) Min strategies

Stochastic Games Reachability objectives The value (in Formal Verification) Min strategies

Stochastic games Antonn Ku cera Preliminaries Games Strategies, plays Objectives Stochastic Games Reachability objectives The value (in Formal Verification) Min strategies Max strategies Determinacy Finite-state games BPA games

773 views • 76 slides
Multigrid methods for two player zero-sum stochastic games Sylvie Detournay INRIA Saclay and

Multigrid methods for two player zero-sum stochastic games Sylvie Detournay INRIA Saclay and

Discounted Stochastic Games Stochastic Games with mean payoff Multigrid methods for two player zero-sum stochastic games Sylvie Detournay INRIA Saclay and CMAP, Ecole Polytechnique Soutenance de th` ese Le 25 septembre, 2012 Sylvie

745 views • 70 slides
Strategy recovery for stochastic mean payoff games Marcello Mamino TU Dresden GRASTA 15,

Strategy recovery for stochastic mean payoff games Marcello Mamino TU Dresden GRASTA 15,

Strategy recovery for stochastic mean payoff games Marcello Mamino TU Dresden GRASTA 15, October 1923, 2015, Montreal Outline Stochastic games What is the solution of a game? Complexity of stochastic games Strategy

680 views • 19 slides
Nash Q-Learning for General-Sum Stochastic Games Hu & Wellman March 6th, 2006 CS286r

Nash Q-Learning for General-Sum Stochastic Games Hu & Wellman March 6th, 2006 CS286r

Nash Q-Learning for General-Sum Stochastic Games Hu & Wellman March 6th, 2006 CS286r Presented by Ilan Lobel Outline Stochastic Games and Markov Perfect Equilibria Bellmans Operator as a Contraction Mapping Stochastic

575 views • 29 slides
CS440/ECE448 Lecture 12: Stochastic Games, Stochastic Search, and Learned Evaluation Functions

CS440/ECE448 Lecture 12: Stochastic Games, Stochastic Search, and Learned Evaluation Functions

CS440/ECE448 Lecture 12: Stochastic Games, Stochastic Search, and Learned Evaluation Functions Slides by Svetlana Lazebnik, 9/2016 Modified by Mark Hasegawa-Johnson, 2/2019 Types of game environments Deterministic Stochastic Perfect

600 views • 38 slides
Games Miheer Dewaskar Chennai Mathematical Institute April 27, 2016 1 / 19 Outline Finite

Games Miheer Dewaskar Chennai Mathematical Institute April 27, 2016 1 / 19 Outline Finite

Games Miheer Dewaskar Chennai Mathematical Institute April 27, 2016 1 / 19 Outline Finite Duration Games Win-Lose Games Payoff Games Infinite Duration Games Parity Games Mean Payoff Games Simple Stochastic Games 2 / 19 Outline Finite

2.02k views • 166 slides
Empirical-evidence Equilibria in Stochastic Games Nicolas Dudebout Outline 2 Stochastic

Empirical-evidence Equilibria in Stochastic Games Nicolas Dudebout Outline 2 Stochastic

Empirical-evidence Equilibria in Stochastic Games Nicolas Dudebout Outline 2 Stochastic games Empirical-evidence equilibria (EEEs) Open questions in EEEs Stochastic Games 3 Game theory Markov decision processes Game Theory

587 views • 56 slides
The Leverage Ratio, Risk-Taking and Bank Stability Assessing the trade-off between risk-taking and

The Leverage Ratio, Risk-Taking and Bank Stability Assessing the trade-off between risk-taking and

The Leverage Ratio, Risk-Taking and Bank Stability Assessing the trade-off between risk-taking and loss absorption Jonathan Acosta Smith*, Michael Grill** and Jan Hannes Lang** *Bank of England **European Central Bank Banking regulation,

549 views • 36 slides
CS440/ECE448 Lecture 12: Stochastic Games, Stochastic Search, and Learned Evaluation Functions

CS440/ECE448 Lecture 12: Stochastic Games, Stochastic Search, and Learned Evaluation Functions

CS440/ECE448 Lecture 12: Stochastic Games, Stochastic Search, and Learned Evaluation Functions Slides by Svetlana Lazebnik, 9/2016 Modified by Mark Hasegawa-Johnson, 2/2019 Reminder: Exam 1 (Midterm) Thu, Feb 28 in class Review in

592 views • 41 slides
Take a risk: Be square in your math classroom! GAMES HISTORY Dr. Mary M. Sullivan Rhode

Take a risk: Be square in your math classroom! GAMES HISTORY Dr. Mary M. Sullivan Rhode

Taking Risks in the New Frontier: Rigor, Reasoning and Relevance ATMIM Spring Conference Worcester State University Friday, March 24, 2017 NUMBERS SHAPE Take a risk: Be square in your math classroom! GAMES HISTORY Dr. Mary M. Sullivan

620 views • 12 slides
that arise in stochastic games Mike Harrison Thera Stochastics May 31, 2017 Aaron Kolb (2016),

that arise in stochastic games Mike Harrison Thera Stochastics May 31, 2017 Aaron Kolb (2016),

Interesting one-dimensional diffusions that arise in stochastic games Mike Harrison Thera Stochastics May 31, 2017 Aaron Kolb (2016), Strategic real options, working paper, Kelly School of Business, Indiana Univ. (submitted for publication)

176 views • 16 slides
The Effect of TARP on The Effect of TARP on Bank Risk- -Taking Taking Bank Risk Lamont Black

