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Modeling Reasoning in Strategic Situations
Avi PfefferMURI Review
Monday, December 17th, 2007
Strategic Situations Scenarios involving multiple agents,
all of which make decisions, and receive rewards based on their decisions
May be competitive, cooperative, or anything in between
May have interesting structure May be extended over time
Strategic Situations Abound Countering terrorist threats Robotic soccer Disaster response Diplomatic relations Auctions Trading
A Key Question
Can we model how agents reason in strategic situations?
Why this Question is Important Modeling how agents reason will
allow us to: predict their behavior develop counter-strategies develop computer systems that help
people in their strategic decision making
analyze situations to determine optimal strategies
allow people to explain their reasoning
Possible Approaches Classical game theory Opponent modeling Behavioral economics Psychological theories
Our Approach Identify the basic reasoning patterns
that can be used to justify decisions underlies sophisticated behavior such
as sacrificing, retaliation and tempting Model and learn the factors
underlying decision-making in particular games
Use the models to develop strategies that work well
Characterizing Reasoning Patterns Informally, a reasoning pattern is a
form of argument that leads to a decision
We characterize reasoning patterns as structures in a graph describing a strategic situation the reasoning patterns capture the way
information is used and manipulated
Reasoning Pattern #1: Direct Effect
An agent takes a decision because of its direct effect on its utility without being mediated by other agents’ actions
Drill
Profit
Reasoning Pattern #2: Manipulation
Child knows about parent’s action Parent does not care about reading, but wants child
to brush teeth Child dislikes brushing teeth but likes being read to Parent can manipulate child
Offer to Read
Parent
Brush Teeth
Child
Reasoning Pattern #3: Signaling
A communicates something that she knows to B, thus influencing B’s behavior
Recommendation
Alice
Choice
Bob
Better Restaurant
Reasoning Pattern #4: Revealing/Denying
Driller cares about oil Tester receives fee if driller drills Tester causes driller to find out (or not) about
information tester herself does not know
Seismic Structure
OilTest Result
Drill
Test
Tester’s Profit Driller’s Profit
A Question For each reasoning pattern, we provide
a graphical criterion to determine if the pattern holds
Intuitively, a node is motivated if the agent owning the node cares about its decision
If a node is motivated, does the graphical criterion characterizing one of the
reasoning patterns necessarily hold?
Answering the question Answer: it depends what strategies
we allow for other agents If we allow arbitrary strategies, any
directed path from a decision node to a utility causes the node to be motivated
But if we restrict attention to a “highly justifiable” class of strategies, we get a more interesting answer
Well-Distinguishing (WD) Strategies: Intuition A strategy is well-distinguishing if
all distinctions that it makes really make a difference whenever the strategy distinguishes
between two states of parents, the agent should receive different utility in the different states
Completeness Result
Theorem: If other agents are playing WD strategies, then a node is motivated only if at least one of the reasoning patterns holds i.e., the four patterns of reasoning are
sufficient to characterize all cases in which an agent cares about a decision
Relationship with Game Theory
Theorem: The set of WD strategies always includes a Nash equilibrium
We can view WD equilibrium as refinement of Nash
Completeness theorem holds for all WD strategies, not just equilibria different assumption from rationality
WD WD equilibria Nash
Learning how People Reason Reasoning patterns give us a
theoretical basis for what arguments a person might make
Can we learn what people actually do in particular games?
Can we use what we learn to develop automatic strategies that perform well?
Learning How to Negotiate Can we learn how people trade off
factors such as self-interest, altruism, etc. in negotiations?
Yes we developed a computer agent using
learned models it performed much better than game-
theoretic agents, and also better than people
Learning Reciprocal Reasoning Do people use reciprocal reasoning
in repeated interactions? retrospective reasoning prospective reasoning
Yes models that factor in reciprocal
reasoning perform better than those that don’t
but prospective may not be as important as retrospective
Reasoning Under Uncertainty When people have uncertainty
about other players, do they use models of the other players?
Yes modeling people as reasoning about
the potential actions of others leads to better performance
but recursive modeling has diminishing returns
Distinguishing Beliefs from Preferences A person’s behavior may be
influenced by both beliefs and preferences can we distinguish between them?
Yes we have created models that are
uniquely identifiable in this scenario, people have almost
correct beliefs
Next Steps Algorithms and analysis tools for
identifying relevant arguments in particular situations
Analyze arguments for key behaviors recruitment to terrorism diplomatic relations, e.g. North Korea
Questions?
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