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Unformatted text preview: 6.207/14.15: Networks Lecture 9: Introduction to Game Theory–1 Daron Acemoglu and Asu Ozdaglar MIT October 13, 2009 1 Networks: Lecture 9 Introduction Outline Decisions, Utility Maximization Games and Strategies Best Responses and Dominant Strategies Nash Equilibrium Applications Next Lecture: Mixed Strategies, Existence of Nash Equilibria, and Dynamic Games. Reading: Osborne, Chapters 12. EK, Chapter 6. 2 Networks: Lecture 9 Introduction Motivation In the context of social networks, or even communication networks, agents make a variety of choices. For example: What kind of information to share with others you are connected to. How to evaluate information obtained from friends, neighbors, coworkers and media. Whether to trust and form friendships. Which of the sellers in your neighborhood to use. Which websites to visit. How to map your drive in the morning (or equivalently how to route your network traﬃc). In all of these cases, interactions with other agents you are connected to affect your payoff, wellbeing, utility. How to make decisions in such situations? → “multiagent decision theory” or game theory . 3 Networks: Lecture 9 Introduction “Rational DecisionMaking” Powerful working hypothesis in economics: individuals act rationally in the sense of choosing the option that gives them higher “payoff”. Payoff here need not be monetary payoff. Social and psychological factors inﬂuence payoffs and decisions. Nevertheless, the rational decisionmaking paradigm is useful because it provides us with a (testable) theory of economic and social decisions. We often need only ordinal information; i.e., two options a and b , and we imagine a (realvalued) utility function u ( ) that represents · the ranking of different options, and we simply check whether u ( a ) ≥ u ( b ) or u ( a ) ≤ u ( b ) . In these cases, if a utility function u ( ) represents preferences, so does · any strictly monotonic transformation of u ( ) . · But in game theory we often need cardinal information because decisions are made under natural or strategic uncertainty. The theory of decisionmaking under uncertainty was originally developed by John von Neumann and Oskar Morgenstern. 4 Networks: Lecture 9 Introduction DecisionMaking under Uncertainty von Neumann and Morgenstern posited a number of “reasonable” axioms that rational decisionmaking under uncertainty should satisfy. From these, they derived the expected utility theory . Under uncertainty, every choice induces a lottery , that is, a probability distribution over different outcomes. E.g., one choice would be whether to accept a gamble which pays $10 with probability 1/2 and makes you lose $10 with probability 1/2....
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This note was uploaded on 06/12/2010 for the course EECS 6.207J taught by Professor Acemoglu during the Fall '09 term at MIT.
 Fall '09
 Acemoglu

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