Note:
This post represents the synthesis of the thoughts, procedures and experiences
of others as represented in the articles read in advance (see previous posts)
and the discussion among the students and instructor during the Advanced
Analytic Techniques class at Mercyhurst University, in September 2018 regarding
Game Theory as an Analytic Method, specifically. This technique was evaluated
based on its overall validity, simplicity, flexibility and its ability to
effectively use unstructured data.
Description:
Game theory is a method
for determining optimal strategies for two or more players with numerous
available strategies. Typically this “game” is displayed using a matrix of
payoffs. The underlying assumption is
that players will act in a manner consistent with their own rational
self-interest with the default assumption being that each player will choose a
optimal strategy of maximizing his/her personal payoff. However, the
application of game theory introduces a multitude of variables which will
influence how a player goes about selecting their moves such as whether they
are aware of the moves of other players, whether the game is sequential or
simultaneous, whether the game is cooperative or non-cooperative, and many
other potential factors.
Strengths:
- Develops a
framework for analyzing decision-making
- Quantitative
technique that players can use to arrive at an optimal strategy
- Use to develop
and impose desired outcomes
Weaknesses:
- Assumes rational, intelligent decision makers
- Assumes that players have the knowledge about their own
pay-offs and pay-offs of others
- Payoffs can be arbitrary/subject to interpretation
- Gets more complicated the closer it gets to reality
How-To**:
**There is an extensive
range of models that fall within the parameters of game theory. Our
exercise introduced one of the most basic and classic examples of game theory: The
Prisoner’s Dilemma.
- Define layers or decision
makers
- Determine list of strategies
- Determine outcomes resulting
from each strategy
- Determine payoffs from the
outcomes
Application
of Technique:
Scenario: This is a game show
wherein one player can win money, both players can win money, or neither player can win
money. $100,000 is up for grabs. The players can choose to split the money or steal the money. If
both players choose to “split”, they both walk away with $50,000, if one player chooses to
“steal” and the other chooses to “split”, the player who chose to “steal” walks away with $100,000 and
the player who chose to “split” walks away with $0. If both players choose to “steal”, both
players walk away with $0.
We split 6 players into 3 teams of 2. Each player had two cups with lids -- One cup with a paper inside that said “Split”, the other cup with a paper inside that said, “steal." Players had to decide, given the situation, whether to “steal” or “split” with the other player. Assuming that players make a decision that results in the best possible outcome for each, they would presumably “steal,” resulting in neither player receiving the money.
In the case of our class, 2
teams successfully “split” and the 3rd team resulted in a “steal”/ “split”
opposition.
For Further Information:
Posts
I was very pleased to see this blog and its assessment of game theory as an analytic tool. There are however some myths about game theory, one of which is repeated in this summary findings, which cannot go undiscussed.
ReplyDeleteIt is a common and pernicious myth that game theory "Assumes rational, intelligent decision makers". It does not. The assumption is made for convenience in elementary texts or in advanced texts that are focussed on research into the mathematics theorems of game theory. Even the elementary texts discuss the best moves if one doubts the rationality of an adversary in the analysis.
Game theory DEFINES rationality -- specifically it defines "common rationality" (or sometimes "mutual rationality" -- in a deeper and more specific way than psychology or social science defines rationality -- which allows it to be operationalised. One "can" assume rationality in a game theoretic analysis if the purpose of the analysis is normative. If the purpose is descriptive or if it deals with potentially irrational opponents and is normative, then one can use the definition of common rationality to explore multiple levels of irrationality by all players and explore the difference between (1) genuine irrationality at multiple levels, (2) deception about one's own and others' payoffs, (3) ignorance about own and others' payoffs, while using the payoff analysis for strategic form, sequential move, or hybrid games.
Defining player rationality to mean the player makes the best possible decision for him or herself, then "Common rationality" is loosely defined to mean: "players are rational, AND players assume the other players are rational, AND players assume that the other players assume they are rational, and so on ad infinitum. One can therefore explore levels of irrationality by doing the payoff analysis using the appropriate deviations from the assumed best payoffs in the matrix or tree. (Search for "common rationality", "mutual rationality"
This opens up game theory as a technique for a deeper intelligence analysis of adversaries than is often assumed, since understanding the adversary payoffs is a key intelligence requirement and hiding one's own and/or faking irrationality can be key strategic moves.
Stephen Downes-Martin
Reference "Assumes that players have the knowledge about their own pay-offs and pay-offs of others".
ReplyDeleteBeing required to insert values for payoffs is not the same thing as assuming those are the real payoffs.
One can use game theory to explore deviations from assumed payoffs and then compare the results over time with the real world to refine the payoffs and understanding of the adversaries.
For multiple players and many sequential moves, I recommend the computer program GAMBIT.
ReplyDeletehttp://www.gambit-project.org/
One's pproach to game theory as a practioner rather than a mathematics researcher depends on whether you are using game theory as a normative tool, a predictive/descriptive tool, or a thinking tool to capture what is known and not known about the situation, or some combination.
ReplyDeleteStephen Downes-Martin
Stephen, these are all excellent points and distinctions-- thank you for taking the time to share them. I think you add to the notion that Game Theory, if we are to use it properly and to its highest potential as an analytic technique, must not be oversimplified. It should allow for nuance and variables.
DeleteI think "understanding the adversary payoffs", as you mentioned, is a daunting task. Do you find any additional analytic method yields a particularly robust understanding of said payoffs? Or is that knowledge something we analysts can only come by via research and investigation?
Jillian
DeleteNo single tool will provide you a robust understanding of the payoffs in every situation (or even in most!). The analyst must be expert at several and have a solid working competency at many analytic tools, a combination of which are tailored to the situation. Your blog is on the right track in looking at multiple techniques. (By the way, side note, I recommend adding "System Thinking" to the list. It is the qualitative precursor to the quantitative System Dynamics method and is a good way of describing what we know and critically what we do not know.)
I recommend initially rank ordering the payoffs for the adversary and oneself (or more generally for all the "players"), this preference ranking is an intelligence assessment in its own right, but you must use all the tools at your disposal and a wide diversity of inputs to the analysis to obtain this. Then do a sensitivity analysis over multiple values of the payoffs while maintaining the ranking of the payoff values, using Monte Carlo simulation over the game tree (using GAMBIT) to look for intervals of values that matter to us and to the adversary, and by how much they matter when the payoff values move into different value intervals.
That tells us how much effort we should spend on understanding which situations the adversary prefers over which and by how much, but without having to specify exact cardinal values for the payoffs (by specifying ranges instead).
All the best, Stephen
https://sites.google.com/site/stephendownesmartin/
Let me clarify ... My recommendation concerning sensitivity analysis using Monte Carlo simulation is a recommendation for a research project. (I have done sensitivity analysis manually for two person play ... slow!) Optimization software is another tool to apply within simulation ... optimizing the benefit function for different players.
Delete