Rational decisions in non-probabilistic setting

Transcription

1 Computational Logic Seminar, Graduate Center CUNY Rational decisions in non-probabilistic setting Sergei Artemov October 20,

2 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. 2

3 Uncertainty without probabilities? 3

4 Uncertainty without probabilities? 4

5 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? 5

6 Centipede 6

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8 Another paradigm: knowledge 8

9 Maximin and Knowledge converge 9

10 Strategies, moves, outcomes... 10

11 Highest Known Payoff of a strategy 11

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16 Highest Known Payoff of a move 16

17 Best Known Strategy 17

18 Best Known Move 18

19 Best Known Move: uniqueness 19

20 Maximin meets Knowledge 20

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22 KBR decision method 22

23 Why KBR is so special for PI games? 23

24 Why KBR is so special for PI games? 24

25 Nash and subgame perfect equilibria 25

26 Backward induction 26

27 Pure Maximin 27

28 Eliminating dominated strategies 28

29 Proof of KBR-theorem 29

30 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! 30

31 Model predictions: Full knowledge is power 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. 31

32 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. 32

33 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. 33

34 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. 34

35 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. 35