Dominant and Dominated Strategies
|
|
- Sandra Flynn
- 6 years ago
- Views:
Transcription
1 Dominant and Dominated Strategies Carlos Hurtado Department of Economics University of Illinois at Urbana-Champaign Junel 8th, 2016 C. Hurtado (UIUC - Economics) Game Theory
2 On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
3 The Extensive Form Representation of a Game On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
4 The Extensive Form Representation of a Game What is a Game? From the noncooperative point of view, a game is a multi-person decision situation defined by its structure, which includes: - Players: Independent decision makers - Rules: Which specify the order of players decisions, their feasible decisions at each point they are called upon to make one, and the information they have at such points. - Outcome: How players decisions jointly determine the physical outcome. - Preferences: players preferences over outcomes. C. Hurtado (UIUC - Economics) Game Theory 1 / 39
5 The Extensive Form Representation of a Game Examples Matching Pennies (version A). Players: There are two players, denoted 1 and 2. Rules: Each player simultaneously puts a penny down, either heads up or tails up. Outcomes: If the two pennies match, player 1 pays 1 dollar to player 2; otherwise, player 2 pays 1 dollar to player 1. Matching Pennies (version B). Players: There are two players, denoted 1 and 2. Rules: Player 1 puts a penny down, either heads up or tails up. Then, Player 2 puts a penny down, either heads up or tails up. Outcomes: If the two pennies match, player 1 pays 1 dollar to player 2; otherwise, player 2 pays 1 dollar to player 1. C. Hurtado (UIUC - Economics) Game Theory 2 / 39
6 The Extensive Form Representation of a Game Examples Matching Pennies (version C). Players: There are two players, denoted 1 and 2. Rules: Player 1 puts a penny down, either heads up or tails up, without letting player 2 know his decision. Player 2 puts a penny down, either heads up or tails up. Outcomes: If the two pennies match, player 1 pays 1 dollar to player 2; otherwise, player 2 pays 1 dollar to player 1. Matching Pennies (version D). Players: There are two players, denoted 1 and 2. Rules: Players flip a fair coin to decide who begins. The looser puts a penny down, either heads up or tails up. Then, the winner puts a penny down, either heads up or tails up. Outcomes: If the two pennies match, the looser pays 1 dollar to player 2; otherwise, the winner pays 1 dollar to player 1. C. Hurtado (UIUC - Economics) Game Theory 3 / 39
7 The Extensive Form Representation of a Game The Extensive Form Representation of a Game Some games that are important in economics have simultaneous moves. Simultaneous means strategically simultaneous, in the sense that players decisions are made without knowledge of others decisions. It need not mean literal synchronicity, although that is sufficient for strategic simultaneity. But many important games have at least some sequential decisions, with some later decisions made with knowledge of others earlier decisions. We need a way to describe and analyze both kinds of game. One way to describe either kind of game is via the extensive form or game tree, which shows a game s sequence of decisions, information, outcomes, and payoffs. C. Hurtado (UIUC - Economics) Game Theory 4 / 39
8 The Extensive Form Representation of a Game The Extensive Form Representation of a Game A version of Matching Pennies with sequential decisions, in which Player 1 moves first and player 2 observes 1 s decision before 2 chooses his decision. C. Hurtado (UIUC - Economics) Game Theory 5 / 39
9 The Extensive Form Representation of a Game The Extensive Form Representation of a Game We can represent the usual Matching Pennies with simultaneous decisions by introducing an information set, which includes the decision nodes a player cannot distinguish and at which he must therefore make the same decision, as in the circled nodes. C. Hurtado (UIUC - Economics) Game Theory 6 / 39
10 The Extensive Form Representation of a Game The Extensive Form Representation of a Game The order in which simultaneous decision nodes are listed has some flexibility, as in previous case, where player 2 could have been at the top. For sequential decisions the order must respect the timing of information flows. (Information about decisions already made, as opposed to predictions of future decisions, has no reverse gear.) All decision nodes in an information set must belong to the same player and have the same set of feasible decisions. (Why?) Players are normally assumed necessarily to have perfect recall of their own past decisions (and other information). If so, the tree must reflect this. Definition A game is one of perfect information if each information set contains a single decision node. Otherwhise, it is a game of imperfect information. C. Hurtado (UIUC - Economics) Game Theory 7 / 39
11 The Extensive Form Representation of a Game The Extensive Form Representation of a Game This is an example of a game with simultaneous decision nodes and players with perfect recall of their own past decisions. C. Hurtado (UIUC - Economics) Game Theory 8 / 39
12 The Extensive Form Representation of a Game The Extensive Form Representation of a Game This is an example of a game with simultaneous decision nodes and players without perfect recall of their own past decisions. C. Hurtado (UIUC - Economics) Game Theory 9 / 39
13 The Extensive Form Representation of a Game The Extensive Form Representation of a Game This is another example of a game with simultaneous decision nodes and players without perfect recall of their own past decisions. C. Hurtado (UIUC - Economics) Game Theory 10 / 39
14 The Extensive Form Representation of a Game The Extensive Form Representation of a Game Shared uncertainty (in economics symmetric information ) can be modeled by introducing moves by an artificial player (without preferences) called Nature, who chooses the structure of the game randomly, with commonly known probabilities. C. Hurtado (UIUC - Economics) Game Theory 11 / 39
15 Strategies and the Normal Form Representation of a Game On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
16 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game For sequential games it is important to distinguish strategies from decisions or actions. A strategy is a complete contingent plan for playing the game, which specifies a feasible decision for each of a player s information sets in the game. Recall that his decision must be the same for each decision node in an information set. A strategy is like a detailed manual of actions, not like a single decision or action. C. Hurtado (UIUC - Economics) Game Theory 12 / 39
