Questions tagged [evolutionary-game-theory]
Evolutionary game theory is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled.
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sample variance correction without sample size?
Does Bessel's correction have some generalization to if we do not know the sample size itself but instead do have some rate of occurrence estimate, or a probability estimate or similar?
I was ...
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Questions about an dynamics equation derivation
When reading a paper, i find it's difficult to derive the following equation.
In the paper, authors define:
$f_A=(1-\omega)+\omega[(k-1)q_{A|A}*a+[(k-1)q_{B|A}+1]*b]$
$f_B=(1-\omega)+\omega[(k-1)q_{A|...
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Correlated equilibrium proved by convexity (Games Theory)
I am finding very hard to understand how convexity works and why a correlated strategy if a convex linear combination of Nashes is a correlated equilibrium.
(Both concepts of Correlated strat. and ...
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Binary Differencial Evolution Algorithm
I have a optimization problem at hand and I am using Evolution Algorithm to solve it. Problem looks like following:
max f(x), where x is a vector with 4 elements ...
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Preimage of 1 orthogonal to 1 for skew-symmetric matrix
$$
\newcommand{\1}{\mathbf{1}}
\newcommand{\im}{\text{Im }}
\newcommand{\Span}[1]{\langle #1 \rangle}
\newcommand{\orth}[1]{ #1^{\perp}}
$$
Let $A$ be an $n \times n$ skew-symmetric matrix. Define $\1 ...
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Interpreting replicator dynamic for simplest population model
Suppose the simplest population model where we track the size $y$ of a population:
$$\frac{dy}{dt} = ry$$
for a positive constant $r$ and some $y$ such that $y(0) > 0$.
For this population model ...
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Is there any "Nash equilibrium" between two populations?
Let's say there are two populations $P_1$ and $P_2$, with population profiles $\boldsymbol{x}_1$ and $\boldsymbol{x}_2$. Given an arbitrary $\boldsymbol{x}_1$, $P_2$ converges to an ESS equal $\...
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On the necessary condition for evolutionary stability
According to (2007) Population Games. In: Game Theory. Springer Undergraduate Mathematics Series. Springer, London, page 142:
A necessary condition for evolutionary stability is
$\sigma^* \in \...
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Evolutionarily stable strategy and Harm thy neighbor
I'm studying ESS, and I have found the harm my neighbor example on wikipedia:
https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy
in Examples of differences between Nash equilibria and ...
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Probability of Extinction in microbial cell line
Suppose a single cell microbe can replicate into two cells during replication event. The probability that a cell is still alive until this event is given by $x$. Suppose we start with one single cell ...
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Three players mixed strategy nash equilibrium problem
The table above represents payoff for three players game accordingly. The probability for z1 is z and z2 is (1-z), r1 is r and r2 is (1-r) meanwhile for p1 is p and p2 is (1-p).
Firstly, I would like ...
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How is the replicator dynamic a gradient flow of the Fisher information metric?
I am trying to understand how the replicator dynamic can be derived as a gradient flow of the Fisher information metric (aka Shahshahani metric). I have a question about understanding a particular ...
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Checking whether a Mixed Strategy Nash Equilibrium is Evolutionary Stable
Taking the classic Hawk-Dove game
I know that there are 3 mixed strategy Nash Equilibria, (H,D), (D,H), and the mixed strategy ((7/12, 5/12), (7/12,5/12)), where those are probabilities of playing H ...
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Lyapunov Function for Competition Equations
I am trying to show that the function
$$Q(x,y)=be(x-\bar{x})^2+2ce(x-\bar{x})(y-\bar{y}) +cf(y-\bar{y})^2$$ is a Lyapunov function for the competition equations:
$$\dot{x}=x(a-bx-cy)$$
$$\dot{y}=y(d-...
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Game Theory - Mixed strategy ESS
I have a payoff matrix of a symmetric game like this:
$ \begin{matrix}
& A & B \\
A & (3, 3) & (1, 2) \\
B & (2, 1) & (5, 5)
\end{matrix} $
I found that $(A, A)$ and $(B, ...
user411568
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A question on repeated game theory
I recently have come across a business problem which could be convereted into a game problem as follows:
Imagine an infinitely repeated game between two players in which the firts player (leader) ...
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find equation based on multiple sets of 2 variables and results
I'm currently trying to reverse engineer a few equations used in a game, and have collected what seems to be all the relevant data.
In the example below, result speed is definitely based solely on ...
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Finding ESS in pure and mixed strategies
I have to find all the ESS(pure and mixed, in this game)
$\left(
\begin{array}{c|ccc}
& A & B & C\\
\hline
A &0,0& 3,1 &0,0\\
B &1,3& 0,0 &0,...
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How can the replicator equation be forward invariant when payoffs are negative?
Hi I'm self learning in game-theory and one of the most used equations is the replicator equation, which simulates how frequencies of a certain strategy change in a population of players.
$$\frac{...
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Repeated prisoner's dilemma with a random number of repetitions
During my summer study I have thought of the following problem. My knowledge about game theory is at the level of "Introduction to game theory" by Osborne.
Problem: Given a two-players repeated ...
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Existence test for a strategy that is dominated by a mixed strategy
I have a problem in evolutionary optimization that I think resembles a question that arises in game theory. Suppose a population lives in a fluctuating environment. The environment $G_t$ takes on one ...
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Fields of Interest in Game Theory for a Mathematics Dissertation
So In my final year of my Undergraduate Degree (Studying Mathematics and Economics) I have decided to focus my Undergraduate project on Game Theory.
I have done quite a bit of research, and I get ...
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Two questions about Nash Equilibrium
I'm reading an introductory book on game theory, but I'm confused by Nash Equilibrium, can someone explain to me the following questions?
Will the iterated elimination of strictly dominated ...
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Why do symmetric Nash equilibria satisfies $f_i(e^j_i,x_i) = f_i(x_i,x_i)$
Some simple notations
Let $I = \{1, \ldots, N\}$ and consider a $N$ player game with strategies $S = \{1, \ldots, n \}$.
Let $e^j_i = [0, \ldots, \underline{1}_\text{jth position}, \ldots 0]$ denote $...
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Useful analogy to interpret the notion of evolutionary stable strategy (ESS)
I am seeking a good analogy to understand the concept of evolutionary stable strategy (state)
Let $\pi$ denote the fitness of a population, $\pi_{ij}$ is the fitness of strategy $i$ against strategy $...
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