Homework 10 1. For this question, use the extensive form game
... The first two pure strategies are strictly dominated. Finding the mixed strategy Nash Equilibrium is left as an easy exercise. 4. Prove formally that every game satisfying perfect recall is linear. Solution: Assume an EFG has perfect recall for all i. Suppose by contradiction there exist x1 ∈ u, x2 ...
... The first two pure strategies are strictly dominated. Finding the mixed strategy Nash Equilibrium is left as an easy exercise. 4. Prove formally that every game satisfying perfect recall is linear. Solution: Assume an EFG has perfect recall for all i. Suppose by contradiction there exist x1 ∈ u, x2 ...
Document
... – Left is more nature for an army: swords in right hand, mounting horses. (Napolean liked the other way.) – Sweden switched from left to right in 1967. ...
... – Left is more nature for an army: swords in right hand, mounting horses. (Napolean liked the other way.) – Sweden switched from left to right in 1967. ...
Slide 1
... Computing P1’s best response to a mixed strategy by P2 represents P1’s uncertainty about what P2 will do. Let (q,1-q) denote the mixed strategy in which P2 plays H with probability q. Let (r, 1-r) denote the mixed strategy in which P1 plays H with probability r. ...
... Computing P1’s best response to a mixed strategy by P2 represents P1’s uncertainty about what P2 will do. Let (q,1-q) denote the mixed strategy in which P2 plays H with probability q. Let (r, 1-r) denote the mixed strategy in which P1 plays H with probability r. ...
cs2005gametheory - University of Exeter
... • North route is two days, Southern route is three days. • It takes one day for Kenny to switch routes. ...
... • North route is two days, Southern route is three days. • It takes one day for Kenny to switch routes. ...
Lecture 5: Mixed strategies and expected payoffs
... The expected value can be written using the scalar product: if x and y are two vectors in RN then the scalar product is given by hx, yi = ...
... The expected value can be written using the scalar product: if x and y are two vectors in RN then the scalar product is given by hx, yi = ...
Formal Theory Exam 2008
... The following normal form represents the game for the case of a strong challenger. What are the Nash equilibria to this game? ...
... The following normal form represents the game for the case of a strong challenger. What are the Nash equilibria to this game? ...
Lecture 3: Continuous Congestion Games 1 Review: Atomic
... [Note : A compact set is one that is bounded and contains the limit of every convergent sequence of elements the set. For example, [0, ∞) is not compact because it is not bounded, and [0, 2) is not compact because we can construct an infinite sequence of numbers converging to 2, but 2 is not in the ...
... [Note : A compact set is one that is bounded and contains the limit of every convergent sequence of elements the set. For example, [0, ∞) is not compact because it is not bounded, and [0, 2) is not compact because we can construct an infinite sequence of numbers converging to 2, but 2 is not in the ...
Game Theory Lecture 2: Strategic form games and NE
... randomization ⇒ equilibrium is a steady state of players’ beliefs about others’ actions Problem: all opponenets have same belief! predictive power of equilibrium appears smaller nice mathematical tool that guarantees equilibrium existence in finite games Problem: some interpretation and connection t ...
... randomization ⇒ equilibrium is a steady state of players’ beliefs about others’ actions Problem: all opponenets have same belief! predictive power of equilibrium appears smaller nice mathematical tool that guarantees equilibrium existence in finite games Problem: some interpretation and connection t ...
Quantum Nash Equilibrium
... The formal definition [3] of a mixed game is as follows. The strategy space of the mixed game of G, which we will denote Gmix , for player 1 is the set of probability distributions over S, which we will denote ∆(S), similarly the strategy space for player 2 is the set of probability distributions ov ...
... The formal definition [3] of a mixed game is as follows. The strategy space of the mixed game of G, which we will denote Gmix , for player 1 is the set of probability distributions over S, which we will denote ∆(S), similarly the strategy space for player 2 is the set of probability distributions ov ...
Given two digits, can you make the greatest fraction? The least
... a. Each player rolls the number cubes to get two digits. b. The player uses those digits to write the greatest possible fraction the digits can make. (This will always be a whole or mixed number.) c. The player with the greater number wins a point; no points are given for a tie. d. The first player ...
... a. Each player rolls the number cubes to get two digits. b. The player uses those digits to write the greatest possible fraction the digits can make. (This will always be a whole or mixed number.) c. The player with the greater number wins a point; no points are given for a tie. d. The first player ...
Why Scrabble is Such a Great Game Words and
... fun of playing with words, and it's hard to find a game with more appeal. No two games are ever the same, even between the same opponents who may play each other hundreds or thousands of times over a lifetime. Granted, it's not for the simple-minded or weak of constitution. To be good, one must stud ...
... fun of playing with words, and it's hard to find a game with more appeal. No two games are ever the same, even between the same opponents who may play each other hundreds or thousands of times over a lifetime. Granted, it's not for the simple-minded or weak of constitution. To be good, one must stud ...
Executive MPA Foundation Week II Economics I-IV
... neither player has any incentive to change given the strategy of others • Players in games may have dominant or non-dominant strategies – Dominant strategy - when a player has a strategy in a game that produces better results regardless of the strategy chosen by other players (opponents) • Each play ...
