w1 what is an agent, utility, rationality also w2 normal form games

Question 1

what is an agent

Answer 1

computer system that can make independent actions on behalf of user/owner. user does not need to tell them everything that needs to be done

it has its own goals and behaviours and it is autonommous, adaptable and modiyable

Question 2

what are the four axioms four that involve outcome and preferences

Answer 2

completeness
outcome 1 is preferred over outcome 2 (vise versa) or about the same

transitivity
if a < b and b < c then a < c

continutuy
there is a probability p that the outcome b is equally prefered to outcome a with probablity p and outcome c with probabiltiy 1 - p

independence
if o1 is less prefereed than o2 then a gamble involving o1 is less prefered than gamble of o2 IF the chances of getting o3 are the same in both gambles

Question 3

what is utility

Answer 3

the amount of happiness you get from consuming goods and services

Question 4

what is rational choice therory and how does it relate to utility

Answer 4

Rational Choice Theory is the idea that people make decisions by logically choosing the option that gives them the greatest benefit or satisfaction, based on their preferences and available information.

It relates to utility because utility represents the measure of satisfaction or benefit someone gets from a choice. In simple terms:

People are assumed to act rationally by choosing the option that maximizes their utility (happiness, profit, or preference).
For example, if choosing between two snacks, a rational person picks the one they enjoy more (higher utility).

Question 5

what are the three diff ways agents tolerate risk

Answer 5

they can be risk adverse, neutral, seeking risk

seeking prefers higher expected utiltiy even if they come with less certainty

Question 6

what do we consider for agent design

Answer 6

build agents capable of independent, autonomous action, so that they can successfully carry out tasks we delegate to them

Question 7

what do we consider about agent society design

Answer 7

build agents that are capable of interacting (cooperating, coordinating, negotiating) with other agents in order to successfully carry out those delegated tasks, especially when the other agents cannot be assumed to share the same interests/goals

Question 8

what is a multiagent system

Answer 8

a system that consists of many agents that interact with each other,

agents can interact with different goals and motivations

Question 9

what types of games are we dealing with in ai 2

Answer 9

simultanous action (ie rock paper scissors)/normal form and turn based (like chess)/ extensive form

Question 10

what things do you need in a game

Answer 10

set of players, strategies, outcomes and game rule and payoff

Question 11

how to solve a game

Answer 11

dominant strategy equilibirum,
nash equilibrium

Question 12

what is the differenbce between better and best response

Answer 12

better response is favourable but not the best but best is best

Question 13

what is dominance

Answer 13

stratagy a dominates b if a always results in a better payoff than by playing b no matter what other players do

dominate stratgey doesnt always exist in a game

Question 14

what is a pure strategy vs mixed strategy

Answer 14

pure strategy is deterministic action of a player
A pure strategy is a deterministic approach where a player chooses a specific action with certainty every time a particular situation arises.

mixed strategy is probablity distrubution over pure strategies

mixed Adds an element of randomness to choices, making the player’s actions less predictable.
Useful in games with incomplete information or when trying to counter opponents.
Example:
In Rock-Paper-Scissors, a mixed strategy could involve choosing:
Rock with 50% probability,
Paper with 30%, and
Scissors with 20%.

Question 15

what is pure nash equilibrium vs mixed nash equilibrium

Answer 15

each player has chosen a strategy and no player can benefit more by changing their strategy while the other doesnt change theirs

mixed nash equilibrium is when palyers could used mixed stratigies
A Nash equilibrium where at least one player uses a mixed strategy, choosing between actions probabilistically. The outcome is stable when considering the expected payoffs.
In Rock-Paper-Scissors, the mixed Nash equilibrium is for each player to choose Rock, Paper, and Scissors with equal probabilities (⅓ each). This ensures no player can gain an advantage by deviating.

Question 16

what is a support of a strategy

Answer 16

the set of actions that a player assigns positive probability to when using a mixed strategy. In other words, it includes all the actions that the player might choose with some chance, not the ones they ignore (probability = 0)

number of non zero elements in the vector

number of strategies the player can play with positive probabilities

Question 18

what is the support lemma for a mixed nash equilibrium

Answer 18

Given a finite strategy game, (x, y) is a mixed Nash equilibrium iff every pure strategy in the support of x is a best response to y, and vice versa

Alternatively speaking, all pure strategies in the support of the mixed strategy must yield an equal expected payoff.

the actions in the support of a player’s mixed strategy must provide the same expected payoff for that player. Additionally, any action outside the support must provide a payoff no greater than those in the support