17 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game C. Hurtado (UIUC - Economics) Game Theory 13 / 39
18 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game It is assumed that conditional on what a player observes, he can predict the probability distributions of his own and others future decisions and their consequences. If players have this kind of foresight, then their rational sequential decision-making in real time should yield exactly the same distribution of decisions as simultaneous choice of fully contingent strategies at the start of play. The player writes his own manual of actions. Then he will give you (a neutral referee) the manual and let you play out the game. You will tell him who won. Because strategies are complete contingent plans, players must be thought of as choosing them simultaneously (without observing others strategies), independently, and irrevocably at the start of play. C. Hurtado (UIUC - Economics) Game Theory 14 / 39
19 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game Why a strategy must be a complete contingent plan, specifying decisions even for a player s own nodes that he knows will be ruled out by his own earlier decisions? Otherwise, other players strategies would not contain enough information for a player to evaluate the consequences of his own alternative strategies. We would then be unable to correctly formalize the idea that a strategy choice is rational. Putting the point in an only seemingly different way, in individual decision theory, zero probability events can be ignored as irrelevant, at least for expected-utility maximizers. But in games zero-probability events cannot be ignored because what has zero probability is endogenously determined by players strategies. C. Hurtado (UIUC - Economics) Game Theory 15 / 39
20 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game Player 2 strategies: Strategy 1 (s 1): Play H if player 1 plays H; Play H if player 1 plays T Strategy 2 (s 2): Play H if player 1 plays H; Play T if player 1 plays T Strategy 3 (s 3): Play T if player 1 plays H; Play H if player 1 plays T Strategy 4 (s 4): Play T if player 1 plays H; Play T if player 1 plays T C. Hurtado (UIUC - Economics) Game Theory 16 / 39
21 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game A game maps strategy profiles (one for each player) into payoffs (with outcomes implicit). A game form maps strategy profiles into outcomes, without specifying payoffs. Specifying strategies make it possible to describe an extensive-form game s relationship between strategy profiles and payoffs by its (unique) normal form or payoff matrix or (usually when strategies are continuously variable) payoff function. C. Hurtado (UIUC - Economics) Game Theory 17 / 39
22 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game C. Hurtado (UIUC - Economics) Game Theory 18 / 39
23 Strategies and the Normal Form Representation of a Game Strategies and the Normal Form Representation of a Game The mapping from the normal to the extensive form isn t univalent: the normal form for Matching Pennies version B has possible extensive forms other than the one depicted before: C. Hurtado (UIUC - Economics) Game Theory 19 / 39
24 Randomized Choices On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
25 Randomized Choices Randomized Choices In game theory it is useful to extend the idea of strategy from the unrandomized (pure) notion we have considered to allow mixed strategies (randomized strategy choices). Example: Matching Pennies Version A has no appealing pure strategies, but there is a convincingly appealing way to play using mixed strategies: randomizing (Why?) Our definitions apply to mixed as well as pure strategies, given that the uncertainty about outcomes that mixed strategies cause is handled (just as for other kinds of uncertainty) by assigning payoffs to outcomes so that rational players maximize their expected payoffs. Mixed strategies will enable us to show that (reasonably well-behaved) games always have rational strategy combinations. In extensive-form games with perfect recall, mixed strategies are equivalent to behavior strategies, probability distributions over pure decisions at each node (Kuhn s Theorem; see MWG problem 7.E.1). C. Hurtado (UIUC - Economics) Game Theory 20 / 39
26 Exercises On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
27 Exercises Exercises Exercise 1. In a game where player i has N information sets indexed n = 1,, N and M n possible actions at information set n, how many strategies does player i have? Exercise 2. Depict the normal formm of Matching Pennies Version C. C. Hurtado (UIUC - Economics) Game Theory 21 / 39
28 Exercises Exercises Exercise 3. Consider the followign two-player (excluding payoffs): a) What are player 1 s possible strategies? player 2 s? b) Suppose that we change the game by merging the information set of player 1 s second round of moves (so that all the four nodes are now in a single information set). Argue why the game is no longer one of perfect recall. C. Hurtado (UIUC - Economics) Game Theory 22 / 39
29 Formalizing the Game On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
30 Formalizing the Game Formalizing the Game Up to this point we defined game without been formal. Let me introduce some Notation: - set of players: I = {1, 2,, N} - set of actions: i I, a i A i, where each player i has a set of actions A i. - strategies for each player: i I, s i S i, where each player i has a set of pure strategies S i available to him. A strategy is a complete contingent plan for playing the game, which specifies a feasible action of a player s information sets in the game. - profile of pure strategies: s = (s 1, s 2,, s N ) N i=1 Si. Note: let s i = (s 1, s 2,, s i 1, s i+1,, s N ) S i, we will denote s = (s i, s i) (S i, S i). - Payoff function: u i : N Si R, denoted by ui(si, s i) i=1 C. Hurtado (UIUC - Economics) Game Theory 23 / 39
31 Formalizing the Game Formalizing the Game Now we can denote game with pure strategies and complete information in normal form by: Γ N = {I, {S i} i, {u i} i}. What about the games with mix strategies? We have taken it that when a player acts at any information set, he deterministically picks an action from the set of available actions. But there is no fundamental reason why this has to be case. Definition A mixed strategy for player i is a function σ i : S i [0, 1], which assigns a probability σ i(s i) 0 to each pure strategy s i S i, satisfying s i S i σ i(s i) = 1. We denote the set of mixed strategies by (S i). Note that a pure strategy can be viewed as a special case of a mixed strategy in which the probability distribution over the elements of S i is degenerate. C. Hurtado (UIUC - Economics) Game Theory 24 / 39
