The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under (combinatorial-game-theory), and algorithmic aspects (e.g. auctions) are under (algorithmic-game-theory).
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The probability to be attacked with a particular strategy in a P2P network
In a P2P network of $n$ nodes, a fully connected graph, there are $3$ kinds of nodes, using strategy $A$, $B$, $C$. with probability $P_a$, $P_b$ and $P_c$.
The payoff matrix is the same of Rock Paper ...
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1answer
118 views
Is game theory a part of math? [closed]
I'm going to write project paper for my course, "The History of Math". My field is 'game theory'.
However, I'm in doubt that game theory is really part of math, since it comes from economics (for ...
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30 views
Existence of asymmetric equilibria in the dollar auction game
Consider a game in which an auctioneer sells one dollar to the highest bidder. The high bidder wins the dollar, but every bidder pays their bid. Concretely, assume that there are two bidders ...
4
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55 views
algebraic or homotopical proof for Kakutani fixed point theorem
As Kakutani fixed point theorem is a genral case of Brouwer fixed point theorem, and one can read the proof from homotopy theory books. I wonder if there is any proof for the Kakutani using homotopy ...
7
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2answers
136 views
What is the name of a game that cannot be won until it is over?
Consider the following game:
The game is to keep a friend's secret. If you ever tell the secret, you lose. As long as you don't you are winning. Clearly, it's a game that takes a lifetime to win.
...
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0answers
26 views
The Notion Of Degenerate Two Player Game
I try to get the intuitive understanding of the notion "degenerate two player game".
Definition. A two-player game is called non degenerate if no mixed strategy
of support size $k$ has more than $k$ ...
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0answers
24 views
Applications of Scoring Play Combinatorial Game Theory
I'm currently looking into economic applications of scoring play combinatorial game theory. Details of the theory can be found in this paper.
http://arxiv.org/abs/1202.4653
A friend of mine ...
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34 views
Game tie probability
If we have 3 players, playing extreme RPS game like image below:
How much tie probabilities?
Thanks
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0answers
23 views
Open infinite games and payoff functions
Let $A,B\subseteq\mathbb{N}$ and $d(A,B)=\sum_{n\in A\Delta B}2^{-n}$, where $A\Delta B = (A\cup B)\setminus (A\cap B)$, be a metric on subsets of the natural numbers. I'm asked to show that for ...
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0answers
66 views
Infinite games and pay-off functions
I'm asked to prove that, in a version of the Gale-Stewart game where the two players alternately pick zero or one, the pay-off function cannot be continuous. From what i have read, the pay-off ...
3
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0answers
49 views
Terminology questions about a game where one may “save his progress” at the cost of a turn.
The game is for $p$ players who each start at square $1$. Each turn, a player can either roll an $m$-sided dice or place a marker on his current square. If he rolls $x\in\{2,\ldots, m\}$, he ...
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40 views
Nash equilibria in 3-player game
Consider 3-player game.
Players $x,y,z$, each player has two strategies. $x$: $x_1$ and $x_2$, $y$: $y_1$ and $y_2$, $z:z_1$ and $z_2$.
The outcome of the game are represented by the triple ...
3
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1answer
37 views
Stability under supremum of sets of social choice function with single peaked preferences
Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455.
The setting is as follows:
A non-empty finite set of ...
3
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2answers
54 views
probable squares in a square cake
There is a probability density function defined on the square [0,1]x[0,1].
The pdf is finite, i.e., the cumulative density is positive only for pieces with positive area.
Now Alice and Bob play a ...
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0answers
51 views
You are Johnny Depp 3!
An extension of this question.
As @Jared stated in his answer the solution is:
we assume that the head pirate chooses between multiple possible proposals that maximize his profit by rewarding ...
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3answers
200 views
A number guessing game
Alice chose a positive integer $n$ and Bob tries to guess it.
In every turn, Bob will guess an integer $x$ $(x>0)$:
If $x$ equals $n$, then Alice tells Bob that he found it, and the game ends.
...
