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Nash Equilibrium In Game Theory ~xRay Pixy

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 Video Link  CLICK HERE... Learn Nash Equilibrium In Game Theory Step-By-Step Using Examples. Video Chapters: Nash Equilibrium  00:00 Introduction 00:19 Topics Covered 00:33 Nash Equilibrium  01:55 Example 1  02:30 Example 2 04:46 Game Core Elements 06:41 Types of Game Strategies 06:55  Prisoner’s Dilemma  07:17  Prisoner’s Dilemma Example 3 09:16 Dominated Strategy  10:56 Applications 11:34 Conclusion The Nash Equilibrium is a concept in game theory that describes a situation where no player can benefit by changing their strategy while the other players keep their strategies unchanged.  No player can increase their payoff by changing their choice alone while others keep theirs the same. Example : If Chrysler, Ford, and GM each choose their production levels so that no company can make more money by changing their choice, it’s a Nash Equilibrium Prisoner’s Dilemma : Two criminals are arrested and interrogated separately. Each has two ...
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Firefly Optimization Algorithm

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Firefly algorithm is a swarm-based metaheuristic algorithm that was introduced by Yang. Firefly Algorithm is inspired by the FLASHING Behavior of Fireflies. 

Assumptions

  • Fireflies are attracted to each other.
  • Attractiveness is proportional to BRIGHTNESS. 
  • Less Brighter Firefly is attracted to the Brighter Firefly.
  • Attractiveness decrease as the distance between 2 fireflies increase.
  • If brightness for both is the same, fireflies move randomly.
  • New Solutions are generated by Random walks & the Attraction of fireflies.

Firefly Optimization Algorithm Steps
  1. Initialize Parameters.
  2. Generate Population of n Fireflies.
  3. Calculate Fitness Value for Each Firefly.
  4. Check stopping criteria if (CurrentIteration := 1 to MaximumIteration ).
  5.  Update Position and Light Intensity for Each Firefly.
  6. Report the Best Solution.
Initialize Parameters, Population of Fire Fly Swarm.
Population Size (n) = 20;
Maximum Iteration (Maxt) = 50;
Dimension (d) = 10;
Upper Bound [UB] = 100;
Lower Bound [LB] = -100;

Calculate Fitness Value [Light Intensity] for Each FireFly.
The light intensity of Firefly (i.e., 𝐼_𝑖) at 𝑥_𝑖 is computed by the Value of the Objective Function.

Firefly Position Updated as:
For i = 1 to n -1;
For j = i + 1 to n;
  IF ( 𝑰_𝒋 > 𝑰_𝒊 )
      Update Position. [move Firefly i towards Firefly j ];
    End IF
  End For
 End For

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