# Tagged Questions

Algorithmic game theory is an area in the intersection of game theory and algorithm design, whose objective is to design algorithms in strategic environments. (Def: http://en.m.wikipedia.org/wiki/Algorithmic_game_theory)

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### Big Balloon Game

The problem In this game, you are given empty balloons one by one, and for each balloon you are to inflate it with air until you are satisfied. If it does not burst, you gain happiness points ...
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### Find 2 points defined by another point and two vectors

This is my scenario: (More info after the image) Let me first point out that I am coming from a programer background and for me vectors are defined using two numbers: $x$ and $y$. For example: A ...
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### Monte Carlo Search Tree iterations

I have had this example in my exam last week and I can not figure out how to solve it. I have watched lots of tutorials on Monte Carlo Search Tree but I can't still understand this algorithm properly. ...
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### Strategy of ball math game

Found math game: http://www.emathhelp.net/math-games-and-logic-puzzles/rgbw/ What is a strategy for it? I can make 15 white balls max. Any thoughts?
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### A variation of Nim game

There are two players X and Y . They write N integers on paper ( A_1 , A_2 , A_3 , .... A_N ). They have also p integers (b_1 , b_2 , b_3 , .... b_p ) . Now , Player X always takes turn first . He ...
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### Strategy optimisation

This is a question from the Singapore Invitational Mathematics Challenge 2016. The question paper can be found here. (Part C:Question 2) http://www.nushigh.edu.sg/qql/slot/u90/file/simc/...
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### Guess the number despite false answer

This is the Guess-The-Number game with a twist! Variant 1 Take any positive integer $n$. The game-master chooses an $n$-bit integer $x$. The player makes queries one by one, each of the ...
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### How does this textbook compute the Nash Equilibrium of the two person zero sum game?

In Tamer Basar Noncooperative Game theory pg $33$ there is a $2 \times 3$ game (zero sum game) $A = \begin{bmatrix} 1 & 3 & 0 \\ 6 & 2 & 7 \end{bmatrix}$ (each element is a cost, ...
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Let $x$ be the mixed strategy of player $1$ Then the mixed strategy for player $1$ is calculated with respect to $[1, 0], [0, 1]$, the pure strategies of player $2$. i.e. $x^*$ = $\max \min x^TA([1,... 1answer 56 views ### Using trigonometry to calculate a players angle of movement according to mouse position in a game This is a question related to programming but it is mostly pure mathematics and that is why I am asking it here. Please don't tell me to move this to the Programming Stack Exchange. It is here for a ... 1answer 68 views ### Nash equilibrium for n players game There is a question that I am trying to solve but I am not sure about my approach and is hoping I could get some help. Here is the question: There are$n$companies sharing a water reservoir, let's ... 1answer 43 views ### Mechanism design with known utilities (game theory) I'm trying to prove that in an n-party setting, where each party has a private value, the dominant strategy is always to reveal it. I'm assuming that parties only care about monetary payoffs and ... 0answers 37 views ### Optimizing generalized ternary search There are$N$socks numbered$1$to$N$, one containing a gift. Dave needs to find the sock with the gift. He can ask some questions in order to find that sock: in each question, Dave chooses$2$... 0answers 84 views ### Find the mixed strategy Nash equilibria in the investment race This is Exercise 35.2 in Rubinstein's "A Course in Game Theory". This problem is very difficult. The lecturer gave us the answer but it's very hard to understand. I paste the problem here: Two ... 1answer 29 views ### Question about usage of$\leq$in definition of Nash equilibrium Quick definition: Given$g$, a strategy N-tuple$u^* = (u_1^*,...,u^*_N)$is said to be a Nash equilibrium if: $$J_i(u_i^*, u^*_{-i}) \leq J_i(u_i, u^*_{-i}), i \in N$$ where$J$is ... 1answer 86 views ### What is the quickest way to find Nash equilibria in two player bimatrix game? Suppose the cost/penalty matrix of a game is given as: $$M = \begin{bmatrix} (-5,-5) & (0,0) \\ (0,0) & (-3,-3) \end{bmatrix}$$ Then the game as two equilibria$(u_{11},u_{21})$and$(u_{12},...
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my text defines player set as: In N-player game $g$, each non-terminating node is partitioned into $N+1$ sets $g^0, ... g^N$. These are player sets. However it makes no attempt to identify ...
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