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What? The study of interacting decision makers Economy Biology - - PowerPoint PPT Presentation
What? The study of interacting decision makers Economy Biology - - PowerPoint PPT Presentation
What is game theory? What is game theory? How do we study it? What is game theory? How do we study it? Where is research headed? What? The study of interacting decision makers Economy Biology Sociology Computer Science Engineering Different
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What is game theory? How do we study it?
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What is game theory? How do we study it? Where is research headed?
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What?
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The study of interacting decision makers
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Economy
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Biology
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Sociology
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Computer Science
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Engineering
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Different agendas
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What?
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What?
◮ study of interacting decision makers
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What?
◮ study of interacting decision makers ◮ interdisciplinary field
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What?
◮ study of interacting decision makers ◮ interdisciplinary field ◮ different agendas
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How?
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Decision maker
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Decision maker
◮ choices, C
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Decision maker
◮ choices, C ◮ preferences,
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Decision maker
◮ choices, C ◮ preferences,
utility function, u : C → R c1 c2 ⇐ ⇒ u(c1) ≥ u(c2)
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C = {L, R}
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C = {L, R} u : C → R L → 0 R → 1
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C = {L, R} u : C → R L → 0 R → 1 u L R 1
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K P r(t) e(t) s(t) y(t) −
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K P r(t) e(t) s(t) y(t) −
◮ C = {stabilizing controller K}
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K P r(t) e(t) s(t) y(t) −
◮ C = {stabilizing controller K} ◮ u(K) = −τr(K)
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Optimality
Decision maker:
◮ choices, C ◮ utility function, u
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Optimality
Decision maker:
◮ choices, C ◮ utility function, u
Goal of decision maker: max
c∈C u(c)
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Game Theory
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Game Theory
◮ players, {i}
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Game Theory
◮ players, {i} ◮ choices for player i, Ci
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Game Theory
◮ players, {i} ◮ choices for player i, Ci ◮ joint choices, C =
i Ci
c ∈ C = (ci, c−i)
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Game Theory
◮ players, {i} ◮ choices for player i, Ci ◮ joint choices, C =
i Ci
c ∈ C = (ci, c−i)
◮ utility function for player i, ui : C → R
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Optimality?
Goal of decision maker i: max
c∈C ui(ci, c−i)
- = max
c∈C ui(ci)
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Example: Prisoner’s dilemma
C D C 2, 2 − 1, 3 D 3, −1 0, 0
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Example: Prisoner’s dilemma
C D C 2 − 1 D 3
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Example: Prisoner’s dilemma
C C 2 D 3
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Example: Prisoner’s dilemma
C C 2 D 3 Best response, BRi : C−i ⇒ Ci
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Example: Prisoner’s dilemma
C C 2 D 3 Best response, BRi : C−i ⇒ Ci
◮ BR1(C) = {D}
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Example: Prisoner’s dilemma
D C − 1 D Best response, BRi : C−i ⇒ Ci
◮ BR1(C) = {D}
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Example: Prisoner’s dilemma
D C − 1 D Best response, BRi : C−i ⇒ Ci
◮ BR1(C) = {D}, BR1(D) = {D}
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Example: Prisoner’s dilemma
C D C 2, 2 − 1, 3 D 3, −1 0, 0 Best response, BRi : C−i ⇒ Ci
◮ BR1(C) = {D}, BR1(D) = {D}
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Example: Prisoner’s dilemma
C D C 2, 2 − 1, 3 D 3, −1 0, 0 Best response, BRi : C−i ⇒ Ci
◮ BR1(C) = {D}, BR1(D) = {D} ◮ BR2(C) = {D}, BR2(D) = {D}
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Nash equilibrium
a∗ = (a∗
i, a∗ −i) is a Nash equilibrium:
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Nash equilibrium
a∗ = (a∗
i, a∗ −i) is a Nash equilibrium:
◮ ∀i, a∗
i is a best response to a∗ −i
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Nash equilibrium
a∗ = (a∗
i, a∗ −i) is a Nash equilibrium:
◮ ∀i, a∗
i is a best response to a∗ −i
◮ no unilateral deviation is profitable
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Nash equilibrium
a∗ = (a∗
i, a∗ −i) is a Nash equilibrium:
◮ ∀i, a∗
i is a best response to a∗ −i
◮ no unilateral deviation is profitable ◮ ∀i, ∀ai ∈ Ai,
ui(a∗
i, a∗ −i) ≥ ui(ai, a∗ −i)
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Existence of Nash equilibria
Every n-player game has a Nash equilibrium.
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Extensions
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Extensions
◮ history-dependent strategy
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Extensions
◮ history-dependent strategy ◮ imperfect information
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Extensions
◮ history-dependent strategy ◮ imperfect information ◮ cooperation
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Extensions
◮ history-dependent strategy ◮ imperfect information ◮ cooperation ◮ large populations
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Back to the agendas
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Back to the agendas
◮ descriptive
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Back to the agendas
◮ descriptive ◮ predictive
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Back to the agendas
◮ descriptive ◮ predictive ◮ manipulative
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How?
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How?
◮ interacting decision maker
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How?
◮ interacting decision maker ◮ best response
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How?
◮ interacting decision maker ◮ best response ◮ Nash equilibrium
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Where?
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Learning
Controls ⇒ Game Theory:
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Learning
Controls ⇒ Game Theory:
◮ stability and robustness
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Learning
Controls ⇒ Game Theory:
◮ stability and robustness ◮ derivative control
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Decentralized control
Game Theory ⇒ Controls:
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Decentralized control
Game Theory ⇒ Controls:
◮ network formation
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Decentralized control
Game Theory ⇒ Controls:
◮ network formation ◮ communication limitations
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Dynamic Games
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Dynamic Games
◮ network security
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Dynamic Games
◮ network security ◮ learning in repeated games
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Where?
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Where?
◮ learning
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Where?
◮ learning ◮ decentralized control
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Where?
◮ learning ◮ decentralized control ◮ dynamic games
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