... neither player has any incentive to change given the strategy of others • Players in games may have dominant or non-dominant strategies – Dominant strategy - when a player has a strategy in a game that produces better results regardless of the strategy chosen by other players (opponents) • Each play ...
GEK1544 The Mathematics of Games Suggested Solutions to
... 1. Consider a zero sum game between players A and B, with the payoffs for A shown in the following diagram . ...
... 1. Consider a zero sum game between players A and B, with the payoffs for A shown in the following diagram . ...
02/27 - David Youngberg
... ii. Zero-sum game—when the total payoff from each player equals zero. In other words, to be better off, someone else must be equally worse off. iii. We assume that each player is pessimistic about their chances of doing well. You figure your opponent will do their best as they can to stop you from ...
... ii. Zero-sum game—when the total payoff from each player equals zero. In other words, to be better off, someone else must be equally worse off. iii. We assume that each player is pessimistic about their chances of doing well. You figure your opponent will do their best as they can to stop you from ...
oligopoly, strategy and game theory
... a. (identical product) steel, aluminum, copper, oil refining b. (differentiated product) automobiles, cigarettes 3. focus on the concept that any one firm=s actions are likely to trigger a reaction by its competitors; before the first firm acts, it must consider these reactions= i.e., it must behave ...
... a. (identical product) steel, aluminum, copper, oil refining b. (differentiated product) automobiles, cigarettes 3. focus on the concept that any one firm=s actions are likely to trigger a reaction by its competitors; before the first firm acts, it must consider these reactions= i.e., it must behave ...
Lecture 4
... Best response for a player is a mapping from actions by the others to the action (or actions) that maximizes the player’s payoffs given the actions of the others. In Nash equilibrium, every player is doing the best response to what the other players are ...
... Best response for a player is a mapping from actions by the others to the action (or actions) that maximizes the player’s payoffs given the actions of the others. In Nash equilibrium, every player is doing the best response to what the other players are ...
- the Modeling Commons!
... turtle is unhappy with their choice, they will take some probability away from that option and move it towards a “better” option. Once again, a strategy is “better” if it gives that turtle a higher payoff given the other turtles’ choices. This process will continue until the probability distribution ...
... turtle is unhappy with their choice, they will take some probability away from that option and move it towards a “better” option. Once again, a strategy is “better” if it gives that turtle a higher payoff given the other turtles’ choices. This process will continue until the probability distribution ...
Introduction to Game Theory, Behavior and Networks
... – for every player i, their distribution is a best response to all the others • i.e. cannot get higher (average or expected) payoff by changing distribution • only consider unilateral deviations by each player! ...
... – for every player i, their distribution is a best response to all the others • i.e. cannot get higher (average or expected) payoff by changing distribution • only consider unilateral deviations by each player! ...
Part 3.6
... Y would copy him and win everything. Similarly, Y cannot stick to a single strategy, or X will do the opposite. Both players must use a mixed strategy, and furthermore the choice at every turn must be absolutely independent of the previous turns. Assume that X decides that he will put up 1 hand with ...
... Y would copy him and win everything. Similarly, Y cannot stick to a single strategy, or X will do the opposite. Both players must use a mixed strategy, and furthermore the choice at every turn must be absolutely independent of the previous turns. Assume that X decides that he will put up 1 hand with ...
PPT - CIS @ UPenn - University of Pennsylvania
... – a1 is a best response to a2, a2 is a best response to a1 (e.g. (confess, confess) in PD) – neither player can unilaterally improve their payoff – More generally, every player is best-responding to the other N-1 players ...
... – a1 is a best response to a2, a2 is a best response to a1 (e.g. (confess, confess) in PD) – neither player can unilaterally improve their payoff – More generally, every player is best-responding to the other N-1 players ...
BASICS I. INTRODUCTION A. free rider problem
... combinations. Another example - espionage activities, treaty to retaliate against state sponsors of terrorism. ...
... combinations. Another example - espionage activities, treaty to retaliate against state sponsors of terrorism. ...
sumL14 - CIS @ Temple University
... Let (S, f) be a game with n players, where Si is the strategy set for player i, S=S1 X S2 ... X Sn is the set of strategy profiles and f=(f1(x), ..., fn(x)) is the payoff function for x S. Let xi be a strategy profile of player i and x-i be a strategy profile of all players except for player i. Whe ...
... Let (S, f) be a game with n players, where Si is the strategy set for player i, S=S1 X S2 ... X Sn is the set of strategy profiles and f=(f1(x), ..., fn(x)) is the payoff function for x S. Let xi be a strategy profile of player i and x-i be a strategy profile of all players except for player i. Whe ...
PPT - UNC Computer Science
... • If a player has a dominant strategy, there exists a Nash equilibrium in which the player plays that strategy and the other player plays the best response to that strategy • If both players have strictly dominant strategies, there exists a Nash equilibrium in which they play those strategies ...
... • If a player has a dominant strategy, there exists a Nash equilibrium in which the player plays that strategy and the other player plays the best response to that strategy • If both players have strictly dominant strategies, there exists a Nash equilibrium in which they play those strategies ...