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Questions tagged [evolutionary-game-theory]

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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, ...
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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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Pure strategies that are Evolutionary Stable?

I am currently struggling with this symmetric game with finding all pure stategies that are evolutionary stable. I know that strategy "A" or "a" is evolutionary stable since it is a strict NE. How do ...
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understanding pure and mixed Evolutionary stable strategies

I am trying to understand ESS-pure and mixed. Here is what I know of two strategies $A$ and $B$ and their fitness: ...
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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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1answer
308 views

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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1answer
223 views

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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277 views

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 $e^j_i = [0, \ldots, \underline{1}_\text{jth position}, \ldots 0]$ ...
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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 $...