NetLogo User Community Models
by Jeff Russell (Submitted: 09/05/2007)
WHAT IS IT?
This is a simple model of two driver types on a two lane road. If a right-hand side driver meets a left-hand side driver, one driver will die. The simulation is used to help students understand the concept of Evolutionarily Stable Strategies as part of a Game Theory course via the self-directed series of questions outlined below.
HOW TO USE IT AND THINGS TO NOTICE: MAYBERRY SELF DIRECTED EXERCISE
PURPOSE: To gain familiarity with NetLogo, to understand the Evolutionarily Stable Strategy (ESS) equilibrium concept, and to see how ESS relates to Nash Equilibrium.
Open Mayberry and click on "setup".
All drivers know to head towards the main road. If drivers encounter each other off the road, there are no crashes.
CLASSICAL GAME THEORY APPLIED TO MAYBERRY
John Nash gets up in the morning, makes his coffee, gets in his car, heads for the road.
QUESTION 2: If John knows the other driver is also rational and is capable of calculating the necessary expected payoffs (classical game theory assumptions), what should John do, assuming both drivers move (change lanes) simultaneously? (No correct answer, this highlights the fact that Nash defines an equilibrium, yet does not say how to get there)
Assuming there is a 50% chance for each type of driver to die in a collision, the Normal form of this game is:
QUESTION 3: What are the two Nash Equilibrium?
QUESTION 4: Which Nash Equilibrium is "better" or more likely? (Again, no way to tell how to get there.)
EVOLUTIONARY GAME THEORY APPLIED TO MAYBERRY
Now we change the story to match evolutionary game theory assumptions.
Maynard Smith gets up in the morning, makes his coffee, gets in his car, drives to the road. Maynard is talking on his cell phone, eating a pop tart, tuning his radio, not paying any attention to his driving.
QUESTION 5: What will happen? Will either driver change their driving strategy?
EVOLUTIONARILY STABLE STRATEGIES (ESS)
Designate the always right strategy as the incumbents. (s*)
Start with a large incumbent population (set start-rts at 80) and a small mutant invasion (set start-lefts at 20)
Give each driver-type the same probability of death, so set the Prob-left-die slider at 0.5
QUESTION 6: Calculate the starting expected payoffs for each driver-type:
prob lhs is equal to the number of left-hand drivers/total number of drivers.
prob-left-die is determined by the slider in the Netlogo program.
a. Starting expected payoff for right-hand drivers =
b. Starting expected payoff for left-hand drivers = (you calculate below)
QUESTION 7: Survival
b. Which driver-type do you think will survive?
c. Is an initial population of right-hand drivers an ESS against a small invasion of left-hand drivers? Why?
d. Run the Mayberry simulation five times: Do the results support your answer in question c?
=>The "invasion barrier" (minimum number of invading left-side drivers) for
EXTENDING THE MODEL
QUESTION 9 (OPTIONAL): Modify the Mayberry program so that drivers don't turn around at the edge of the screen; instead, they "wrap" around the screen and reappear on the road on the other edge of the screen. This is accomplished by turning off the part of the program that tells the drivers to turn around. The easiest way to turn off code is to type a semicolon in front of the code so that it becomes comments. This avoids losing necessary code by mistake.
After this modification, try a simulation of equal number of right and left-side drivers, and a 50% prob-left-die. Run the simulation a few times and describe what seems to be happening. Explain the results in terms of the pure Nash equilibrium from Question 3 above.
"Evolutionary Game Theory_Big Bird Replicator Dynamic" is a more complex approach to evolutionary game theory that models a "replicator dynamic" to find stability in a two-species simulation.
CREDITS AND REFERENCES
Author: Dr. Jeffrey E. Russell
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