The Effect of TARP on The Effect of TARP on Bank Risk- -Taking Taking Bank Risk Lamont Black

The Effect of TARP on The Effect of TARP on Bank Risk- -Taking Taking Bank Risk Lamont Black and Lieu Hazelwood Federal Reserve Board of Governors FDIC/JFSR 11 th Annual Bank Research Conference September 2011 The views expressed do not

362 views • 24 slides
The Leverage Ratio, Risk-Taking and Bank Stability Assessing the trade-off between risk-taking and

The Leverage Ratio, Risk-Taking and Bank Stability Assessing the trade-off between risk-taking and

The Leverage Ratio, Risk-Taking and Bank Stability Assessing the trade-off between risk-taking and loss absorption Michael Grill*, Jan Hannes Lang* and Jonathan Smith** *European Central Bank **European Central Bank and University of Cambridge

524 views • 39 slides
Using Stochastic Optimization to Improve Risk Prioritization 0 Limitations of the Risk Cube

Using Stochastic Optimization to Improve Risk Prioritization 0 Limitations of the Risk Cube

Using Stochastic Optimization to Improve Risk Prioritization 0 Limitations of the Risk Cube Method Traditional risk management relies on the 5 risk cube to develop a probability-weighted 4 metric for ranking risks for mitigation 3

301 views • 27 slides
Rational Learning of Mixed Equilibiria in Stochastic Games Michael Bowling UAI Workshop:

Rational Learning of Mixed Equilibiria in Stochastic Games Michael Bowling UAI Workshop:

Rational Learning of Mixed Equilibiria in Stochastic Games Michael Bowling UAI Workshop: Beyond MDPs June 30, 2000 Joint work with Manuela Veloso Overview Stochastic Game Framework Existing Techniques ... ... and Their

338 views • 22 slides
Exploiting Seam s in Mobile Phone Gam es Gregor Broll (Embedded Interaction Research Group, LMU

Exploiting Seam s in Mobile Phone Gam es Gregor Broll (Embedded Interaction Research Group, LMU

PerGam es 2 0 0 6 W orkshop at the Pervasive, Dublin I reland May 7 th 2 0 0 6 Exploiting Seam s in Mobile Phone Gam es Gregor Broll (Embedded Interaction Research Group, LMU Munich) Steve Benford, Leif Opperm ann (MRL, University of Nottingham)

124 views • 8 slides
Extending Dependencies with Conditions Loreto Bravo University of Edinburgh Wenfei Fan

Extending Dependencies with Conditions Loreto Bravo University of Edinburgh Wenfei Fan

Extending Dependencies with Conditions Loreto Bravo University of Edinburgh Wenfei Fan University of Edinburgh & Bell Laboratories Shuai Ma University of Edinburgh 1 Outline Why Conditional Dependencies? Data Cleaning

565 views • 28 slides
Data & Visual Analytics We work with (really) large data. 4 Lesson 1 You need to learn many

Data & Visual Analytics We work with (really) large data. 4 Lesson 1 You need to learn many

10 Lessons Learned from Working with Tech Companies (e.g., Google, eBay, Symantec, Intel) Duen Horng (Polo) Chau Associate Director, MS Analytics Assistant Professor, CSE, College of Computing Georgia Tech 1 Google Polo

734 views • 52 slides
Review: important OS concepts Time-sharing, context, context-switch Interprocess

Review: important OS concepts Time-sharing, context, context-switch Interprocess

Review: important OS concepts Time-sharing, context, context-switch Interprocess communication Exception control flow Priority and scheduling Cache and memory hierarchy (this lecture) Cache & Memory Hierarchy Recall our

517 views • 23 slides
Introduction to Machine Learning CART: Advantages & Disadvantages

Introduction to Machine Learning CART: Advantages & Disadvantages

Introduction to Machine Learning CART: Advantages & Disadvantages compstat-lmu.github.io/lecture_i2ml ADVANTAGES Fairly easy to understand, interpret and visualize. Not much preprocessing required: automatic handling of non-numeric

192 views • 8 slides
CPSC 121: Models of Computation Module 3: Representing Values in a Computer Module 3: Coming

CPSC 121: Models of Computation Module 3: Representing Values in a Computer Module 3: Coming

CPSC 121: Models of Computation Module 3: Representing Values in a Computer Module 3: Coming up... Pre-class quiz #4 is due Tuesday January 23 rd at 19:00. Assigned reading for the quiz: Epp, 4 th edition: 2.3 Epp, 3 rd edition: 1.3 Rosen, 6 th

1.02k views • 45 slides
Lower Bounds for L 1 Discrepancy Armen Vagharshakyan Brown University January 10, 2013 Armen

Lower Bounds for L 1 Discrepancy Armen Vagharshakyan Brown University January 10, 2013 Armen

Introduction to discrepancy Estimates Roths method Elements of proof Closing remarks Lower Bounds for L 1 Discrepancy Armen Vagharshakyan Brown University January 10, 2013 Armen Vagharshakyan Lower Bounds for L 1 Discrepancy Introduction

699 views • 12 slides
Measuring Sample Quality with Steins Method Lester Mackey Joint work with Jackson Gorham

Measuring Sample Quality with Steins Method Lester Mackey Joint work with Jackson Gorham

Measuring Sample Quality with Steins Method Lester Mackey Joint work with Jackson Gorham , Andrew Duncan , Sebastian Vollmer Microsoft Research , Opendoor Labs , University of Sussex , University of Warwick

331 views • 32 slides

More recommend