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1answer
48 views
AI strategies for losing positions [closed]
I have a card game that I am analyzing with Maple. Actually, it's a series of card games, one for every parameter k, where k is a natural number (representing the number of ranks of cards used in the ...
6
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2answers
255 views
You are Johnny Depp 2!
An extension of this question repeated below.
A band of 9 pirates have just finished their latest conquest -
looting, killing and sinking a ship. The loot amounts to 1000 gold
coins.
...
4
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1answer
41 views
Finding maximum score in a “bubble pop” game
Consider the following game: there is a n×n field, where each cell is randomly coloured in one of m colours. Let a group of cells be a set of same-coloured cells s.t. every cell in a group has at ...
2
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2answers
74 views
nash equilibirum help! seems tricky
Any advice for finding all nash equilibrium for this symmetric game? (B,B) looks like one but I feel like there are more. I tried looking for strictly dominant strategies, but only A weakly dominates ...
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1answer
57 views
Optimal strategy for a mixed game
I'm trying to understand what is the optimal strategy for a mixed game.
I can illustrate the game as a trading system where you can go Long or Short.
Going Long will give 80% win rate and going short ...
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5answers
131 views
Game Theory Question about Financial Markets
This is a recent quote from one of the outstanding bond portfolio managers:
"First of all, for every buyer there is a seller. Therefore, in order for someone to sell their bonds and buy stocks means ...
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0answers
29 views
Strictly Dominated and Never Best Response in LP
There is a well known notion of Strategic Dominance in Game Theory.
I am interested in elimination of strictly dominated strategies by Linear Programming and in LP for definition of never best ...
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1answer
32 views
Using limit argument with non-continuous social-choice functions
This question is related to another question of mine Invariance of strategy-proof social choice function when peaks are made close from solution, and it revolves around the use of limit arguments with ...
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1answer
58 views
Invariance of strategy-proof social choice function when peaks are made close from solution
A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428.
The setting is as follows:
A finite set ...
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2answers
58 views
Game Theory: Penalty Shot Game
Given a game matrix for the penalty shot game:
(1/2,-1/2) (-1,1)
(-1,1) (1/3,-1/3)
What is the minimax ...
2
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1answer
44 views
Is there an example of zero-sum game that has a Nash equilibrium which is not subgame perfect?
As a refinement of Nash equilibrium, it is known that not all Nash equilibria are subgame perfect. But it seems to me in zero-sum games of perfect information, Nash equilibrium coincides with subgame ...
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0answers
32 views
Collapsing of data points without Normalisation [closed]
Am trying to formulate a model with different data sets. What is the best way to bring them together without using normalisation? What algorithms?
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1answer
67 views
Two Player Game Useless Strategy
Let's consider the variant of dominated strategy which is the pure strategy that is not a best response to any mixed strategy of the opponent (two player game). Intuitively it sounds like more ...
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0answers
25 views
Algorithm to verify that a weak Nash equilibrium is an ESS, or a strict Nash equilibrium
Is there any algorithm that might assist me in checking whether a weak Nash equilibrium in a signalling game is also an Evolutionarily Stable Strategy, or a strict Nash?
4
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0answers
57 views
Linear Independence Game
Suppose you have a set $X$ of vectors in $\mathbb{F}_2^n$, with $|X| \ge n+1$, and consider the following game. On their turn, each player (2 player game) chooses from $X$ one vector and sets it aside ...
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1answer
38 views
Concept of efficiency in auctions
I have some confusions about the concept of "efficiency" in auction theory.
One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well ...
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1answer
41 views
Question on the use of induction in the Electronic Mail Game
In Rubinstein's Electronic Mail Game, Player I and Player II's strategies take the form as $s_i : \mathbb{N} \to \{A,B\}$, $(i =1,2)$.
Rubinstein shows that the pair of constant functions, $s_1(t_1) ...
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1answer
102 views
Can game theory model altruistic behaviour? [closed]
Can game theory be used to model altruistic behaviour?
The best I have heard is that a player is willing to forgo immediate gains if the opposite player does the same for gain at some later point.
...