32 Formalizing the Game Example Meeting in New York: - Players: Two players, 1 and 2 - Rules: The two players can not communicate. They are suppose to meet in NYC at noon to have lunch but they have not specify where. Each must decide where to go (only one choice). - Outcomes: If they meet each other, they enjoy other s company. Otherwise, they eat alone. - Payoffs: They attach a monetary value of 100 USD to other s company and 0 USD to eat alone. player 1 player 2 A B C A 100,100 0,0 0,0 B 0,0 100,100 0,0 C. Hurtado (UIUC - Economics) Game Theory 25 / 39
33 Formalizing the Game Example Meeting in New York: - set of players: I = {1, 2} - set of actions: A 1 = {A, B}, and A 2 = {A, B, C} - strategies for each player: S 1 = A 1, and S 2 = A 2 (Why?) - Payoff function: u i : 2 Si R, denoted by ui(si, s i) i=1 u(s i, s i) = { if s i = s i if s i s i Player 2 - pure strategies: S 2 = {A, B, C}. Player 2 has 3 pure strategies. - mixed strategies: (S 2) = {(σ 2 1, σ 2 2, σ 2 3) R 3 σ 2 m 0 m = 1, 2, 3 and 3 m=1 σ2 m = 1} C. Hurtado (UIUC - Economics) Game Theory 26 / 39
34 Dominant and Dominated Strategies On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
35 Dominant and Dominated Strategies Dominant and Dominated Strategies Now we turn to the central question of game theory: What should be expected to observe in a game played by rational agents who are fully knowledgeable about the structure of the game and each others rationality? To keep matters simple we initially ignore the possibility that players might randomize in their strategy choices. The prisoner s dilemma: * Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. * The prosecutors do not have enough evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. * Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. * Here is the offer: - If A and B each betray the other, each of them serves 2 years in prison - If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa) - If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge) C. Hurtado (UIUC - Economics) Game Theory 27 / 39
36 Dominant and Dominated Strategies Dominant and Dominated Strategies Let me put prisoner s dilemma as a game of trust: player 1 player 2 trust cheat trust 5,5 1,10 cheat 10,1 2,2 Observe that regardless of what her opponent does, player i is strictly better off playing Cheat rather than Trust. This is precisely what is meant by a strictly dominant strategy. Player 2 plays Trust. Player 1 knows that 10 > 5, better to Cheat. Player 2 plays Cheat. Player 1 knows that 2 > 1, better to Cheat. Regardless of the other s strategies, it is always better to Cheat. Note that both would be better off if they both play trust. Lesson: self-interested behavior in games may not lead to socially optimal outcomes. C. Hurtado (UIUC - Economics) Game Theory 28 / 39
37 Dominant and Dominated Strategies Dominant and Dominated Strategies Definition A strategy s i S i is a strictly dominant strategy for player i if for all s i s i and all s i S i, u i (s i, s i ) > u i ( s i, s i ). A strictly dominant strategy for i uniquely maximizes her payoff for any strategy profile of all other players. If such a strategy exists, it is highly reasonable to expect a player to play it. In a sense, this is a consequence of a player s rationality. C. Hurtado (UIUC - Economics) Game Theory 29 / 39
38 Dominant and Dominated Strategies Dominant and Dominated Strategies What about if a strictly dominant strategy doesn t exist? player 1 player 2 a b c A 5,5 0,10 3,4 B 3,0 2,2 4,5 You can easily convince yourself that there are no strictly dominant strategies here for either player. Notice that regardless of whether Player 1 plays A or B, Player 2 does strictly better by playing b rather than a. That is, a is strictly dominated by b. C. Hurtado (UIUC - Economics) Game Theory 30 / 39
39 Dominant and Dominated Strategies Dominant and Dominated Strategies Definition A strategy s i S i is strictly dominated for player i if there exists a strategy s i S i such that for all s i S i, u i ( s i, s i ) > u i (s i, s i ). In this case, we say that s i strictly dominates s i. In words, s i strictly dominates s i if it yields a strictly higher payoff regardless of what (pure) strategy rivals use. Note that the definition would also permits us to use mixed strategies Using this terminology, we can restate the definition of strictly dominant: A strategy s i is strictly dominant if it strictly dominates all other strategies. It is reasonable that a player will not play a strictly dominated strategy, a consequence of rationality, again. C. Hurtado (UIUC - Economics) Game Theory 31 / 39
40 Iterated Delation of Strictly Dominated Strategies On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
41 Iterated Delation of Strictly Dominated Strategies Iterated Delation of Strictly Dominated Strategies player 1 player 2 a b c A 5,5 0,10 3,4 B 3,0 2,2 4,5 We argued that a is strictly dominated (by b) for Player 2; hence rationality of Player 2 dictates she won t play it. We can push the logic further: if Player 1 knows that Player 2 is rational, he should realize that Player 2 will not play strategy a. Notice that we are now moving from the rationality of each player to the mutual knowledge of each player s rationality. Once Player 1 realizes that 2 will not play a and deletes this strategy from the strategy space, then strategy A becomes strictly dominated by strategy B for Player 2. If we iterate the knowledge of rationality once again, then Player 2 realizes that 1 will not play A, and hence deletes A. Player 2 should play c. We have arrived at a solution. C. Hurtado (UIUC - Economics) Game Theory 32 / 39
42 Iterated Delation of Strictly Dominated Strategies Iterated Delation of Strictly Dominated Strategies Definition A game is strict-dominance solvable if iterated deletion of strictly dominated strategies results in a unique strategy profile. Since in principle we might have to iterate numerous times in order to solve a strict-dominance solvable game, the process can effectively can only be justified by common knowledge of rationality. As with strictly dominant strategies, it is also true that most games are not strict-dominance solvable. You might worry whether the order in which we delete strategies iteratively matters. Insofar as we are working with strictly dominated strategies so far, it does not. C. Hurtado (UIUC - Economics) Game Theory 33 / 39
43 Iterated Delation of Dominated Strategies On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
