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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.972 Game Theory and Mechanism Design (MIT) 6.972 Game Theory and Mechanism Design (MIT)

Description

This course is offered to graduates and is an introduction to fundamentals of game theory and mechanism design with motivations drawn from various applications including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, and pricing. Emphasis is placed on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notions in different environments. Topics covered include: normal form games, learning in games, supermodular games, potential games, dynamic games, subgame perfect equilibrium, bargaining, repeated games, auctions, mechanism design, cooperative game theory, network and congestion games, and price of anarchy. This course is offered to graduates and is an introduction to fundamentals of game theory and mechanism design with motivations drawn from various applications including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, and pricing. Emphasis is placed on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notions in different environments. Topics covered include: normal form games, learning in games, supermodular games, potential games, dynamic games, subgame perfect equilibrium, bargaining, repeated games, auctions, mechanism design, cooperative game theory, network and congestion games, and price of anarchy.

Subjects

game theory | game theory | mechanism design | mechanism design | mathematical tools | mathematical tools | normal form games | normal form games | existence and computation of equilibria | existence and computation of equilibria | supermodular games | supermodular games | potential games | potential games | subgame perfect equilibrium | subgame perfect equilibrium | dynamic games | dynamic games | bargaining | bargaining | repeated games | repeated games | games with incomplete/imperfect information | games with incomplete/imperfect information | auctions | auctions | cooperative game theory | cooperative game theory | network and congestion games | network and congestion games | pricing | pricing | price of anarchy | price of anarchy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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14.123 Microeconomic Theory III (MIT) 14.123 Microeconomic Theory III (MIT)

Description

This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation. This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation.

Subjects

microeconomics | microeconomics | microeconomic theory | microeconomic theory | preference | preference | utility representation | utility representation | expected utility | expected utility | positive interpretation | positive interpretation | normative interpretation | normative interpretation | risk | risk | stochastic dominance | stochastic dominance | insurance | insurance | finance | finance | supermodularity | supermodularity | comparative statics | comparative statics | decision theory | decision theory | game theory | game theory | rationalizability | rationalizability | iterated strict dominance | iterated strict dominance | iterated conditional dominance | iterated conditional dominance | bargaining | bargaining | equilibrium | equilibrium | sequential equilibrium | sequential equilibrium | trembling-hand perfection | trembling-hand perfection | signaling games | signaling games | auctions | auctions | global games | global games | repeated games | repeated games | correlation | correlation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.254 Game Theory with Engineering Applications (MIT) 6.254 Game Theory with Engineering Applications (MIT)

Description

This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from engineered/networked systems (including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, multi-agent systems, pricing and investment decisions in the Internet), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments. This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from engineered/networked systems (including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, multi-agent systems, pricing and investment decisions in the Internet), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments.

Subjects

game theory | game theory | strategic form games | strategic form games | learning | evolution | and computation | learning | evolution | and computation | extensive games with perfect information | extensive games with perfect information | repeated games | repeated games | games with incomplete information | games with incomplete information | mechanism design | mechanism design | network effects | network effects | games over networks | games over networks

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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14.15J Networks (MIT) 14.15J Networks (MIT)

