Download Rational decisions in non-probabilistic setting

Computational Logic Seminar, Graduate Center CUNY
Rational decisions
in non-probabilistic setting
Sergei Artemov
October 20, 2009
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In this talk
The knowledge-based rational decision model (KBR-model)
offers an approach to rational decision making in a nonprobabilistic setting, e.g., in perfect information games with
deterministic payoffs. The KBR-model is an epistemically explicit
form of standard game-theoretical assumptions, e.g., Harsanyi's
Maximin Postulate. This model suggests following maximin
strategy over all scenarios which the agent considers possible to
the best of his knowledge.
In this talk, we compare KBR with other approaches and show
that KBR is the only non-probabilistic decision making method
which is definitive, rational, and based exclusively on knowledge.
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Uncertainty without probabilities?
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Uncertainty without probabilities?
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Epistemic Game Theory
First admitted that epistemic states matter and studied
conditions under which standard game theoretical solutions
hold (backward induction, Nash, etc.).
Is still on the way towards developing a coherent theory of
games in which epistemic states of players are a legitimate part
of the game specification?
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Centipede
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Another paradigm: knowledge
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Maximin and Knowledge converge
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Strategies, moves, outcomes...
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Highest Known Payoff of a strategy
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Highest Known Payoff of a move
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Best Known Strategy
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Best Known Move
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Best Known Move: uniqueness
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Maximin meets Knowledge
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KBR decision method
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Why KBR is so special for PI games?
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Why KBR is so special for PI games?
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Nash and subgame perfect equilibria
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Backward induction
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Pure Maximin
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Eliminating dominated strategies
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Proof of KBR-theorem
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Active manipulation
Suppose A is not aware of B and
C’s rationality. Then A moves
left to secure payoff 2. Actually,
A gets 4 which is more than
expected. Suppose also that B
and C are smart enough to
understand this. Then B can
manipulate A by leaking the true
information that C is rational. A then knows that right secures his
payoff 3, which is higher than A’s known payoff of left: A plays
right and gets 3 (less), B gets 4 (much more) and C gets 3 (more).
C does not have an incentive to disclose that B is rational, hence
B wins without ever making a move!
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Full knowledge is power
Model predictions:
Every game with rational players has a solution. Rational
players know which moves to make at each node.
Those who know the game in full know its solution, i.e.,
know everybody’s moves.
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Partial knowledge can hurt
Model predictions:
More knowledge yields a higher known payoff but not
necessarily a higher actual payoff. So
nothing but the truth
can be misleading.
Knowing
the whole truth
however, yields a higher actual payoff.
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When knowledge does not matter
Model predictions:
In strictly competitive (e.g. zero-sum) games, all players’
epistemic states lead to the same (maximin) solution.
Maybe this is why military actions (typical zero-sum games) do
not require sophisticated reasoning about other players:
just do it
normally suffices.
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Conclusions
Do we recommend playing perfect information games using KBR
strategy?
1. Not if you can responsibly assign probabilities to your
opponents' responses, otherwise
2. To the best of your knowledge, rule out all impossible strategies
of the game. If some uncertainly remains, it's this: you cannot
know more. Deal with this uncertainty using KBR; this is the only
rational method of playing PI games.
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Acknowledgments
To all Computational Logic Seminar participants who have
had patience to listen to so many iterations of this work.
Special thanks to Adam Brandenburger, Mel Fitting, Vladimir
Krupski, Loes Olde Loohuis, Elena Nogina, Graham Priest,
and Cagil Tasdemir.
Many thanks to Karen Kletter for selflessly editing endless
versions of this paper.
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