44 Iterated Delation of Dominated Strategies Iterated Delation of Dominated Strategies Definition A strategy s i S i is a weakly dominant strategy for player i if for all s i s i and all s i S i, u i (s i, s i ) u i ( s i, s i ), and for at least one choice of s i the inequality is strict. Definition A strategy s i S i is weakly dominated for player i if there exists a strategy s i S i such that for all s i S i, u i ( s i, s i ) u i (s i, s i ), and for at least one choice of s i the inequality is strict. In this case, we say that s i weakly dominates s i. Definition A game is weakly-dominance solvable if iterated deletion of weakly dominated strategies results in a unique strategy profile. C. Hurtado (UIUC - Economics) Game Theory 34 / 39
45 Iterated Delation of Dominated Strategies Iterated Delation of Dominated Strategies Using this terminology, we can restate the definition of weakly dominant: A strategy s i is weakly dominant if it weakly dominates all other strategies. You might worry whether the order in which we delete strategies iteratively matters. Delation of dominated strategies could leave to different outcomes. P2 L R U 5,1 4,0 P1 M 6,0 3,1 D 6,4 4,4 P2 P2 L R L R P1 U 5,1 4,0 D 6,4 4,4 P1 M 6,0 3,1 D 6,4 4,4 C. Hurtado (UIUC - Economics) Game Theory 35 / 39
46 Exercises On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory
47 Exercises Exercises Exercise 1. Prove that a player can have at most one strictly dominant strategy. Exercise 2. Apply the iterated elimination of strictly dominated strategies to the following normal form games. Note that in some cases there may remain more that one strategy for each player. Say exactly in what order you eliminated rows and columns. Exercise 3. Apply the iterated elimination of dominated strategies to the following normal form games. Note that in some cases there may remain more that one strategy for each player. Say exactly in what order you eliminated rows and columns. C. Hurtado (UIUC - Economics) Game Theory 36 / 39
48 Exercises Exercises Exercise 2 (cont.). C. Hurtado (UIUC - Economics) Game Theory 37 / 39
49 Exercises Exercises Exercise 2 (cont.). C. Hurtado (UIUC - Economics) Game Theory 38 / 39
50 Exercises Exercises Exercise 2 (cont.). C. Hurtado (UIUC - Economics) Game Theory 39 / 39
Dominant and Dominated Strategies
Dominant and Dominated Strategies Carlos Hurtado Department of Economics University of Illinois at Urbana-Champaign hrtdmrt2@illinois.edu May 29th, 2015 C. Hurtado (UIUC - Economics) Game Theory On the
More informationDynamic Games: Backward Induction and Subgame Perfection
Dynamic Games: Backward Induction and Subgame Perfection Carlos Hurtado Department of Economics University of Illinois at Urbana-Champaign hrtdmrt2@illinois.edu Jun 22th, 2017 C. Hurtado (UIUC - Economics)
More informationGame Theory. Wolfgang Frimmel. Dominance
Game Theory Wolfgang Frimmel Dominance 1 / 13 Example: Prisoners dilemma Consider the following game in normal-form: There are two players who both have the options cooperate (C) and defect (D) Both players
More informationAdvanced Microeconomics (Economics 104) Spring 2011 Strategic games I
Advanced Microeconomics (Economics 104) Spring 2011 Strategic games I Topics The required readings for this part is O chapter 2 and further readings are OR 2.1-2.3. The prerequisites are the Introduction
More informationFinite games: finite number of players, finite number of possible actions, finite number of moves. Canusegametreetodepicttheextensiveform.
A game is a formal representation of a situation in which individuals interact in a setting of strategic interdependence. Strategic interdependence each individual s utility depends not only on his own
More informationLecture 6: Basics of Game Theory
0368.4170: Cryptography and Game Theory Ran Canetti and Alon Rosen Lecture 6: Basics of Game Theory 25 November 2009 Fall 2009 Scribes: D. Teshler Lecture Overview 1. What is a Game? 2. Solution Concepts:
More informationDominance and Best Response. player 2
Dominance and Best Response Consider the following game, Figure 6.1(a) from the text. player 2 L R player 1 U 2, 3 5, 0 D 1, 0 4, 3 Suppose you are player 1. The strategy U yields higher payoff than any
More informationGame Theory and Randomized Algorithms
Game Theory and Randomized Algorithms Guy Aridor Game theory is a set of tools that allow us to understand how decisionmakers interact with each other. It has practical applications in economics, international
More informationGame Theory Refresher. Muriel Niederle. February 3, A set of players (here for simplicity only 2 players, all generalized to N players).
Game Theory Refresher Muriel Niederle February 3, 2009 1. Definition of a Game We start by rst de ning what a game is. A game consists of: A set of players (here for simplicity only 2 players, all generalized
More informationEC3224 Autumn Lecture #02 Nash Equilibrium
Reading EC3224 Autumn Lecture #02 Nash Equilibrium Osborne Chapters 2.6-2.10, (12) By the end of this week you should be able to: define Nash equilibrium and explain several different motivations for it.
More information(a) Left Right (b) Left Right. Up Up 5-4. Row Down 0-5 Row Down 1 2. (c) B1 B2 (d) B1 B2 A1 4, 2-5, 6 A1 3, 2 0, 1
Economics 109 Practice Problems 2, Vincent Crawford, Spring 2002 In addition to these problems and those in Practice Problems 1 and the midterm, you may find the problems in Dixit and Skeath, Games of
More informationReading Robert Gibbons, A Primer in Game Theory, Harvester Wheatsheaf 1992.
Reading Robert Gibbons, A Primer in Game Theory, Harvester Wheatsheaf 1992. Additional readings could be assigned from time to time. They are an integral part of the class and you are expected to read
More informationIntroduction to Game Theory
Introduction to Game Theory Lecture 2 Lorenzo Rocco Galilean School - Università di Padova March 2017 Rocco (Padova) Game Theory March 2017 1 / 46 Games in Extensive Form The most accurate description
More informationGame Theory: The Basics. Theory of Games and Economics Behavior John Von Neumann and Oskar Morgenstern (1943)
Game Theory: The Basics The following is based on Games of Strategy, Dixit and Skeath, 1999. Topic 8 Game Theory Page 1 Theory of Games and Economics Behavior John Von Neumann and Oskar Morgenstern (1943)
More informationSummary Overview of Topics in Econ 30200b: Decision theory: strong and weak domination by randomized strategies, domination theorem, expected utility
Summary Overview of Topics in Econ 30200b: Decision theory: strong and weak domination by randomized strategies, domination theorem, expected utility theorem (consistent decisions under uncertainty should
More informationSection Notes 6. Game Theory. Applied Math 121. Week of March 22, understand the difference between pure and mixed strategies.