Description

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a

Subjects

networks | networks | crowds | crowds | markets | markets | highly connected world | highly connected world | social networks | social networks | economic networks | economic networks | power networks | power networks | communication networks | communication networks | game theory | game theory | graph theory | graph theory | branching processes | branching processes | random graph models | random graph models | rich get richer phenomena | rich get richer phenomena | power laws | power laws | small worlds | small worlds | Erd?s-Renyi graphs | Erd?s-Renyi graphs | degree distributions | degree distributions | phase transitions | phase transitions | connectedness | connectedness | and giant component | and giant component | link analysis | link analysis | web search | web search | navigation | navigation | decentralized search | decentralized search | preferential attachment | preferential attachment | epidemics | epidemics | diffusion through networks | diffusion through networks | SIR | SIR | (susceptible | (susceptible | infected | infected | removed) | removed) | SIS | SIS | susceptible) | susceptible) | strategies | strategies | payoffs | payoffs | normal forms | normal forms | Nash equilibrium | Nash equilibrium | traffic networks | traffic networks | negative externalities | negative externalities | Braess' paradox | Braess' paradox | potential games | potential games | myopic behavior | myopic behavior | fictitious play | fictitious play | repeated games | repeated games | prisoner's dilemma | prisoner's dilemma | cooperation | cooperation | perfect information | perfect information | imperfect information | imperfect information | positive externalities | positive externalities | strategic complements | strategic complements | path dependence | path dependence | diffusion of innovation | diffusion of innovation | contagion pheonomena | contagion pheonomena | Bayes's rule | Bayes's rule | Bayesian Nash equilibrium | Bayesian Nash equilibrium | first price auctions | first price auctions | second price auctions | second price auctions | social learning | social learning | Bayesian learning | Bayesian learning | copying | copying | herding | herding | herd behavior | herd behavior | informational cascades | informational cascades | decisions | decisions | social choice | social choice | Condorcet jury theorem | Condorcet jury theorem | political economy | political economy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete mathematics | discrete | math | mathematics | seminar | presentations | student presentations | oral | communication | stable marriage | dych | emergency | response vehicles | ambulance | game theory | congruences | color theorem | four color | cake cutting | algorithm | RSA | encryption | numberical integration | sorting | post correspondence problem | PCP | ramsey | van der waals | fibonacci | recursion | domino | tiling | towers | hanoi | pigeonhole | principle | matrix | hamming | code | hat game | juggling | zero-knowledge | proof | repeated games | lewis carroll | determinants | infinitude of primes | bridges | konigsberg | koenigsberg | time series analysis | GARCH | rational | recurrence | relations | digital | image | compression | quantum computing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

Site sourced from

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6.972 Game Theory and Mechanism Design (MIT)

Description

This course is offered to graduates and is an introduction to fundamentals of game theory and mechanism design with motivations drawn from various applications including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, and pricing. Emphasis is placed on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notions in different environments. Topics covered include: normal form games, learning in games, supermodular games, potential games, dynamic games, subgame perfect equilibrium, bargaining, repeated games, auctions, mechanism design, cooperative game theory, network and congestion games, and price of anarchy.

Subjects

game theory | mechanism design | mathematical tools | normal form games | existence and computation of equilibria | supermodular games | potential games | subgame perfect equilibrium | dynamic games | bargaining | repeated games | games with incomplete/imperfect information | auctions | cooperative game theory | network and congestion games | pricing | price of anarchy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

Site sourced from

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14.123 Microeconomic Theory III (MIT)

Description

This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation.

Subjects

microeconomics | microeconomic theory | preference | utility representation | expected utility | positive interpretation | normative interpretation | risk | stochastic dominance | insurance | finance | supermodularity | comparative statics | decision theory | game theory | rationalizability | iterated strict dominance | iterated conditional dominance | bargaining | equilibrium | sequential equilibrium | trembling-hand perfection | signaling games | auctions | global games | repeated games | correlation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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14.15J Networks (MIT)

Description

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a

Subjects

networks | crowds | markets | highly connected world | social networks | economic networks | power networks | communication networks | game theory | graph theory | branching processes | random graph models | rich get richer phenomena | power laws | small worlds | Erd?s-Renyi graphs | degree distributions | phase transitions | connectedness | and giant component | link analysis | web search | navigation | decentralized search | preferential attachment | epidemics | diffusion through networks | SIR | (susceptible | infected | removed) | SIS | susceptible) | strategies | payoffs | normal forms | Nash equilibrium | traffic networks | negative externalities | Braess' paradox | potential games | myopic behavior | fictitious play | repeated games | prisoner's dilemma | cooperation | perfect information | imperfect information | positive externalities | strategic complements | path dependence | diffusion of innovation | contagion pheonomena | Bayes's rule | Bayesian Nash equilibrium | first price auctions | second price auctions | social learning | Bayesian learning | copying | herding | herd behavior | informational cascades | decisions | social choice | Condorcet jury theorem | political economy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.254 Game Theory with Engineering Applications (MIT)

Description

This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from engineered/networked systems (including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, multi-agent systems, pricing and investment decisions in the Internet), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments.

Subjects

game theory | strategic form games | learning | evolution | and computation | extensive games with perfect information | repeated games | games with incomplete information | mechanism design | network effects | games over networks

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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