2
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0answers
41 views
Is there a game of perfect information that only has a mixed strategy equilibrium?
It is known that certain simultaneous games, say, matching pennies with no pure strategy equilibrium, have a mixed strategy equilibrium.
Is simulaneous move at some stage a necessary ingredient of ...
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0answers
79 views
Is quantum game theory reducible to classical game theory?
Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
Superposed initial states,
Quantum ...
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1answer
72 views
Maxmin strategy and Nash equilibrium
It's well known fact that maxmin strategy in Nash equilibrium in the two-players zero-sum finite game, but to prove it?
How to show that maxmin strategy is actually Nash equilibrium in the case of ...
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0answers
52 views
Game theory: Efficient and stable mechanisms
I am having some trouble understanding the notion of efficient and stable mechanisms in game theory. Could someone explain both concepts informally?
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1answer
39 views
circular table game
"Suppose there are $n$ chairs around a circular table that are labelled from $0$ to $n-1$ in order. So chair $i$ is in between chairs $i-1$ and $i+1$ mod $n$. There are two infinitely smart players ...
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0answers
50 views
What are the best known sets of strategies for winning in Toads and Frogs?
So reading on game theory, I stumbled upon the Toads and Frogs game. Regretfully, contrary to other combinatorial games I know of, I couldn't find any information on what's the most-likely-to-win ...
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1answer
29 views
Question on the construction of mapping from space of strategy profile into itself in Nash(1951)
To appeal to Brouwer fixed point theorem, Nash(1951) constructed a continuous mapping $\operatorname{T}$ from strategy profile space into inself:
For player $i$, the probability of a pure strategy ...
5
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2answers
78 views
Does there exist a finite fair gamble game with one dishonest coin?
I am thinking, maybe a well known problem, of
whether there exists a fair gamble game for two persons by tossing one dishonest coin that will always stop(one winner is selected) at no more than $N$ ...
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0answers
25 views
Stable Matching Optimal Strategy Existence
There is a famous stable marriage problem.
It's well known that the standard algorithm for stable marriage problem proposed by Shapley and Gale is man-optimal, men get a best according to their ...
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1answer
36 views
How to define a mixed strategy in a game with a countable action space
Suppose in a two player zero-sum game, player I chooses a number $m$ from $\mathbb{Z}$, and player II chooses $n$ from $\mathbb{Z}$.
If $m-n =1$, then player I recieves a payoff of $1$, while ...
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1answer
64 views
A Gale-Stewart version of hawk-dove game
Suppose, in a two-player $\omega$-game of perfect information, player I or player II's action space at an arbitary stage $i$, $A_i$, is fixed as $\{H, D\}$ ($H$ and $D$ denote Hawk and Dove ...
3
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0answers
64 views
Unexpected hanging paradox maxmin strategies
I have a question about strategies of the players of Unexpected hanging paradox (I am very sorry for a long topic, topic exist already for a while, during this time I try to develop idea how to solve ...
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1answer
30 views
Finding a dual Linear-Program
We are trying to prove Von-Neumann's MINIMAX Theorem namely
$$\max_{x\in\Delta_{n}}\min_{y\in\Delta_{m}}y^{T}Ax=\max_{x\in\Delta_{n}}\min_{1\leqslant i\leqslant n}(Ax)_{i}$$
(Here $\Delta_k$ is the ...
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2answers
61 views
Minimax solution for Zero-Sum Game
I try to understand the way to finding the minimax solution to zero-sum game.
The following example is takes from Wikipedia. Minimax
Wikipedia: The following example of a zero-sum game, where A ...
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1answer
38 views
gain-floor and loss-ceiling in minimax theorem
I am little bit confused by the lemma preceding to minimax theorem in game theory .
I use the following material for studying GAME THEORY AND THE MINIMAX THEOREM.
gain-floor definition. A ...
6
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1answer
70 views
Find the value of a function with definite integrals
I am trying to understand a paper of Maynard Smith (1974), that connects biology with game theory. I don't want to overwhelm you with useless stuff, but I have this definite integrals:
...