Section Notes 6 Game Theory Applied Math 121 Week of March 22, 2010 Goals for the week be comfortable with the elements of game theory. understand the difference between pure and mixed strategies. be able
More informationGame Theory. Lecture Notes By Y. Narahari. Department of Computer Science and Automation Indian Institute of Science Bangalore, India August 2012
Game Theory Lecture Notes By Y. Narahari Department of Computer Science and Automation Indian Institute of Science Bangalore, India August 01 Rationalizable Strategies Note: This is a only a draft version,
More informationGAME THEORY: STRATEGY AND EQUILIBRIUM
Prerequisites Almost essential Game Theory: Basics GAME THEORY: STRATEGY AND EQUILIBRIUM MICROECONOMICS Principles and Analysis Frank Cowell Note: the detail in slides marked * can only be seen if you
More informationGame theory attempts to mathematically. capture behavior in strategic situations, or. games, in which an individual s success in
Game Theory Game theory attempts to mathematically capture behavior in strategic situations, or games, in which an individual s success in making choices depends on the choices of others. A game Γ consists
More information2. Basics of Noncooperative Games
2. Basics of Noncooperative Games Introduction Microeconomics studies the behavior of individual economic agents and their interactions. Game theory plays a central role in modeling the interactions between
More informationCS510 \ Lecture Ariel Stolerman
CS510 \ Lecture04 2012-10-15 1 Ariel Stolerman Administration Assignment 2: just a programming assignment. Midterm: posted by next week (5), will cover: o Lectures o Readings A midterm review sheet will
More informationUPenn NETS 412: Algorithmic Game Theory Game Theory Practice. Clyde Silent Confess Silent 1, 1 10, 0 Confess 0, 10 5, 5
Problem 1 UPenn NETS 412: Algorithmic Game Theory Game Theory Practice Bonnie Clyde Silent Confess Silent 1, 1 10, 0 Confess 0, 10 5, 5 This game is called Prisoner s Dilemma. Bonnie and Clyde have been
More informationRationality and Common Knowledge
4 Rationality and Common Knowledge In this chapter we study the implications of imposing the assumptions of rationality as well as common knowledge of rationality We derive and explore some solution concepts
More informationRationality, Dominance and Best Response
Rationality, Dominance and Best Response Brett Devine ECONS 424 - Strategy & Game Theory School of Economic Sciences Rationality A player is rational when she acts in her own best interests. Given a player
More informationMultiagent Systems: Intro to Game Theory. CS 486/686: Introduction to Artificial Intelligence
Multiagent Systems: Intro to Game Theory CS 486/686: Introduction to Artificial Intelligence 1 Introduction So far almost everything we have looked at has been in a single-agent setting Today - Multiagent
More informationCMU-Q Lecture 20:
CMU-Q 15-381 Lecture 20: Game Theory I Teacher: Gianni A. Di Caro ICE-CREAM WARS http://youtu.be/jilgxenbk_8 2 GAME THEORY Game theory is the formal study of conflict and cooperation in (rational) multi-agent
More informationNormal Form Games: A Brief Introduction
Normal Form Games: A Brief Introduction Arup Daripa TOF1: Market Microstructure Birkbeck College Autumn 2005 1. Games in strategic form. 2. Dominance and iterated dominance. 3. Weak dominance. 4. Nash
More information1. Introduction to Game Theory
1. Introduction to Game Theory What is game theory? Important branch of applied mathematics / economics Eight game theorists have won the Nobel prize, most notably John Nash (subject of Beautiful mind
More informationLecture 11 Strategic Form Games
Lecture 11 Strategic Form Games Jitesh H. Panchal ME 597: Decision Making for Engineering Systems Design Design Engineering Lab @ Purdue (DELP) School of Mechanical Engineering Purdue University, West
More informationDomination Rationalizability Correlated Equilibrium Computing CE Computational problems in domination. Game Theory Week 3. Kevin Leyton-Brown
Game Theory Week 3 Kevin Leyton-Brown Game Theory Week 3 Kevin Leyton-Brown, Slide 1 Lecture Overview 1 Domination 2 Rationalizability 3 Correlated Equilibrium 4 Computing CE 5 Computational problems in
More informationIntroduction to Game Theory
Introduction to Game Theory Managing with Game Theory Hongying FEI Feihy@i.shu.edu.cn Poker Game ( 2 players) Each player is dealt randomly 3 cards Both of them order their cards as they want Cards at
More informationComputational Methods for Non-Cooperative Game Theory
Computational Methods for Non-Cooperative Game Theory What is a game? Introduction A game is a decision problem in which there a multiple decision makers, each with pay-off interdependence Each decisions
More informationECON 282 Final Practice Problems
ECON 282 Final Practice Problems S. Lu Multiple Choice Questions Note: The presence of these practice questions does not imply that there will be any multiple choice questions on the final exam. 1. How
More informationTHEORY: NASH EQUILIBRIUM
THEORY: NASH EQUILIBRIUM 1 The Story Prisoner s Dilemma Two prisoners held in separate rooms. Authorities offer a reduced sentence to each prisoner if he rats out his friend. If a prisoner is ratted out
More informationCSCI 699: Topics in Learning and Game Theory Fall 2017 Lecture 3: Intro to Game Theory. Instructor: Shaddin Dughmi
CSCI 699: Topics in Learning and Game Theory Fall 217 Lecture 3: Intro to Game Theory Instructor: Shaddin Dughmi Outline 1 Introduction 2 Games of Complete Information 3 Games of Incomplete Information
More informationU strictly dominates D for player A, and L strictly dominates R for player B. This leaves (U, L) as a Strict Dominant Strategy Equilibrium.
