# Tagged Questions

The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under [tag:combinatorial-game-theory], and algorithmic aspects (e.g. auctions) are under [tag:algorithmic-game-theory].

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### Representations Verse Solution Concepts

In Game Theory, we generally refer to "normal form" and "extensive form" as representations. And, we generally describe "Nash Equilibrium," "strictly dominated strategies," "maxmin strategies," ...
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### Can a modified $19\times19$ checkerboard be tiled with decominoes ($10\times1$ rectangles)

Consider a $19\times19$ checkerboard with the center square removed, the four corner squares removed, and with four extra squares-one above the center square of the top row, one below the bottom ...
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### Nim game real life applications

I've learned how to prove and apply the Nim game strategy in discrete mathematics, but I was wondering if there is any real life examples and application for this theory. I searched online and didn't ...
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### Game theory, Book by Tirole and Fudenberg, Never a weak best response,unclear example

In this book, I have the following problem: on page 446, there is a sentence: Note that $(0.9,0.9)$ is not removed by NWBR, as D is not dominated after C is deleted. I do not understand this "as". ...
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### Pick a number that is better than your friends

Consider the following game. There are $n$ players, each one has to pick a (real) number $x$ between $0$ and $100$. There is one round to the game. The winner is the person whose number is closest ...
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### A game with coin toss

So I have a game between two players, p1 and p2. Someone(nature?) tosses a biased coin with 80% chance on head. p1 observes the outcome of it and write on a piece of paper head/tail(not neccessarily ...
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### does individually strategy proof implies coalitionally strategy proof?

Suppose $F$ is a social choice function \begin{equation*}F:N\rightarrow A\end{equation*} where $N=\{1,...,n\}$ is the set of agents and $A$ is a finite set of outcomes. suppose that $F$ is ...
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### Finding an equilibrium to this game

So this question was given in an exam: One of Player 1 and Player 2 need to wake up in the morning to receive a package. Neither wants to wake up early and that is the cost to each player. Both the ...
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### Game theory - coalition game question

The following is a question from a past exam that I am studying: For a 3-person game of perfect information. Let S denote the set {1,2,3}. First player A chooses i ϵ S. Then player B, knowing i ...
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### Probability in the board game “Istanbul”

I tried this game yesterday with a couple of friends (really interesting, although I did not win, I would definitely recommend it) here is a small piece of the game: A player first calls out a ...
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### Optimal strategy in chicken game

Consider a one-shot, simultaneous chicken game, as described here: https://en.wikipedia.org/wiki/Chicken_(game) Assume that I'm playing this game against a player that I consider to be of similar ...
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### Replicator equation for mixed strategies?

The the replicator equation is usually defined for pure strategies. More specifically, the replicator eqn for $n$ strategies is given by: \dot x_{i} = x_{i} \left( \sum_{j=1}^{n} ...
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### Algorithm for assigning users to “buckets” according to users' preferences and ranking

Suppose there is a set of $n$ users which must each be assigned to one, and only one, of $k$ mutually exclusive "buckets". However, the number of users allocated to the $i$-th bucket must be no lower ...
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### Bayesian Equilibrium

We have to answer the following question, and I can make some progress on the first couple of parts but get stuck in finishing them off. The third part I'm not sure where to start! *Consider the ...
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### How do I prove using strong form induction a statement regarding winning strategies in this coin game?

Consider a game in which, initially, there is a pile of n coins placed on a table. There are two players who alternate turns. Each player, on her or his turn, removes either one, two, or three coins ...
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### obtaining cases from the integral equation

I'm struggling with the recalculation of the formal model from the published article by Epstein and O'Halloran (1994), and I am failing miserably when it comes to understanding of their calculation, ...
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### Bayesian game theory

We have to answer this question and I think I have done part (a) right but get stuck at part (b). Since $-0.5 \le \varepsilon_i \le 0.5 \ \forall i$, I seem to get a solution of the NE being TR, which ...
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### Winning Strategy with Addition to X=0

Problem: Two players play the following game. Initially, X=0. The players take turns adding any number between 1 and 10 (inclusive) to X. The game ends when X reaches 100. The player who reaches 100 ...
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### Expected value, discrete random variable,discount factor

This example is taken from HERE ,page 424: What is the expected value $X(v)$ of this series: $X(v)=E(\Sigma_{t=0}^{\infty}\delta^t p_t(v))$ where $p_t(v)\in[0,1]$ with $\delta\in(0,1)$? Are all data ...
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### Disprove that the given strategy pair is a solution to the game.

Problem: For the following matrix game, prove or disprove that the given strategy pair is a solution to the game. \begin{align} A &= \begin{bmatrix} -1 & 2 & -3 \\ 3 & -4 & ...
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### Payoff Matrix/ How to fill positions in the matrix — Game Theory.

The Problem state: P1 and P2 each have three cards: a king, a queen, and a jack. They play their cards, one at a time, with the high card winning the trick (K>Q>J) and the playing of equal cards ...
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### Why doesn't the frequency of a strategy reach zero under the replicator dynamics?

Background The replicator equation with $n$ strategies is given by the differential equation: \dot x_{i} = x_{i} \left( \sum_{j=1}^{n} a_{ij}x_{j} - \phi \right) \qquad i = 1, ...
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### Information sets in Extensive Form Game with imperfect information

I have constructed an extensive form game with imperfect information given in the attached image. I am however a little uncertain as to whether my information sets are actually admissible if I, for ...
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### When does a matrix game and the sign flipped matrix game have the same nash equilibria?

Given a game $G$, we can construct another $G'$, by a positive scaling i.e. $\lambda \in \mathbb{R}_{++}$, s.t. each entry of $A$ is scaled by $\lambda$ Obviously, $G$ and $G'$ have the same nash ...