Problem Set 3 (Game Theory) Do five of nine. 1. Games in Strategic Form Underline all best responses, then perform iterated deletion of strictly dominated strategies. In each case, do you get a unique
More informationGame Theory and Economics of Contracts Lecture 4 Basics in Game Theory (2)
Game Theory and Economics of Contracts Lecture 4 Basics in Game Theory (2) Yu (Larry) Chen School of Economics, Nanjing University Fall 2015 Extensive Form Game I It uses game tree to represent the games.
More informationNORMAL FORM (SIMULTANEOUS MOVE) GAMES
NORMAL FORM (SIMULTANEOUS MOVE) GAMES 1 For These Games Choices are simultaneous made independently and without observing the other players actions Players have complete information, which means they know
More informationECO 199 B GAMES OF STRATEGY Spring Term 2004 B February 24 SEQUENTIAL AND SIMULTANEOUS GAMES. Representation Tree Matrix Equilibrium concept
CLASSIFICATION ECO 199 B GAMES OF STRATEGY Spring Term 2004 B February 24 SEQUENTIAL AND SIMULTANEOUS GAMES Sequential Games Simultaneous Representation Tree Matrix Equilibrium concept Rollback (subgame
More informationFirst Prev Next Last Go Back Full Screen Close Quit. Game Theory. Giorgio Fagiolo
Game Theory Giorgio Fagiolo giorgio.fagiolo@univr.it https://mail.sssup.it/ fagiolo/welcome.html Academic Year 2005-2006 University of Verona Web Resources My homepage: https://mail.sssup.it/~fagiolo/welcome.html
More informationLECTURE 26: GAME THEORY 1
15-382 COLLECTIVE INTELLIGENCE S18 LECTURE 26: GAME THEORY 1 INSTRUCTOR: GIANNI A. DI CARO ICE-CREAM WARS http://youtu.be/jilgxenbk_8 2 GAME THEORY Game theory is the formal study of conflict and cooperation
More information2. The Extensive Form of a Game
2. The Extensive Form of a Game In the extensive form, games are sequential, interactive processes which moves from one position to another in response to the wills of the players or the whims of chance.
More information8.F The Possibility of Mistakes: Trembling Hand Perfection
February 4, 2015 8.F The Possibility of Mistakes: Trembling Hand Perfection back to games of complete information, for the moment refinement: a set of principles that allow one to select among equilibria.
More informationMultiagent Systems: Intro to Game Theory. CS 486/686: Introduction to Artificial Intelligence
Multiagent Systems: Intro to Game Theory CS 486/686: Introduction to Artificial Intelligence 1 1 Introduction So far almost everything we have looked at has been in a single-agent setting Today - Multiagent
More information1\2 L m R M 2, 2 1, 1 0, 0 B 1, 0 0, 0 1, 1
Chapter 1 Introduction Game Theory is a misnomer for Multiperson Decision Theory. It develops tools, methods, and language that allow a coherent analysis of the decision-making processes when there are
More informationTopic 1: defining games and strategies. SF2972: Game theory. Not allowed: Extensive form game: formal definition
SF2972: Game theory Mark Voorneveld, mark.voorneveld@hhs.se Topic 1: defining games and strategies Drawing a game tree is usually the most informative way to represent an extensive form game. Here is one
More information2. Extensive Form Games
Lecture Notes By Y. Narahari Department of Computer Science and Automation Indian Institute of Science Bangalore, India July 0. Extensive Form Games Note: his is a only a draft version, so there could
More informationAdvanced Microeconomics: Game Theory
Advanced Microeconomics: Game Theory P. v. Mouche Wageningen University 2018 Outline 1 Motivation 2 Games in strategic form 3 Games in extensive form What is game theory? Traditional game theory deals
More informationExtensive Form Games. Mihai Manea MIT
Extensive Form Games Mihai Manea MIT Extensive-Form Games N: finite set of players; nature is player 0 N tree: order of moves payoffs for every player at the terminal nodes information partition actions
More informationECO 220 Game Theory. Objectives. Agenda. Simultaneous Move Games. Be able to structure a game in normal form Be able to identify a Nash equilibrium
ECO 220 Game Theory Simultaneous Move Games Objectives Be able to structure a game in normal form Be able to identify a Nash equilibrium Agenda Definitions Equilibrium Concepts Dominance Coordination Games
More informationLecture Notes on Game Theory (QTM)
Theory of games: Introduction and basic terminology, pure strategy games (including identification of saddle point and value of the game), Principle of dominance, mixed strategy games (only arithmetic
More informationECON 312: Games and Strategy 1. Industrial Organization Games and Strategy
ECON 312: Games and Strategy 1 Industrial Organization Games and Strategy A Game is a stylized model that depicts situation of strategic behavior, where the payoff for one agent depends on its own actions
More informationAppendix A A Primer in Game Theory
Appendix A A Primer in Game Theory This presentation of the main ideas and concepts of game theory required to understand the discussion in this book is intended for readers without previous exposure to
More informationMulti-player, non-zero-sum games
Multi-player, non-zero-sum games 4,3,2 4,3,2 1,5,2 4,3,2 7,4,1 1,5,2 7,7,1 Utilities are tuples Each player maximizes their own utility at each node Utilities get propagated (backed up) from children to
More information3 Game Theory II: Sequential-Move and Repeated Games
3 Game Theory II: Sequential-Move and Repeated Games Recognizing that the contributions you make to a shared computer cluster today will be known to other participants tomorrow, you wonder how that affects
More informationGame Theory Lecturer: Ji Liu Thanks for Jerry Zhu's slides
Game Theory ecturer: Ji iu Thanks for Jerry Zhu's slides [based on slides from Andrew Moore http://www.cs.cmu.edu/~awm/tutorials] slide 1 Overview Matrix normal form Chance games Games with hidden information
More informationAdversarial Search and Game Theory. CS 510 Lecture 5 October 26, 2017
Adversarial Search and Game Theory CS 510 Lecture 5 October 26, 2017 Reminders Proposals due today Midterm next week past midterms online Midterm online BBLearn Available Thurs-Sun, ~2 hours Overview Game
More informationResource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Game Theory
Resource Allocation and Decision Analysis (ECON 8) Spring 4 Foundations of Game Theory Reading: Game Theory (ECON 8 Coursepak, Page 95) Definitions and Concepts: Game Theory study of decision making settings
More information1. Simultaneous games All players move at same time. Represent with a game table. We ll stick to 2 players, generally A and B or Row and Col.
I. Game Theory: Basic Concepts 1. Simultaneous games All players move at same time. Represent with a game table. We ll stick to 2 players, generally A and B or Row and Col. Representation of utilities/preferences
More informationChapter 3 Learning in Two-Player Matrix Games
Chapter 3 Learning in Two-Player Matrix Games 3.1 Matrix Games In this chapter, we will examine the two-player stage game or the matrix game problem. Now, we have two players each learning how to play
More informationSimultaneous Move Games
Simultaneous Move Games These notes essentially correspond to parts of chapters 7 and 8 of Mas-Colell, Whinston, and Green. Most of this material should be a review from BPHD 8100. 1 Introduction Up to
More informationGame Theory ( nd term) Dr. S. Farshad Fatemi. Graduate School of Management and Economics Sharif University of Technology.
Game Theory 44812 (1393-94 2 nd term) Dr. S. Farshad Fatemi Graduate School of Management and Economics Sharif University of Technology Spring 2015 Dr. S. Farshad Fatemi (GSME) Game Theory Spring 2015
More informationGame, Set, and Match Carl W. Lee September 2016
Game, Set, and Match Carl W. Lee September 2016 Note: Some of the text below comes from Martin Gardner s articles in Scientific American and some from Mathematical Circles by Fomin, Genkin, and Itenberg.
More informationAsynchronous Best-Reply Dynamics
Asynchronous Best-Reply Dynamics Noam Nisan 1, Michael Schapira 2, and Aviv Zohar 2 1 Google Tel-Aviv and The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel. 2 The
More informationNORMAL FORM GAMES: invariance and refinements DYNAMIC GAMES: extensive form
1 / 47 NORMAL FORM GAMES: invariance and refinements DYNAMIC GAMES: extensive form Heinrich H. Nax hnax@ethz.ch & Bary S. R. Pradelski bpradelski@ethz.ch March 19, 2018: Lecture 5 2 / 47 Plan Normal form
More informationESSENTIALS OF GAME THEORY
ESSENTIALS OF GAME THEORY 1 CHAPTER 1 Games in Normal Form Game theory studies what happens when self-interested agents interact. What does it mean to say that agents are self-interested? It does not necessarily
More informationGames. Episode 6 Part III: Dynamics. Baochun Li Professor Department of Electrical and Computer Engineering University of Toronto
Games Episode 6 Part III: Dynamics Baochun Li Professor Department of Electrical and Computer Engineering University of Toronto Dynamics Motivation for a new chapter 2 Dynamics Motivation for a new chapter
More informationGame Theory. Department of Electronics EL-766 Spring Hasan Mahmood
Game Theory Department of Electronics EL-766 Spring 2011 Hasan Mahmood Email: hasannj@yahoo.com Course Information Part I: Introduction to Game Theory Introduction to game theory, games with perfect information,
More informationGame Theory. Wolfgang Frimmel. Subgame Perfect Nash Equilibrium
Game Theory Wolfgang Frimmel Subgame Perfect Nash Equilibrium / Dynamic games of perfect information We now start analyzing dynamic games Strategic games suppress the sequential structure of decision-making
More informationFebruary 11, 2015 :1 +0 (1 ) = :2 + 1 (1 ) =3 1. is preferred to R iff
February 11, 2015 Example 60 Here s a problem that was on the 2014 midterm: Determine all weak perfect Bayesian-Nash equilibria of the following game. Let denote the probability that I assigns to being
More informationfinal examination on May 31 Topics from the latter part of the course (covered in homework assignments 4-7) include:
The final examination on May 31 may test topics from any part of the course, but the emphasis will be on topic after the first three homework assignments, which were covered in the midterm. Topics from
More information4. Game Theory: Introduction
4. Game Theory: Introduction Laurent Simula ENS de Lyon L. Simula (ENSL) 4. Game Theory: Introduction 1 / 35 Textbook : Prajit K. Dutta, Strategies and Games, Theory and Practice, MIT Press, 1999 L. Simula
More informationDominant Strategies (From Last Time)
Dominant Strategies (From Last Time) Continue eliminating dominated strategies for B and A until you narrow down how the game is actually played. What strategies should A and B choose? How are these the
More informationEconS Game Theory - Part 1
EconS 305 - Game Theory - Part 1 Eric Dunaway Washington State University eric.dunaway@wsu.edu November 8, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 28 November 8, 2015 1 / 60 Introduction Today, we
More informationCPS 570: Artificial Intelligence Game Theory
CPS 570: Artificial Intelligence Game Theory Instructor: Vincent Conitzer What is game theory? Game theory studies settings where multiple parties (agents) each have different preferences (utility functions),
More information1 Simultaneous move games of complete information 1
1 Simultaneous move games of complete information 1 One of the most basic types of games is a game between 2 or more players when all players choose strategies simultaneously. While the word simultaneously
More informationNon-Cooperative Game Theory
Notes on Microeconomic Theory IV 3º - LE-: 008-009 Iñaki Aguirre epartamento de Fundamentos del Análisis Económico I Universidad del País Vasco An introduction to. Introduction.. asic notions.. Extensive
More informationCHAPTER LEARNING OUTCOMES. By the end of this section, students will be able to:
CHAPTER 4 4.1 LEARNING OUTCOMES By the end of this section, students will be able to: Understand what is meant by a Bayesian Nash Equilibrium (BNE) Calculate the BNE in a Cournot game with incomplete information
More informationGame theory. Logic and Decision Making Unit 2
Game theory Logic and Decision Making Unit 2 Introduction Game theory studies decisions in which the outcome depends (at least partly) on what other people do All decision makers are assumed to possess
More informationMultiagent Systems: Intro to Game Theory. CS 486/686: Introduction to Artificial Intelligence
Multiagent Systems: Intro to Game Theory CS 486/686: Introduction to Artificial Intelligence 1 Introduction So far almost everything we have looked at has been in a single-agent setting Today - Multiagent
More informationDR. SARAH ABRAHAM CS349 UNINTENDED CONSEQUENCES
DR. SARAH ABRAHAM CS349 UNINTENDED CONSEQUENCES PRESENTATION: SYSTEM OF ETHICS WHY DO ETHICAL FRAMEWORKS FAIL? Thousands of years to examine the topic of ethics Many very smart people dedicated to helping
More informationDECISION MAKING GAME THEORY
DECISION MAKING GAME THEORY THE PROBLEM Two suspected felons are caught by the police and interrogated in separate rooms. Three cases were presented to them. THE PROBLEM CASE A: If only one of you confesses,
More informationDominance Solvable Games
Dominance Solvable Games Felix Munoz-Garcia EconS 503 Solution Concepts The rst solution concept we will introduce is that of deleting dominated strategies. Intuitively, we seek to delete from the set
More informationMath 464: Linear Optimization and Game
Math 464: Linear Optimization and Game Haijun Li Department of Mathematics Washington State University Spring 2013 Game Theory Game theory (GT) is a theory of rational behavior of people with nonidentical
More informationECON 301: Game Theory 1. Intermediate Microeconomics II, ECON 301. Game Theory: An Introduction & Some Applications
ECON 301: Game Theory 1 Intermediate Microeconomics II, ECON 301 Game Theory: An Introduction & Some Applications You have been introduced briefly regarding how firms within an Oligopoly interacts strategically
More informationGame Theory two-person, zero-sum games
GAME THEORY Game Theory Mathematical theory that deals with the general features of competitive situations. Examples: parlor games, military battles, political campaigns, advertising and marketing campaigns,
More informationMicroeconomics of Banking: Lecture 4
Microeconomics of Banking: Lecture 4 Prof. Ronaldo CARPIO Oct. 16, 2015 Administrative Stuff Homework 1 is due today at the end of class. I will upload the solutions and Homework 2 (due in two weeks) later
More informationMixed Strategies; Maxmin
Mixed Strategies; Maxmin CPSC 532A Lecture 4 January 28, 2008 Mixed Strategies; Maxmin CPSC 532A Lecture 4, Slide 1 Lecture Overview 1 Recap 2 Mixed Strategies 3 Fun Game 4 Maxmin and Minmax Mixed Strategies;
More informationRECITATION 8 INTRODUCTION
ThEORy RECITATION 8 1 WHAT'S GAME THEORY? Traditional economics my decision afects my welfare but not other people's welfare e.g.: I'm in a supermarket - whether I decide or not to buy a tomato does not
More informationNote: A player has, at most, one strictly dominant strategy. When a player has a dominant strategy, that strategy is a compelling choice.
Game Theoretic Solutions Def: A strategy s i 2 S i is strictly dominated for player i if there exists another strategy, s 0 i 2 S i such that, for all s i 2 S i,wehave ¼ i (s 0 i ;s i) >¼ i (s i ;s i ):
More informationEconS Representation of Games and Strategies
EconS 424 - Representation of Games and Strategies Félix Muñoz-García Washington State University fmunoz@wsu.edu January 27, 2014 Félix Muñoz-García (WSU) EconS 424 - Recitation 1 January 27, 2014 1 /
More informationIntroduction to Game Theory
Introduction to Game Theory Part 1. Static games of complete information Chapter 1. Normal form games and Nash equilibrium Ciclo Profissional 2 o Semestre / 2011 Graduação em Ciências Econômicas V. Filipe
More informationBackward Induction and Stackelberg Competition
Backward Induction and Stackelberg Competition Economics 302 - Microeconomic Theory II: Strategic Behavior Shih En Lu Simon Fraser University (with thanks to Anke Kessler) ECON 302 (SFU) Backward Induction
More informationIntroduction to (Networked) Game Theory. Networked Life NETS 112 Fall 2016 Prof. Michael Kearns
Introduction to (Networked) Game Theory Networked Life NETS 112 Fall 2016 Prof. Michael Kearns Game Theory for Fun and Profit The Beauty Contest Game Write your name and an integer between 0 and 100 Let
More informationChapter 13. Game Theory
Chapter 13 Game Theory A camper awakens to the growl of a hungry bear and sees his friend putting on a pair of running shoes. You can t outrun a bear, scoffs the camper. His friend coolly replies, I don
More informationEcon 302: Microeconomics II - Strategic Behavior. Problem Set #5 June13, 2016
Econ 302: Microeconomics II - Strategic Behavior Problem Set #5 June13, 2016 1. T/F/U? Explain and give an example of a game to illustrate your answer. A Nash equilibrium requires that all players are
More informationElements of Game Theory
Elements of Game Theory S. Pinchinat Master2 RI 20-202 S. Pinchinat (IRISA) Elements of Game Theory Master2 RI 20-202 / 64 Introduction Economy Biology Synthesis and Control of reactive Systems Checking
More informationLeandro Chaves Rêgo. Unawareness in Extensive Form Games. Joint work with: Joseph Halpern (Cornell) Statistics Department, UFPE, Brazil.
Unawareness in Extensive Form Games Leandro Chaves Rêgo Statistics Department, UFPE, Brazil Joint work with: Joseph Halpern (Cornell) January 2014 Motivation Problem: Most work on game theory assumes that:
More informationIntroduction to Game Theory
Chapter 11 Introduction to Game Theory 11.1 Overview All of our results in general equilibrium were based on two critical assumptions that consumers and rms take market conditions for granted when they
More informationBasic Solution Concepts and Computational Issues
CHAPTER asic Solution Concepts and Computational Issues Éva Tardos and Vijay V. Vazirani Abstract We consider some classical games and show how they can arise in the context of the Internet. We also introduce
More information